pycosat: bindings to picosat (a SAT solver)
PicoSAT is a popular SAT solver written by Armin Biere in pure C. This package provides efficient Python bindings to picosat on the C level, i.e. when importing pycosat, the picosat solver becomes part of the Python process itself. For ease of deployment, the picosat source (namely picosat.c and picosat.h) is included in this project. These files have been extracted from the picosat source (picosat-957.tar.gz).
pycosat module has two functions
both of which take an iterable of clauses as an argument. Each clause
is itself represented as an iterable of (non-zero) integers.
- The function
solvereturns one of the following:
- one solution (a list of integers)
- the string "UNSAT" (when the clauses are unsatisfiable)
- the string "UNKNOWN" (when a solution could not be determined within the propagation limit)
itersolve returns an iterator over solutions. When the
propagation limit is specified, exhausting the iterator may not yield all
- Both functions take the following keyword arguments:
prop_limit: the propagation limit (integer)
vars: number of variables (integer)
verbose: the verbosity level (integer)
Let us consider the following clauses, represented using the DIMACS cnf format:
p cnf 5 3 1 -5 4 0 -1 5 3 4 0 -3 -4 0
Here, we have 5 variables and 3 clauses, the first clause being (x1 or not x5 or x4). Note that the variable x2 is not used in any of the clauses, which means that for each solution with x2 = True, we must also have a solution with x2 = False. In Python, each clause is most conveniently represented as a list of integers. Naturally, it makes sense to represent each solution also as a list of integers, where the sign corresponds to the Boolean value (+ for True and - for False) and the absolute value corresponds to ith variable:
>>> import pycosat >>> cnf = [[1, -5, 4], [-1, 5, 3, 4], [-3, -4]] >>> pycosat.solve(cnf) [1, -2, -3, -4, 5]
This solution translates to: x1 = x5 = True, x2 = x3 = x4 = False
To find all solutions, use
>>> for sol in pycosat.itersolve(cnf): ... print sol ... [1, -2, -3, -4, 5] [1, -2, -3, 4, -5] [1, -2, -3, 4, 5] ... >>> len(list(pycosat.itersolve(cnf))) 18
In this example, there are a total of 18 possible solutions, which had to be an even number because x2 was left unspecified in the clauses.
The fact that
itersolve returns an iterator, makes it very elegant
and efficient for many types of operations. For example, using
itertools module from the standard library, here is how one
would construct a list of (up to) 3 solutions:
>>> import itertools >>> list(itertools.islice(pycosat.itersolve(cnf), 3)) [[1, -2, -3, -4, 5], [1, -2, -3, 4, -5], [1, -2, -3, 4, 5]]
Implementation of itersolve
How does one go from having found one solution to another solution?
The answer is surprisingly simple. One adds the inverse of the already
found solution as a new clause. This new clause ensures that another
solution is searched for, as it excludes the already found solution.
Here is basically a pure Python implementation of
itersolve in terms
def py_itersolve(clauses): # don't use this function! while True: # (it is only here to explain things) sol = pycosat.solve(clauses) if isinstance(sol, list): yield sol clauses.append([-x for x in sol]) else: # no more solutions -- stop iteration return
This implementation has several problems. Firstly, it is quite slow as
pycosat.solve has to convert the list of clauses over and over and over
again. Secondly, after calling
py_itersolve the list of clauses will
be modified. In pycosat,
itersolve is implemented on the C level,
making use of the picosat C interface (which makes it much, much faster
than the naive Python implementation above).