diff options
| author | Matthew Sotoudeh <matthew@masot.net> | 2023-06-03 14:51:16 -0700 |
|---|---|---|
| committer | Matthew Sotoudeh <matthew@masot.net> | 2023-06-03 14:51:16 -0700 |
| commit | d8c82a8431b10de05ce5921d98fa7ec60ecf5df0 (patch) | |
| tree | dcebb9ba5964e11060e0659657844db1683bed5d /sat-chaff | |
dump of labs
Diffstat (limited to 'sat-chaff')
| -rw-r--r-- | sat-chaff/PRELAB.md | 71 | ||||
| -rw-r--r-- | sat-chaff/README.md | 189 | ||||
| -rw-r--r-- | sat-chaff/code/.gitignore | 2 | ||||
| -rw-r--r-- | sat-chaff/code/Makefile | 12 | ||||
| -rw-r--r-- | sat-chaff/code/basic.c | 250 | ||||
| -rwxr-xr-x | sat-chaff/code/cross_check.sh | 16 | ||||
| -rw-r--r-- | sat-chaff/code/fast.c | 307 | ||||
| -rw-r--r-- | sat-chaff/matthew_output/xcheck_p5.output | 375 | ||||
| -rw-r--r-- | sat-chaff/matthew_output/xcheck_p7.output | 32780 | ||||
| -rw-r--r-- | sat-chaff/test_inputs/aim-100.dimacs | 171 | ||||
| -rw-r--r-- | sat-chaff/test_inputs/aim-50.dimacs | 91 | ||||
| -rw-r--r-- | sat-chaff/test_inputs/big.dimacs | 3669 | ||||
| -rw-r--r-- | sat-chaff/test_inputs/dubois22.dimacs | 190 | ||||
| -rw-r--r-- | sat-chaff/test_inputs/p10.dimacs | 577 | ||||
| -rw-r--r-- | sat-chaff/test_inputs/p2.dimacs | 25 | ||||
| -rw-r--r-- | sat-chaff/test_inputs/p5.dimacs | 98 | ||||
| -rw-r--r-- | sat-chaff/test_inputs/p7.dimacs | 221 | ||||
| -rw-r--r-- | sat-chaff/test_inputs/p8.dimacs | 314 | ||||
| -rw-r--r-- | sat-chaff/test_inputs/p9.dimacs | 432 | ||||
| -rw-r--r-- | sat-chaff/test_inputs/test.dimacs | 3 |
20 files changed, 39793 insertions, 0 deletions
diff --git a/sat-chaff/PRELAB.md b/sat-chaff/PRELAB.md new file mode 100644 index 0000000..98b7862 --- /dev/null +++ b/sat-chaff/PRELAB.md @@ -0,0 +1,71 @@ +# SAT/Symex+SMT Labs Prelab + +By Wednesday, we will make a symbolic execution (symex) engine for a simple +little "assembly language." Think of a symex engine as a tool that tries to +generate inputs to your program that cause it to execute a certain line. For +example, in this program: +``` +load 0 0 ; r0 = memory[r0] +immediate 1 10 ; r1 = 10 +branch_eq 0 1 2 ; if r0 == r1 goto l1 else goto l2 +l1: fail +l2: exit +``` +The symex engine will attempt to find initial registers & memory values that +cause the `fail` instruction to be reached. In this case, it will say setting +`r0 = 0`, `memory[0] = 10` does the trick. + +Symex engines are built on SMT solvers which are built on SAT solvers. +Roughly, SAT solvers are symex for when you have no branching, no memory, and +finitely-many boolean registers. The only operations allowed are "and," "or," +and "not." SMT solvers add support for int (non-boolean) values and memory. +Symex engines add support for branching, loops, and some assembly/code syntax. + +### Monday: SAT Solver Prelab +SAT solvers solve _boolean constraints_. For example, you can say "find an +assignment for $x$, $y$, $z$ such that: (i) $z$ is true, (ii) if $x$ and $y$ +are true then $z$ is false, and (iii) either $x$ or $y$ is true." + +In order to keep SAT solvers as simple and fast as possible, the input language +describing constraints for most SAT solvers is pretty restrictive. Here's an +example: +``` +c Amazing comment!! +p cnf 3 3 +3 0 +-1 -2 -3 0 +1 2 0 +``` +- Initial lines can start with `c` for `c`omments. +- The `p` (for `p`roblem?) line tells us how many variables and how many + clauses (remaining lines). +- The constraints are given in AND of OR form; each line represents an OR and + every line has to be satisfied (AND). +- Every line ends in `0` (variables are numbered starting from `1`). +- `n` means that variable should be true, `-n` means false. +- The basic idea is to assign each variable true or false so that every line + "predicts" at least one variable's true/falseness correctly. +In the above example, line `3 0` means "variable 3 should be true," the next +line means "either variable 1 is false, or variable 2 is false, or variable 3 +is false," and the last line means "either variable 1 is true or variable 2 is +true." If you think about it, those constraints are exactly the same as (i), +(ii), (iii) from earlier. + +You can plug this in to minsat (or the [web +version](http://logicrunch.it.uu.se:4096/~wv/minisat/)) to get a solution: +``` +SATISFIABLE + +-1 2 3 0 +``` +This means there is a solution, namely, variable 1 false, variable 2 true, and +variable 3 true. + +We'll be writing our own version of minisat, including a few hacks to speed it +up. We'll be basing our version on the SAT solver called Chaff, which you +should read about +[here](https://www.princeton.edu/~chaff/publication/DAC2001v56.pdf) +(specifically sections 1 and 2!). + +### SMT/Symex Prelab +TODO diff --git a/sat-chaff/README.md b/sat-chaff/README.md new file mode 100644 index 0000000..1fb5a92 --- /dev/null +++ b/sat-chaff/README.md @@ -0,0 +1,189 @@ +# Chaff/SAT Solver Lab + +In this lab we'll be reproducing the Chaff paper. In particular, we'll focus on +the following two claims: +1. In a normal SAT solver, around 90% of the time is spent in boolean + constraint propagation. +2. Using watched literals instead of a counter can achieve a ~5--10x speedup + over the basic DP SAT solver algorithm. + +There isn't a lot of code to write in the first place. My version of part 1 +ends up with ~150 loc (~25 lines over the starter code) and my version of part +2 end sup with ~190 loc (~30 lines over the start code). But there are a fairly +large number of interacting data structures (mostly simple heap arrays) so it +may longer than expected. If you'd like more of a challenge, try starting all +the functions from scratch or try implementing some of the remaining tricks in +the "What's Next?" section below! + +## Part 1: Implement & profile the basic DP algorithm +#### Implementation +Implement the `assert(!"Implement me!");` locations in `basic.c`. The comments +should instruct you on what to do. I would highly recommend first reading the +comments in the data structures section. + +The program accepts DIMACS input on `stdin`. To run this on a file +`foo.dimacs`, use: +``` +$ cat foo.dimacs | ./basic +``` + +#### Debugging +Note that SAT solvers are surprisingly difficult to implement correctly. +If you make a mistake it's liable to keep getting the right answer on 90% of +inputs, or all inputs that don't repeat literals in a clause, or ... + +To counteract this, we're going to use the same cross checking approach we've +used forever in this class: observe some part of the execution that is supposed +to be invariant to our optimizations, and compare multiple implementations with +respect to that observation. + +The obvious choice for observation is sat vs. unsat, but that's too coarse. +Instead, we'll print out the sequence of decisions and compare those. This is +already done for you, you don't need to modify anything (see the call to +`xprintf` in `decide()`). + +To cross-check your basic implementation against mine, try: +``` +./cross_check.sh basic_vs_matthew +``` + +To help with debugging, you can uncomment the `-fsanitize=address` line in the +`Makefile` and `make -B` to build with sanitizers. But make sure to re-comment +& re-build before profiling! + +#### Profiling +The Chaff paper motivates their watched literals hack by the following +observation: "In practice, for most SAT problems, a major potion (greater than +90% in most cases) of the solvers' run time is spent in the BCP process. +Therefore, an efficient BCP engine is key to any SAT solver." + +Let's see if we can reproduce this claim. Install `perf` and run the following: +``` +$ make -B +$ cat ../test_inputs/p8.dimacs | sudo perf record ./basic +$ sudo perf report +``` +You should see in the resulting report that BCP takes about 85% of the time, +pretty close to their claim! + +Now that we're convinced of the problem, let's try out their solution. + +## Part 2: Implement the watched literals optimization +Now we'll be implementing the watched literals optimization. Whereas before +`LIT_TO_CLAUSES[lit]` was an array of all clauses containing the literal `lit`, +now `LIT_TO_CLAUSES[lit]` will be a linked list of only those clauses that are +*watching* the literal `lit`. As in the paper, every clause will be watching +exactly two literals at a time. We're using a linked list to make it updating +which literal is being watched constant-time. + +Your first task is to implement `init_watcher`, which is called by `main()` to +initialize `LIT_TO_CLAUSES` and the watched literals on the clause struct +(replacing `n_zeros`). + +We also have a new `BCP_LIST` data structure. The idea is that `set_literal` +will now immediately identify implied literals, and queue them up in `BCP_LIST` +to be assigned during the `bcp()` phase. You'll notice that `bcp()` has gotten +a _lot_ simpler --- it just does what `set_literal` queued up for it! + +Your second task is to implement `queue_bcp` and `dequeue_bcp`, which are +exactly what they sound like (except, er, it's probably faster to just do a +stack not a queue! doesn't matter for correctness, but I like the sound of the +word "queue" better...). + +The real big task is now implementing `set_literal`. This is where almost all +the serious work of the watched-literals-optimized version is done. This one +function is basically going to do the work of both `set_literal` and `bcp` from +`basic.c`. + +...but, payoff from that is we no longer have to do _anything_ non-trivial in +`unset_latest_assignment`! We literally get to just delete all that code! + +You should be able to copy/paste your `decide()` from `basic.c`. +`resolveConflict()` can also be _almost_ the same --- just remember now you +also have to clear out the pending BCP list! + +After that, you should be good to go. + +To cross-check your basic implementation against your optimized implementation, +try: +``` +./cross_check.sh basic_vs_fast +``` +Note that this cross-checks on a fairly hefty input, and the xcheck logs can be +pretty large (tens of megabytes). So it may take significantly longer to run in +xcheck mode than directly. + +## What's Left? +If you try comparing the time to solve, say, `p9.dimacs` with your `./fast` and +`minisat` you'll find something a bit wacky: our `./fast` is actually faster +than `minisat`! + +Why is this? I don't _think_ it's because of a bug in our solver; if you +compare the number of decisions made (in `xcheck` mode) to the number reported +by `minisat`, it's pretty comparable. + +I think what's happening is much simpler: the pigeonhole formulae (like +`p9.dimacs`) are sort of the "worst possible thing" for SAT solvers. Minisat +has a bunch of extra tricks that try to speed things up in the "happy case," +but none of them are useful for pigeonhole formulae. Instead, they just take up +time without actually improving the search at all. This is a delicate balance, +where some tricks will speed up problems X, Y, Z but slow down A, B, C. More of +an art than a science, etc. + +You can confirm this by finding inputs, like `aim-100.dimacs`, that complete +super fast on minisat but are terrible in our solver. + +What are those extra tricks? A few things: +1. Conflict-driven clause learning (CDCL). Right now, if we get a conflict we + just backtrack to the latest decision not "tried both ways." In essence, all + we learn is that that exact sequence of decisions cannot work. There are + techniques that can spend a little extra time analyzing the conflict in + detail and figure out a new constraint that rules out not just that exact + sequence of decisions, but perhaps other ones as well. More concretely, + imagine some formula where you can prove there is no solution with `1` and + `3` both set to false. The solver may end up in a decision stack like + `[-1,-2,-3]` and then get a conflict. Our current implementation would + backtrack repeatedly, trying `[-1,-2,3]`, `[-1,2,-3]`, `[-1,2,3]`, etc. + Meanwhile, a CDCL implementation would _analyze the conflict_ in detail, and + (if we're lucky) determine that `-1`, `-3` is the "core" of the conflict. It + then produces a new clause that rules this out, i.e., `-1 3` (or `-3 1`). + With this new clause added to the formula, the solver will never even + consider assignment `[-1,2,-3]`, because the `-1` will BCP in `-3`. This + lets us prune our search space more aggressively than just standard + backtracking. A nice interactive explanation of this process is given here: + https://cse442-17f.github.io/Conflict-Driven-Clause-Learning/ +2. In a basic CDCL solver, every time we reach a conflict we actually add a new + clause to the clause list. This is nice because new clauses help prune our + search space (in other words, we get more opportunities for BCP instead of + having to do decide). But it can get messy if we have _way_ too many clauses + (most of them are probably not that useful any more, if we've already + "passed out of that area of the search space"). _Clause deletion heuristics_ + tell us which clauses are probably OK to delete/clean out. See + https://webdocs.cs.ualberta.ca/~mdsolimu/CP19_GluVar_Final.pdf for a + discussion of one approach. +3. Decision heuristics. In our `decide()`, we always just take the + numerically-next unassigned variable and try assigning it to false. This is + not a great idea. If a 100 clauses have that variable in positive form and + only one has it in negative form, it's probably a good idea to try and set + it to true first, as that "gets out of the way" the most clauses at once. + The Chaff paper describes a heuristic called VSIDS that they claim is fast + and pretty good. I bet you could probably implement it with another 100 + lines of code or so. +4. All of the above modifications make the solver very, very stateful. During + the solver run the solver is learning things about the formula that it + didn't know when it started (e.g., VSIDS basically approximates which + variables are more likely to be true vs. false in a solution). Intuitively, + it's possible that you made some bad decisions in the beginning of the solve + that got you stuck in an unproductive part of the search space. But maybe if + you had known all that information early on in the solve, you would have + made better decisions that could have gotten you more quickly into a better + part of the search space. The trick to take advantage of this is to just + randomly restart the solver, but keep some of the information learned during + this attempt around (e.g., the VSIDS counts). +5. I don't think many common solvers actually do this, but another cool one is + _symmetry breaking_. The basic idea is that a lot of problems are symmetric; + think about a formula involving something like `x^2 + y^2`. Any solution + `(x,y)` can be swapped to `(y,x)` to form an equally-good solution. In + theory, then, we can cut down the set of possible solutions we have to think + about by only considering those where `x <= y`. This is called "symmetry + breaking." diff --git a/sat-chaff/code/.gitignore b/sat-chaff/code/.gitignore new file mode 100644 index 0000000..44f88c8 --- /dev/null +++ b/sat-chaff/code/.gitignore @@ -0,0 +1,2 @@ +basic +fast diff --git a/sat-chaff/code/Makefile b/sat-chaff/code/Makefile new file mode 100644 index 0000000..5a37921 --- /dev/null +++ b/sat-chaff/code/Makefile @@ -0,0 +1,12 @@ +.PHONY: clean all + +CFLAGS += -g +CFLAGS += -O3 +# CFLAGS += -fsanitize=address + +all: basic fast +fast: fast.c +basic: basic.c + +clean: + rm -f basic fast xcheck_*.output perf.* diff --git a/sat-chaff/code/basic.c b/sat-chaff/code/basic.c new file mode 100644 index 0000000..3d55d5b --- /dev/null +++ b/sat-chaff/code/basic.c @@ -0,0 +1,250 @@ +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include <assert.h> + +#define append_field(OBJ, FIELD) (*({ \ + (OBJ).FIELD = realloc((OBJ).FIELD, (++((OBJ).n_##FIELD)) * sizeof((OBJ).FIELD[0])); \ + (OBJ).FIELD + ((OBJ).n_##FIELD - 1); \ +})) + +/****** GLOBAL DATA STRUCTURES ******/ + +// Any sequence of events you want to cross-check across the basic & optimized +// solvers can be logged by calling xprintf. It will only log if the LOG_XCHECK +// flag is set by main(), i.e., if the user passes an argument. +int LOG_XCHECK = 0; +#define xprintf(...) { if (LOG_XCHECK) { fprintf(stderr, __VA_ARGS__); } } + +// The number of variables and clauses. This is specified by the "p cnf ..." +// line of the input. +unsigned N_VARS = 0, N_CLAUSES = 0; + +// Each clause is a list of literals, along with a count of the number of +// literals set to zero in the current partial assignment. The clause is +// implied once n_zeros == (n_lits - 1) and falsified if n_zeros == n_lits. +struct clause { + int *literals, n_literals; + int n_zeros; +}; +struct clause *CLAUSES = NULL; + +// The current partial assignment is a simple map from var_id -> assignment. +enum assignment { + UNASSIGNED = -1, + FALSE = 0, + TRUE = 1, +}; +enum assignment *ASSIGNMENT = NULL; + +// We maintain a decision stack that logs every time we assign a variable & +// why. In the Chaff paper a distinction is made between "decisions" and +// "assignments", the latter being assignments as a result of BCP. For us, the +// only difference will be the decision_type. +enum decision_type { + IMPLIED = 0, + TRIED_ONE_WAY = 1, + TRIED_BOTH_WAYS = 2, +}; +struct decision { + unsigned var; + enum decision_type type; +}; +struct decision *DECISION_STACK = NULL; +unsigned N_DECISION_STACK = 0; + +// We maintain a list of literal -> clauses having that literal. For the basic +// implementation, these lists don't need to be changed after initialization so +// we'll just use a simple heap array. +struct clause_list { + struct clause **clauses; + int n_clauses; +}; +struct clause_list *LIT_TO_CLAUSES = NULL; + +/****** HELPER METHODS ******/ + +// LIT_TO_CLAUSES maps literals -> ids. This converts a literal to an index +// into that map. Basically, the ordering goes -1, 1, -2, 2, ... +int literal_to_id(int literal) { + return (2 * abs(literal)) + (literal > 0); +} + +// Uses literal_to_id to index into LIT_TO_CLAUSES +struct clause_list *clauses_touching(int literal) { + return LIT_TO_CLAUSES + literal_to_id(literal); +} + +// Absolute value, used for turning a literal into a variable id. +int abs(int x) { return (x < 0) ? -x : x; } + +int is_literal_true(int lit) { + int var = abs(lit); + return ASSIGNMENT[var] != UNASSIGNED && ASSIGNMENT[var] == (lit > 0); +} + +// Called when a solution is found +int satisfiable() { + printf("SAT\n"); + for (int i = 1; i < N_VARS; i++) + printf("%d ", is_literal_true(i) ? i : -i); + printf("\n"); + return 0; +} + +// Called when it is proved that no solution exists +int unsatisfiable() { printf("UNSAT\n"); return 0; } + +/****** KEY OPERATIONS ******/ + +// Attempt to assign the given literal. Then update all the n_zeros counters. +// If this assignment causes a conflict (i.e., for some clause n_zeros == +// n_literals), this method will return 0. Otherwise it will return 1. +int set_literal(int literal, enum decision_type type) { + int var = abs(literal); + assert(ASSIGNMENT[var] == UNASSIGNED); + // Update the main assignment vector + ASSIGNMENT[var] = literal > 0; + // And add a new node on the decision stack. + DECISION_STACK[N_DECISION_STACK].var = var; + DECISION_STACK[N_DECISION_STACK++].type = type; + + // Update clause counters, check if any is completely false + assert(!"Implement me!"); +} + +// Undo the latest assignment on the decision stack. Then update all the +// n_zeros counters. Note that undoing an assignment can never cause a new +// conflict, so we don't need to report anything. +void unset_latest_assignment() { + // Pop a node off the decision stack + unsigned var = DECISION_STACK[--N_DECISION_STACK].var; + int literal = ASSIGNMENT[var] ? var : -var; + + // Update the partial assignment + ASSIGNMENT[var] = UNASSIGNED; + + // Iterate over the clauses containing -literal and decrement their + // n_zeros since this literal is no longer set. + assert(!"Implement me!"); +} + +/****** DP METHODS ******/ + +// From the paper: "The operation of decide() is to select a variable that is +// not currently assigned, and give it a value. This variable assignment is +// referred to as a decision. As each new decision is made, a record of that +// decision is pushed onto the decision stack. This function will return false +// if no unassigned variables remain and true otherwise." +int decide() { + // Iterate over variables until we find an unassigned one, placing it in v + // (or return 0 if none is found). + int v; + assert(!"Implement me!"); + + // Otherwise, try setting it false. Note this should never cause a + // conflict, otherwise it should have been BCP'd. + assert(set_literal(-v, TRIED_ONE_WAY)); + + // Log this decision for xcheck. + xprintf("Decide: %d\n", -v); + return 1; +} + +// From the paper: "The operation of bcp() ... is to identify any variable +// assignments required by the current variable state to satisfy f. ... if a +// clause consists of only literals with value 0 and one unassigned literal, +// then that unassigned literal must take on a value of 1 to make f sat. ... +// In the pseudo-code from above, bcp() carries out BCP transitively until +// either there are no more implications (in which case it returns true) or a +// conflict is produced (in which case it returns false)." +int bcp() { + int any_change = 0; + for (size_t i = 0; i < N_CLAUSES; i++) { + struct clause *clause = CLAUSES + i; + if ((clause->n_zeros + 1) != clause->n_literals) continue; + + // At this point, the clause is either satisfied or implied. For each + // literal in the clause: + // - If any literal is set to true, this clause is already sat so we + // don't need to do anything. + // - Otherwise, if we find a literal that is unset, try to set it. If + // setting it causes a conflict, return 0. Otherwise, record that + // there was a change and go on to the next clause. + assert(!"Implement me!"); + } + + return any_change ? bcp() : 1; +} + +// From the paper: "... to deal with a conflict, we can just undo all those +// implications, flip the value of the decision assignment, and allow BCP to +// then proceed as normal. If both values have already been tried for this +// decision, then we backtrack through the decision stack until we encounter a +// decision that has not been tried both ways, and proceed from there in the +// manner described above. ... If no decision can be found which has not been +// tried both ways, that indicates that f is not satisfiable." +int resolveConflict() { + // Unwind the decision stack by calling unset_latest_assignment() until we + // find a decision that is only TRIED_ONE_WAY. + // If you have unwinded the entire decision stack, return 0 (the formula is + // unsat!) + assert(!"Implement me!"); + + // Otherwise, take that decision and flip it: + unsigned var = DECISION_STACK[N_DECISION_STACK - 1].var; + + int new_value = !ASSIGNMENT[var]; + unset_latest_assignment(); + set_literal(new_value ? var : -var, TRIED_BOTH_WAYS); + + return 1; +} + +int main(int argc, char **argv) { + LOG_XCHECK = argc > 1; + // Read comment lines at the start. + for (char c; (c = getc(stdin)) == 'c';) + while (getc(stdin) != '\n'); + + assert(scanf(" cnf %u %u\n", &N_VARS, &N_CLAUSES) == 2); + N_VARS++; + + ASSIGNMENT = malloc(N_VARS * sizeof(ASSIGNMENT[0])); + memset(ASSIGNMENT, -1, N_VARS * sizeof(ASSIGNMENT[0])); + + DECISION_STACK = calloc(N_VARS, sizeof(DECISION_STACK[0])); + + CLAUSES = calloc(N_CLAUSES, sizeof(struct clause)); + + LIT_TO_CLAUSES = calloc(N_VARS * 2, sizeof(LIT_TO_CLAUSES[0])); + + for (size_t i = 0; i < N_CLAUSES; i++) { + int literal = 0; + for (assert(scanf("%d ", &literal)); literal; assert(scanf("%d ", &literal))) { + // Dedup any repeated literals in the clause. + int repeat = 0; + for (size_t j = 0; j < CLAUSES[i].n_literals && !repeat; j++) + repeat = (CLAUSES[i].literals[j] == literal); + if (repeat) continue; + + // Append to the clause's literal list. + append_field(CLAUSES[i], literals) = literal; + + // Append to the list of clauses touching this literal. Hint: use + // clauses_touching and append! + assert(!"Implement me"); + } + } + + // Basic DP from the Chaff paper: + if (!bcp()) return unsatisfiable(); // needed to handle unit clauses + while (1) { + if (!decide()) + return satisfiable(); + + while (!bcp()) + if (!resolveConflict()) + return unsatisfiable(); + } +} diff --git a/sat-chaff/code/cross_check.sh b/sat-chaff/code/cross_check.sh new file mode 100755 index 0000000..40818d8 --- /dev/null +++ b/sat-chaff/code/cross_check.sh @@ -0,0 +1,16 @@ +#!/bin/sh + +make -B + +if [ "$1" = "basic_vs_matthew" ] ; then + in_file=../test_inputs/p7.dimacs + cat $in_file | (./basic xcheck 2> xcheck_basic.output) + diff xcheck_basic.output ../matthew_output/xcheck_p7.output +fi + +if [ "$1" = "basic_vs_fast" ] ; then + in_file=../test_inputs/p9.dimacs + cat $in_file | (./basic xcheck 2> xcheck_basic.output) + cat $in_file | (./fast xcheck 2> xcheck_fast.output) + diff xcheck_basic.output xcheck_fast.output +fi diff --git a/sat-chaff/code/fast.c b/sat-chaff/code/fast.c new file mode 100644 index 0000000..09735c1 --- /dev/null +++ b/sat-chaff/code/fast.c @@ -0,0 +1,307 @@ +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include <assert.h> + +#define append_field(OBJ, FIELD) (*({ \ + (OBJ).FIELD = realloc((OBJ).FIELD, (++((OBJ).n_##FIELD)) * sizeof((OBJ).FIELD[0])); \ + (OBJ).FIELD + ((OBJ).n_##FIELD - 1); \ +})) + +/****** GLOBAL DATA STRUCTURES ******/ + +// Any sequence of events you want to cross-check across the basic & optimized +// solvers can be logged by calling xprintf. It will only log if the LOG_XCHECK +// flag is set by main(), i.e., if the user passes an argument. +int LOG_XCHECK = 0; +#define xprintf(...) { if (LOG_XCHECK) { fprintf(stderr, __VA_ARGS__); } } + +// The number of variables and clauses. This is specified by the "p cnf ..." +// line of the input. +unsigned N_VARS = 0, N_CLAUSES = 0; + +// Each clause is a list of literals, along with two of them that are currently +// being watched. Notice there is no counter here! +struct clause { + int *literals, n_literals; + int watching[2]; +}; +struct clause *CLAUSES = NULL; + +// The current partial assignment is a simple map from var_id -> assignment. +enum assignment { + UNASSIGNED = -1, + FALSE = 0, + TRUE = 1, +}; +enum assignment *ASSIGNMENT = NULL; + +// We maintain a decision stack that logs every time we assign a variable & +// why. In the Chaff paper a distinction is made between "decisions" and +// "assignments", the latter being assignments as a result of BCP. For us, the +// only difference will be the decision_type. +enum decision_type { + IMPLIED = 0, + TRIED_ONE_WAY = 1, + TRIED_BOTH_WAYS = 2, +}; +struct decision { + unsigned var; + enum decision_type type; +}; +struct decision *DECISION_STACK = NULL; +unsigned N_DECISION_STACK = 0; + +// In this implementation instead of tracking literal -> clauses containing +// that literal, we only track literal -> clauses *watching* that literal. We +// need to modify this during the solve, so we'll use a linked list instead of +// an array. +struct clause_list { + struct clause *clause; + struct clause_list *next; +}; +struct clause_list **LIT_TO_CLAUSES = NULL; + +// Here we track the list of literal implications discovered when visiting +// clauses. We represent this in two ways, a direct list (BCP_LIST, N_BCP_LIST) +// of the clauses and a bool vector IS_BCP_LISTED to determine if a given +// literal is already in the list. +int *BCP_LIST = NULL; +unsigned N_BCP_LIST = 0; +char *IS_BCP_LISTED = NULL; + +/****** HELPER METHODS ******/ + +// LIT_TO_CLAUSES maps literals -> ids. This converts a literal to an index +// into that map. Basically, the ordering goes -1, 1, -2, 2, ... +int literal_to_id(int literal) { + return (2 * abs(literal)) + (literal > 0); +} + +// Uses literal_to_id to index into LIT_TO_CLAUSES +struct clause_list **clauses_watching(int literal) { + return LIT_TO_CLAUSES + literal_to_id(literal); +} + +// Absolute value, used for turning a literal into a variable id. +int abs(int x) { return (x < 0) ? -x : x; } + +int is_literal_true(int lit) { + int var = abs(lit); + return ASSIGNMENT[var] != UNASSIGNED && ASSIGNMENT[var] == (lit > 0); +} + +// Called when a solution is found +int satisfiable() { + printf("SAT\n"); + for (int i = 1; i < N_VARS; i++) + printf("%d ", is_literal_true(i) ? i : -i); + printf("\n"); + return 0; +} + +// Called when it is proved that no solution exists +int unsatisfiable() { printf("UNSAT\n"); return 0; } + +// Specify the @which'th watched literal for clause CLAUSES[clause_i]. Called +// by main(). +void init_watcher(int clause_i, int which, int literal) { + // Set watching[which] = literal on clause clause_i, then prepend the + // corresponding watching node to the correct LIT_TO_CLAUSES list. + assert(!"Implement me!"); +} + +// Add a literal to the BCP list. +void queue_bcp(int literal) { + // Append the literal to BCP_LIST, if it is not already in the list. Don't + // forget you can use IS_BCP_LISTED as a bool vector version of BCP_LIST. + assert(!"Implement me!"); +} + +// Pop a literal from the BCP list. +int dequeue_bcp() { + // Pop a literal off of BCP_LIST and return it. Don't forget to update + // IS_BCP_LISTED. + assert(!"Implement me!"); +} + +/****** KEY OPERATIONS ******/ + +// Attempt to assign the given literal. Any clauses that are watching -lit get +// visited and processed. +int set_literal(int literal, enum decision_type type) { + int var = abs(literal); + // Update the main assignment vector + ASSIGNMENT[var] = literal > 0; + // And add a new node on the decision stack. + DECISION_STACK[N_DECISION_STACK].var = var; + DECISION_STACK[N_DECISION_STACK++].type = type; + + // Visit any clauses that contain a literal now made false. + for (struct clause_list **w = clauses_watching(-literal); *w;) { + struct clause *clause = (*w)->clause; + int watch_id = (clause->watching[0] == -literal) ? 0 : 1; + int other_watch = clause->watching[!watch_id]; + int new_watch_lit = 0; + + // Look for an unwatched literal not set to zero in this clause, + // placing it in new_watch_lit (or set new_watch_lit = 0 if all + // literals are either watched or zero). + assert(!"Implement me"); + + if (new_watch_lit) { + // Switch the watcher to be watching this new literal instead. + // Note: we need to change both the clause struct itself as well as + // move its watcher element onto the correct linked list in + // LIT_TO_CLAUSES. + assert(!"Implement me"); + } else { + // No other non-zero literal was found in the clause. This is a + // conflict if the other watched literal is zero, else it is an + // implication we need to BCP. + if (is_literal_true(-other_watch)) { + // CONFLICT + return 0; // trigger a resolution. + } else if (is_literal_true(other_watch)) { + // This clause is already sat, don't have to do anything. + } else { + // BCP IMPLICATION, tell bcp() to set other_watch to true. + queue_bcp(other_watch); + } + w = &((*w)->next); + } + } + return 1; +} + +// Undo the latest assignment on the decision stack. Then update all the +// n_zeros counters. Note that undoing an assignment can never cause a new +// conflict, so we don't need to report anything. +void unset_latest_assignment() { + // Pop a node off the decision stack + unsigned var = DECISION_STACK[--N_DECISION_STACK].var; + // Update the partial assignment + ASSIGNMENT[var] = UNASSIGNED; + // No longer need to update any counters or watched literals! +} + +/****** DP METHODS ******/ + +// From the paper: "The operation of decide() is to select a variable that is +// not currently assigned, and give it a value. This variable assignment is +// referred to as a decision. As each new decision is made, a record of that +// decision is pushed onto the decision stack. This function will return false +// if no unassigned variables remain and true otherwise." +int decide() { + // Iterate over variables until we find an unassigned one, placing it in v + // (or return 0 if none is found). This can probably be exactly the same as + // in basic.c. + int v; + assert(!"Implement me!"); + + // Otherwise, try setting it false. Note this should never cause a + // conflict, otherwise it should have been BCP'd. + assert(set_literal(-v, TRIED_ONE_WAY)); + + // Log this decision for xcheck. + xprintf("Decide: %d\n", -v); + return 1; +} + +// From the paper: "The operation of bcp() ... is to identify any variable +// assignments required by the current variable state to satisfy f. ... if a +// clause consists of only literals with value 0 and one unassigned literal, +// then that unassigned literal must take on a value of 1 to make f sat. ... +// In the pseudo-code from above, bcp() carries out BCP transitively until +// either there are no more implications (in which case it returns true) or a +// conflict is produced (in which case it returns false)." +int bcp() { + while (N_BCP_LIST) { + if (!set_literal(dequeue_bcp(), IMPLIED)) + return 0; + } + return 1; +} + +// From the paper: "... to deal with a conflict, we can just undo all those +// implications, flip the value of the decision assignment, and allow BCP to +// then proceed as normal. If both values have already been tried for this +// decision, then we backtrack through the decision stack until we encounter a +// decision that has not been tried both ways, and proceed from there in the +// manner described above. ... If no decision can be found which has not been +// tried both ways, that indicates that f is not satisfiable." +int resolveConflict() { + // Clear the pending BCP list (don't forget IS_BCP_LISTED!), then use + // unset_latest_assignment() to unwind the decision stack until we find a + // decision that is only TRIED_ONE_WAY. If no such decision is found, + // return 0. + assert(!"Implement me!"); + + // Otherwise, take that decision and flip it: + unsigned var = DECISION_STACK[N_DECISION_STACK - 1].var; + + int new_value = !ASSIGNMENT[var]; + unset_latest_assignment(); + set_literal(new_value ? var : -var, TRIED_BOTH_WAYS); + + return 1; +} + +int main(int argc, char **argv) { + LOG_XCHECK = argc > 1; + // Read comment lines at the start. + for (char c; (c = getc(stdin)) == 'c';) + while (getc(stdin) != '\n'); + + assert(scanf(" cnf %u %u\n", &N_VARS, &N_CLAUSES) == 2); + N_VARS++; + + ASSIGNMENT = malloc(N_VARS * sizeof(ASSIGNMENT[0])); + memset(ASSIGNMENT, -1, N_VARS * sizeof(ASSIGNMENT[0])); + + DECISION_STACK = calloc(N_VARS, sizeof(DECISION_STACK[0])); + + CLAUSES = calloc(N_CLAUSES, sizeof(struct clause)); + + LIT_TO_CLAUSES = calloc(N_VARS * 2, sizeof(LIT_TO_CLAUSES[0])); + + BCP_LIST = calloc(2 * N_VARS, sizeof(BCP_LIST[0])); + IS_BCP_LISTED = calloc(2 * N_VARS, sizeof(IS_BCP_LISTED[0])); + + for (size_t i = 0; i < N_CLAUSES; i++) { + int literal = 0; + for (assert(scanf("%d ", &literal)); literal; assert(scanf("%d ", &literal))) { + // Dedup any repeated literals in the clause. + int repeat = 0; + for (size_t j = 0; j < CLAUSES[i].n_literals && !repeat; j++) + repeat = (CLAUSES[i].literals[j] == literal); + if (repeat) continue; + + // Append to the clause's literal list. + append_field(CLAUSES[i], literals) = literal; + } + } + + for (size_t i = 0; i < N_CLAUSES; i++) { + if (!CLAUSES[i].n_literals) return unsatisfiable(); + if (CLAUSES[i].n_literals == 1) { + // If a clause has only one literal, it must be set. + queue_bcp(CLAUSES[i].literals[0]); + } else { + // Watch the first 2 literals. + init_watcher(i, 0, CLAUSES[i].literals[0]); + init_watcher(i, 1, CLAUSES[i].literals[1]); + } + } + + // Basic DP from the Chaff paper: + if (!bcp()) return unsatisfiable(); // needed to handle unit clauses + while (1) { + if (!decide()) + return satisfiable(); + + while (!bcp()) + if (!resolveConflict()) + return unsatisfiable(); + } +} diff --git a/sat-chaff/matthew_output/xcheck_p5.output b/sat-chaff/matthew_output/xcheck_p5.output new file mode 100644 index 0000000..7cdf9e7 --- /dev/null +++ b/sat-chaff/matthew_output/xcheck_p5.output @@ -0,0 +1,375 @@ +Decide: -1 +Decide: -2 +Decide: -3 +Decide: -4 +Decide: -6 +Decide: -7 +Decide: -8 +Decide: -11 +Decide: -12 +Decide: -16 +Decide: -13 +Decide: -16 +Decide: -12 +Decide: -13 +Decide: -17 +Decide: -9 +Decide: -11 +Decide: -12 +Decide: -16 +Decide: -14 +Decide: -16 +Decide: -12 +Decide: -14 +Decide: -17 +Decide: -11 +Decide: -8 +Decide: -9 +Decide: -11 +Decide: -13 +Decide: -16 +Decide: -14 +Decide: -16 +Decide: -13 +Decide: -14 +Decide: -18 +Decide: -11 +Decide: -9 +Decide: -11 +Decide: -7 +Decide: -8 +Decide: -9 +Decide: -12 +Decide: -13 +Decide: -17 +Decide: -14 +Decide: -17 +Decide: -13 +Decide: -14 +Decide: -18 +Decide: -12 +Decide: -9 +Decide: -12 +Decide: -8 +Decide: -9 +Decide: -13 +Decide: -5 +Decide: -6 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SOURCE: Olivier Dubois (dubois@laforia.ibp.fr) +c +c DESCRIPTION: Instance from generator gensathard.c +c +c NOTE: Not satisfiable +c +c d = 22 +c n = 66 +c p = 176 +c r = 3 +p cnf 66 176 + 43 44 1 0 +-43 -44 1 0 + 43 -44 -1 0 +-43 44 -1 0 + 1 45 2 0 + -1 -45 2 0 + 1 -45 -2 0 + -1 45 -2 0 + 2 46 3 0 + -2 -46 3 0 + 2 -46 -3 0 + -2 46 -3 0 + 3 47 4 0 + -3 -47 4 0 + 3 -47 -4 0 + -3 47 -4 0 + 4 48 5 0 + -4 -48 5 0 + 4 -48 -5 0 + -4 48 -5 0 + 5 49 6 0 + -5 -49 6 0 + 5 -49 -6 0 + -5 49 -6 0 + 6 50 7 0 + -6 -50 7 0 + 6 -50 -7 0 + -6 50 -7 0 + 7 51 8 0 + -7 -51 8 0 + 7 -51 -8 0 + -7 51 -8 0 + 8 52 9 0 + -8 -52 9 0 + 8 -52 -9 0 + -8 52 -9 0 + 9 53 10 0 + -9 -53 10 0 + 9 -53 -10 0 + -9 53 -10 0 + 10 54 11 0 +-10 -54 11 0 + 10 -54 -11 0 +-10 54 -11 0 + 11 55 12 0 +-11 -55 12 0 + 11 -55 -12 0 +-11 55 -12 0 + 12 56 13 0 +-12 -56 13 0 + 12 -56 -13 0 +-12 56 -13 0 + 13 57 14 0 +-13 -57 14 0 + 13 -57 -14 0 +-13 57 -14 0 + 14 58 15 0 +-14 -58 15 0 + 14 -58 -15 0 +-14 58 -15 0 + 15 59 16 0 +-15 -59 16 0 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-54 32 0 + 33 -54 -32 0 +-33 54 -32 0 + 34 53 33 0 +-34 -53 33 0 + 34 -53 -33 0 +-34 53 -33 0 + 35 52 34 0 +-35 -52 34 0 + 35 -52 -34 0 +-35 52 -34 0 + 36 51 35 0 +-36 -51 35 0 + 36 -51 -35 0 +-36 51 -35 0 + 37 50 36 0 +-37 -50 36 0 + 37 -50 -36 0 +-37 50 -36 0 + 38 49 37 0 +-38 -49 37 0 + 38 -49 -37 0 +-38 49 -37 0 + 39 48 38 0 +-39 -48 38 0 + 39 -48 -38 0 +-39 48 -38 0 + 40 47 39 0 +-40 -47 39 0 + 40 -47 -39 0 +-40 47 -39 0 + 41 46 40 0 +-41 -46 40 0 + 41 -46 -40 0 +-41 46 -40 0 + 42 45 41 0 +-42 -45 41 0 + 42 -45 -41 0 +-42 45 -41 0 + 43 44 -42 0 +-43 -44 -42 0 + 43 -44 42 0 +-43 44 42 0 + diff --git a/sat-chaff/test_inputs/p10.dimacs b/sat-chaff/test_inputs/p10.dimacs new file mode 100644 index 0000000..478f303 --- /dev/null +++ b/sat-chaff/test_inputs/p10.dimacs @@ -0,0 +1,577 @@ +c pigeon-10: placing 11 pigeons into 10 holes +c +c File generated by 'pigeonhole', (c) Tjark Weber +c +c The SAT encoding of this problem is very straightforward. For each pigeon i +c and each hole j we have a variable x_{n*(i-1)+j} which means that pigeon i +c is placed in hole j. Then we have n+1 clauses which say that a pigeon has +c to be placed in some hole. Then for each hole we have a set of clauses +c ensuring that only one single pigeon is placed into that hole. +c +c This encoding leads to a total of (n+1) * n propositional variables and +c (n+1) + n * (n * (n+1) / 2) clauses. +c +c The resulting SAT problem is unsatisfiable. +c +p cnf 110 561 +1 2 3 4 5 6 7 8 9 10 0 +11 12 13 14 15 16 17 18 19 20 0 +21 22 23 24 25 26 27 28 29 30 0 +31 32 33 34 35 36 37 38 39 40 0 +41 42 43 44 45 46 47 48 49 50 0 +51 52 53 54 55 56 57 58 59 60 0 +61 62 63 64 65 66 67 68 69 70 0 +71 72 73 74 75 76 77 78 79 80 0 +81 82 83 84 85 86 87 88 89 90 0 +91 92 93 94 95 96 97 98 99 100 0 +101 102 103 104 105 106 107 108 109 110 0 +-1 -11 0 +-1 -21 0 +-1 -31 0 +-1 -41 0 +-1 -51 0 +-1 -61 0 +-1 -71 0 +-1 -81 0 +-1 -91 0 +-1 -101 0 +-11 -21 0 +-11 -31 0 +-11 -41 0 +-11 -51 0 +-11 -61 0 +-11 -71 0 +-11 -81 0 +-11 -91 0 +-11 -101 0 +-21 -31 0 +-21 -41 0 +-21 -51 0 +-21 -61 0 +-21 -71 0 +-21 -81 0 +-21 -91 0 +-21 -101 0 +-31 -41 0 +-31 -51 0 +-31 -61 0 +-31 -71 0 +-31 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-79 0 +-69 -89 0 +-69 -99 0 +-69 -109 0 +-79 -89 0 +-79 -99 0 +-79 -109 0 +-89 -99 0 +-89 -109 0 +-99 -109 0 +-10 -20 0 +-10 -30 0 +-10 -40 0 +-10 -50 0 +-10 -60 0 +-10 -70 0 +-10 -80 0 +-10 -90 0 +-10 -100 0 +-10 -110 0 +-20 -30 0 +-20 -40 0 +-20 -50 0 +-20 -60 0 +-20 -70 0 +-20 -80 0 +-20 -90 0 +-20 -100 0 +-20 -110 0 +-30 -40 0 +-30 -50 0 +-30 -60 0 +-30 -70 0 +-30 -80 0 +-30 -90 0 +-30 -100 0 +-30 -110 0 +-40 -50 0 +-40 -60 0 +-40 -70 0 +-40 -80 0 +-40 -90 0 +-40 -100 0 +-40 -110 0 +-50 -60 0 +-50 -70 0 +-50 -80 0 +-50 -90 0 +-50 -100 0 +-50 -110 0 +-60 -70 0 +-60 -80 0 +-60 -90 0 +-60 -100 0 +-60 -110 0 +-70 -80 0 +-70 -90 0 +-70 -100 0 +-70 -110 0 +-80 -90 0 +-80 -100 0 +-80 -110 0 +-90 -100 0 +-90 -110 0 +-100 -110 0 diff --git a/sat-chaff/test_inputs/p2.dimacs b/sat-chaff/test_inputs/p2.dimacs new file mode 100644 index 0000000..b46ad69 --- /dev/null +++ b/sat-chaff/test_inputs/p2.dimacs @@ -0,0 +1,25 @@ +c pigeon-2: placing 3 pigeons into 2 holes +c +c File generated by 'pigeonhole', (c) Tjark Weber +c +c The SAT encoding of this problem is very straightforward. For each pigeon i +c and each hole j we have a variable x_{n*(i-1)+j} which means that pigeon i +c is placed in hole j. Then we have n+1 clauses which say that a pigeon has +c to be placed in some hole. Then for each hole we have a set of clauses +c ensuring that only one single pigeon is placed into that hole. +c +c This encoding leads to a total of (n+1) * n propositional variables and +c (n+1) + n * (n * (n+1) / 2) clauses. +c +c The resulting SAT problem is unsatisfiable. +c +p cnf 6 9 +1 2 0 +3 4 0 +5 6 0 +-1 -3 0 +-1 -5 0 +-3 -5 0 +-2 -4 0 +-2 -6 0 +-4 -6 0 diff --git a/sat-chaff/test_inputs/p5.dimacs b/sat-chaff/test_inputs/p5.dimacs new file mode 100644 index 0000000..00db623 --- /dev/null +++ b/sat-chaff/test_inputs/p5.dimacs @@ -0,0 +1,98 @@ +c pigeon-5: placing 6 pigeons into 5 holes +c +c File generated by 'pigeonhole', (c) Tjark Weber +c +c The SAT encoding of this problem is very straightforward. For each pigeon i +c and each hole j we have a variable x_{n*(i-1)+j} which means that pigeon i +c is placed in hole j. Then we have n+1 clauses which say that a pigeon has +c to be placed in some hole. Then for each hole we have a set of clauses +c ensuring that only one single pigeon is placed into that hole. +c +c This encoding leads to a total of (n+1) * n propositional variables and +c (n+1) + n * (n * (n+1) / 2) clauses. +c +c The resulting SAT problem is unsatisfiable. +c +p cnf 30 81 +1 2 3 4 5 0 +6 7 8 9 10 0 +11 12 13 14 15 0 +16 17 18 19 20 0 +21 22 23 24 25 0 +26 27 28 29 30 0 +-1 -6 0 +-1 -11 0 +-1 -16 0 +-1 -21 0 +-1 -26 0 +-6 -11 0 +-6 -16 0 +-6 -21 0 +-6 -26 0 +-11 -16 0 +-11 -21 0 +-11 -26 0 +-16 -21 0 +-16 -26 0 +-21 -26 0 +-2 -7 0 +-2 -12 0 +-2 -17 0 +-2 -22 0 +-2 -27 0 +-7 -12 0 +-7 -17 0 +-7 -22 0 +-7 -27 0 +-12 -17 0 +-12 -22 0 +-12 -27 0 +-17 -22 0 +-17 -27 0 +-22 -27 0 +-3 -8 0 +-3 -13 0 +-3 -18 0 +-3 -23 0 +-3 -28 0 +-8 -13 0 +-8 -18 0 +-8 -23 0 +-8 -28 0 +-13 -18 0 +-13 -23 0 +-13 -28 0 +-18 -23 0 +-18 -28 0 +-23 -28 0 +-4 -9 0 +-4 -14 0 +-4 -19 0 +-4 -24 0 +-4 -29 0 +-9 -14 0 +-9 -19 0 +-9 -24 0 +-9 -29 0 +-14 -19 0 +-14 -24 0 +-14 -29 0 +-19 -24 0 +-19 -29 0 +-24 -29 0 +-5 -10 0 +-5 -15 0 +-5 -20 0 +-5 -25 0 +-5 -30 0 +-10 -15 0 +-10 -20 0 +-10 -25 0 +-10 -30 0 +-15 -20 0 +-15 -25 0 +-15 -30 0 +-20 -25 0 +-20 -30 0 +-25 -30 0 + diff --git a/sat-chaff/test_inputs/p7.dimacs b/sat-chaff/test_inputs/p7.dimacs new file mode 100644 index 0000000..d217a67 --- /dev/null +++ b/sat-chaff/test_inputs/p7.dimacs @@ -0,0 +1,221 @@ +c pigeon-7: placing 8 pigeons into 7 holes +c +c File generated by 'pigeonhole', (c) Tjark Weber +c +c The SAT encoding of this problem is very straightforward. For each pigeon i +c and each hole j we have a variable x_{n*(i-1)+j} which means that pigeon i +c is placed in hole j. Then we have n+1 clauses which say that a pigeon has +c to be placed in some hole. Then for each hole we have a set of clauses +c ensuring that only one single pigeon is placed into that hole. +c +c This encoding leads to a total of (n+1) * n propositional variables and +c (n+1) + n * (n * (n+1) / 2) clauses. +c +c The resulting SAT problem is unsatisfiable. +c +p cnf 56 204 +1 2 3 4 5 6 7 0 +8 9 10 11 12 13 14 0 +15 16 17 18 19 20 21 0 +22 23 24 25 26 27 28 0 +29 30 31 32 33 34 35 0 +36 37 38 39 40 41 42 0 +43 44 45 46 47 48 49 0 +50 51 52 53 54 55 56 0 +-1 -8 0 +-1 -15 0 +-1 -22 0 +-1 -29 0 +-1 -36 0 +-1 -43 0 +-1 -50 0 +-8 -15 0 +-8 -22 0 +-8 -29 0 +-8 -36 0 +-8 -43 0 +-8 -50 0 +-15 -22 0 +-15 -29 0 +-15 -36 0 +-15 -43 0 +-15 -50 0 +-22 -29 0 +-22 -36 0 +-22 -43 0 +-22 -50 0 +-29 -36 0 +-29 -43 0 +-29 -50 0 +-36 -43 0 +-36 -50 0 +-43 -50 0 +-2 -9 0 +-2 -16 0 +-2 -23 0 +-2 -30 0 +-2 -37 0 +-2 -44 0 +-2 -51 0 +-9 -16 0 +-9 -23 0 +-9 -30 0 +-9 -37 0 +-9 -44 0 +-9 -51 0 +-16 -23 0 +-16 -30 0 +-16 -37 0 +-16 -44 0 +-16 -51 0 +-23 -30 0 +-23 -37 0 +-23 -44 0 +-23 -51 0 +-30 -37 0 +-30 -44 0 +-30 -51 0 +-37 -44 0 +-37 -51 0 +-44 -51 0 +-3 -10 0 +-3 -17 0 +-3 -24 0 +-3 -31 0 +-3 -38 0 +-3 -45 0 +-3 -52 0 +-10 -17 0 +-10 -24 0 +-10 -31 0 +-10 -38 0 +-10 -45 0 +-10 -52 0 +-17 -24 0 +-17 -31 0 +-17 -38 0 +-17 -45 0 +-17 -52 0 +-24 -31 0 +-24 -38 0 +-24 -45 0 +-24 -52 0 +-31 -38 0 +-31 -45 0 +-31 -52 0 +-38 -45 0 +-38 -52 0 +-45 -52 0 +-4 -11 0 +-4 -18 0 +-4 -25 0 +-4 -32 0 +-4 -39 0 +-4 -46 0 +-4 -53 0 +-11 -18 0 +-11 -25 0 +-11 -32 0 +-11 -39 0 +-11 -46 0 +-11 -53 0 +-18 -25 0 +-18 -32 0 +-18 -39 0 +-18 -46 0 +-18 -53 0 +-25 -32 0 +-25 -39 0 +-25 -46 0 +-25 -53 0 +-32 -39 0 +-32 -46 0 +-32 -53 0 +-39 -46 0 +-39 -53 0 +-46 -53 0 +-5 -12 0 +-5 -19 0 +-5 -26 0 +-5 -33 0 +-5 -40 0 +-5 -47 0 +-5 -54 0 +-12 -19 0 +-12 -26 0 +-12 -33 0 +-12 -40 0 +-12 -47 0 +-12 -54 0 +-19 -26 0 +-19 -33 0 +-19 -40 0 +-19 -47 0 +-19 -54 0 +-26 -33 0 +-26 -40 0 +-26 -47 0 +-26 -54 0 +-33 -40 0 +-33 -47 0 +-33 -54 0 +-40 -47 0 +-40 -54 0 +-47 -54 0 +-6 -13 0 +-6 -20 0 +-6 -27 0 +-6 -34 0 +-6 -41 0 +-6 -48 0 +-6 -55 0 +-13 -20 0 +-13 -27 0 +-13 -34 0 +-13 -41 0 +-13 -48 0 +-13 -55 0 +-20 -27 0 +-20 -34 0 +-20 -41 0 +-20 -48 0 +-20 -55 0 +-27 -34 0 +-27 -41 0 +-27 -48 0 +-27 -55 0 +-34 -41 0 +-34 -48 0 +-34 -55 0 +-41 -48 0 +-41 -55 0 +-48 -55 0 +-7 -14 0 +-7 -21 0 +-7 -28 0 +-7 -35 0 +-7 -42 0 +-7 -49 0 +-7 -56 0 +-14 -21 0 +-14 -28 0 +-14 -35 0 +-14 -42 0 +-14 -49 0 +-14 -56 0 +-21 -28 0 +-21 -35 0 +-21 -42 0 +-21 -49 0 +-21 -56 0 +-28 -35 0 +-28 -42 0 +-28 -49 0 +-28 -56 0 +-35 -42 0 +-35 -49 0 +-35 -56 0 +-42 -49 0 +-42 -56 0 +-49 -56 0 + diff --git a/sat-chaff/test_inputs/p8.dimacs b/sat-chaff/test_inputs/p8.dimacs new file mode 100644 index 0000000..2922689 --- /dev/null +++ b/sat-chaff/test_inputs/p8.dimacs @@ -0,0 +1,314 @@ +c pigeon-8: placing 9 pigeons into 8 holes +c +c File generated by 'pigeonhole', (c) Tjark Weber +c +c The SAT encoding of this problem is very straightforward. For each pigeon i +c and each hole j we have a variable x_{n*(i-1)+j} which means that pigeon i +c is placed in hole j. Then we have n+1 clauses which say that a pigeon has +c to be placed in some hole. Then for each hole we have a set of clauses +c ensuring that only one single pigeon is placed into that hole. +c +c This encoding leads to a total of (n+1) * n propositional variables and +c (n+1) + n * (n * (n+1) / 2) clauses. +c +c The resulting SAT problem is unsatisfiable. +c +p cnf 72 297 +1 2 3 4 5 6 7 8 0 +9 10 11 12 13 14 15 16 0 +17 18 19 20 21 22 23 24 0 +25 26 27 28 29 30 31 32 0 +33 34 35 36 37 38 39 40 0 +41 42 43 44 45 46 47 48 0 +49 50 51 52 53 54 55 56 0 +57 58 59 60 61 62 63 64 0 +65 66 67 68 69 70 71 72 0 +-1 -9 0 +-1 -17 0 +-1 -25 0 +-1 -33 0 +-1 -41 0 +-1 -49 0 +-1 -57 0 +-1 -65 0 +-9 -17 0 +-9 -25 0 +-9 -33 0 +-9 -41 0 +-9 -49 0 +-9 -57 0 +-9 -65 0 +-17 -25 0 +-17 -33 0 +-17 -41 0 +-17 -49 0 +-17 -57 0 +-17 -65 0 +-25 -33 0 +-25 -41 0 +-25 -49 0 +-25 -57 0 +-25 -65 0 +-33 -41 0 +-33 -49 0 +-33 -57 0 +-33 -65 0 +-41 -49 0 +-41 -57 0 +-41 -65 0 +-49 -57 0 +-49 -65 0 +-57 -65 0 +-2 -10 0 +-2 -18 0 +-2 -26 0 +-2 -34 0 +-2 -42 0 +-2 -50 0 +-2 -58 0 +-2 -66 0 +-10 -18 0 +-10 -26 0 +-10 -34 0 +-10 -42 0 +-10 -50 0 +-10 -58 0 +-10 -66 0 +-18 -26 0 +-18 -34 0 +-18 -42 0 +-18 -50 0 +-18 -58 0 +-18 -66 0 +-26 -34 0 +-26 -42 0 +-26 -50 0 +-26 -58 0 +-26 -66 0 +-34 -42 0 +-34 -50 0 +-34 -58 0 +-34 -66 0 +-42 -50 0 +-42 -58 0 +-42 -66 0 +-50 -58 0 +-50 -66 0 +-58 -66 0 +-3 -11 0 +-3 -19 0 +-3 -27 0 +-3 -35 0 +-3 -43 0 +-3 -51 0 +-3 -59 0 +-3 -67 0 +-11 -19 0 +-11 -27 0 +-11 -35 0 +-11 -43 0 +-11 -51 0 +-11 -59 0 +-11 -67 0 +-19 -27 0 +-19 -35 0 +-19 -43 0 +-19 -51 0 +-19 -59 0 +-19 -67 0 +-27 -35 0 +-27 -43 0 +-27 -51 0 +-27 -59 0 +-27 -67 0 +-35 -43 0 +-35 -51 0 +-35 -59 0 +-35 -67 0 +-43 -51 0 +-43 -59 0 +-43 -67 0 +-51 -59 0 +-51 -67 0 +-59 -67 0 +-4 -12 0 +-4 -20 0 +-4 -28 0 +-4 -36 0 +-4 -44 0 +-4 -52 0 +-4 -60 0 +-4 -68 0 +-12 -20 0 +-12 -28 0 +-12 -36 0 +-12 -44 0 +-12 -52 0 +-12 -60 0 +-12 -68 0 +-20 -28 0 +-20 -36 0 +-20 -44 0 +-20 -52 0 +-20 -60 0 +-20 -68 0 +-28 -36 0 +-28 -44 0 +-28 -52 0 +-28 -60 0 +-28 -68 0 +-36 -44 0 +-36 -52 0 +-36 -60 0 +-36 -68 0 +-44 -52 0 +-44 -60 0 +-44 -68 0 +-52 -60 0 +-52 -68 0 +-60 -68 0 +-5 -13 0 +-5 -21 0 +-5 -29 0 +-5 -37 0 +-5 -45 0 +-5 -53 0 +-5 -61 0 +-5 -69 0 +-13 -21 0 +-13 -29 0 +-13 -37 0 +-13 -45 0 +-13 -53 0 +-13 -61 0 +-13 -69 0 +-21 -29 0 +-21 -37 0 +-21 -45 0 +-21 -53 0 +-21 -61 0 +-21 -69 0 +-29 -37 0 +-29 -45 0 +-29 -53 0 +-29 -61 0 +-29 -69 0 +-37 -45 0 +-37 -53 0 +-37 -61 0 +-37 -69 0 +-45 -53 0 +-45 -61 0 +-45 -69 0 +-53 -61 0 +-53 -69 0 +-61 -69 0 +-6 -14 0 +-6 -22 0 +-6 -30 0 +-6 -38 0 +-6 -46 0 +-6 -54 0 +-6 -62 0 +-6 -70 0 +-14 -22 0 +-14 -30 0 +-14 -38 0 +-14 -46 0 +-14 -54 0 +-14 -62 0 +-14 -70 0 +-22 -30 0 +-22 -38 0 +-22 -46 0 +-22 -54 0 +-22 -62 0 +-22 -70 0 +-30 -38 0 +-30 -46 0 +-30 -54 0 +-30 -62 0 +-30 -70 0 +-38 -46 0 +-38 -54 0 +-38 -62 0 +-38 -70 0 +-46 -54 0 +-46 -62 0 +-46 -70 0 +-54 -62 0 +-54 -70 0 +-62 -70 0 +-7 -15 0 +-7 -23 0 +-7 -31 0 +-7 -39 0 +-7 -47 0 +-7 -55 0 +-7 -63 0 +-7 -71 0 +-15 -23 0 +-15 -31 0 +-15 -39 0 +-15 -47 0 +-15 -55 0 +-15 -63 0 +-15 -71 0 +-23 -31 0 +-23 -39 0 +-23 -47 0 +-23 -55 0 +-23 -63 0 +-23 -71 0 +-31 -39 0 +-31 -47 0 +-31 -55 0 +-31 -63 0 +-31 -71 0 +-39 -47 0 +-39 -55 0 +-39 -63 0 +-39 -71 0 +-47 -55 0 +-47 -63 0 +-47 -71 0 +-55 -63 0 +-55 -71 0 +-63 -71 0 +-8 -16 0 +-8 -24 0 +-8 -32 0 +-8 -40 0 +-8 -48 0 +-8 -56 0 +-8 -64 0 +-8 -72 0 +-16 -24 0 +-16 -32 0 +-16 -40 0 +-16 -48 0 +-16 -56 0 +-16 -64 0 +-16 -72 0 +-24 -32 0 +-24 -40 0 +-24 -48 0 +-24 -56 0 +-24 -64 0 +-24 -72 0 +-32 -40 0 +-32 -48 0 +-32 -56 0 +-32 -64 0 +-32 -72 0 +-40 -48 0 +-40 -56 0 +-40 -64 0 +-40 -72 0 +-48 -56 0 +-48 -64 0 +-48 -72 0 +-56 -64 0 +-56 -72 0 +-64 -72 0 + diff --git a/sat-chaff/test_inputs/p9.dimacs b/sat-chaff/test_inputs/p9.dimacs new file mode 100644 index 0000000..3dfd7e5 --- /dev/null +++ b/sat-chaff/test_inputs/p9.dimacs @@ -0,0 +1,432 @@ +c pigeon-9: placing 10 pigeons into 9 holes +c +c File generated by 'pigeonhole', (c) Tjark Weber +c +c The SAT encoding of this problem is very straightforward. For each pigeon i +c and each hole j we have a variable x_{n*(i-1)+j} which means that pigeon i +c is placed in hole j. Then we have n+1 clauses which say that a pigeon has +c to be placed in some hole. Then for each hole we have a set of clauses +c ensuring that only one single pigeon is placed into that hole. +c +c This encoding leads to a total of (n+1) * n propositional variables and +c (n+1) + n * (n * (n+1) / 2) clauses. +c +c The resulting SAT problem is unsatisfiable. +c +p cnf 90 415 +1 2 3 4 5 6 7 8 9 0 +10 11 12 13 14 15 16 17 18 0 +19 20 21 22 23 24 25 26 27 0 +28 29 30 31 32 33 34 35 36 0 +37 38 39 40 41 42 43 44 45 0 +46 47 48 49 50 51 52 53 54 0 +55 56 57 58 59 60 61 62 63 0 +64 65 66 67 68 69 70 71 72 0 +73 74 75 76 77 78 79 80 81 0 +82 83 84 85 86 87 88 89 90 0 +-1 -10 0 +-1 -19 0 +-1 -28 0 +-1 -37 0 +-1 -46 0 +-1 -55 0 +-1 -64 0 +-1 -73 0 +-1 -82 0 +-10 -19 0 +-10 -28 0 +-10 -37 0 +-10 -46 0 +-10 -55 0 +-10 -64 0 +-10 -73 0 +-10 -82 0 +-19 -28 0 +-19 -37 0 +-19 -46 0 +-19 -55 0 +-19 -64 0 +-19 -73 0 +-19 -82 0 +-28 -37 0 +-28 -46 0 +-28 -55 0 +-28 -64 0 +-28 -73 0 +-28 -82 0 +-37 -46 0 +-37 -55 0 +-37 -64 0 +-37 -73 0 +-37 -82 0 +-46 -55 0 +-46 -64 0 +-46 -73 0 +-46 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a/sat-chaff/test_inputs/test.dimacs b/sat-chaff/test_inputs/test.dimacs new file mode 100644 index 0000000..7d672fb --- /dev/null +++ b/sat-chaff/test_inputs/test.dimacs @@ -0,0 +1,3 @@ +p cnf 3 2 +1 -3 0 +2 3 -1 0 |