This package provides Python bindings to CryptoMiniSat on the C++ level, i.e. when importing pycryptosat, the CryptoMiniSat solver becomes part of the Python process itself. This package is based on work by Ilan Schnell, who provided the binding as MIT licence, which it stays, though it links to CryptoMiniSat which is LGPL.
The pycryptosat
module has one object, Solver
that has two functions
solve
and add_clause
.
The funcion add_clause()
takes an iterable list of literals such as
[1, 2]
which represents the truth 1 or 2 = True
. For example,
add_clause([1])
sets variable 1
to True
.
The function solve()
solves the system of equations that have been added
with add_clause()
:
>>> from pycryptosat import Solver >>> s = Solver() >>> s.add_clause([1, 2]) >>> sat, solution = s.solve() >>> print sat True >>> print solution (None, True, True)
The return value is a tuple. First part of the tuple indicates whether the
problem is satisfiable. In this case, it's True
, i.e. satisfiable. The second
part is a tuple contains the solution, preceded by None, so you can index into
it with the variable number. E.g. solution[1]
returns the value for
variabe 1
.
The solve()
method optionally takes an argument assumptions
that
allows the user to set values to specific variables in the solver in a temporary
fashion. This means that in case the problem is satisfiable but e.g it's
unsatisfiable if variable 2 is FALSE, then solve([-2])
will return
UNSAT. However, a subsequent call to solve()
will still return a solution.
If instead of an assumption add_clause()
would have been used, subsequent
solve()
calls would have returned unsatisfiable.
Solver
takes the following keyword arguments:confl_limit
: the propagation limit (integer)verbose
: the verbosity level (integer)
The confl_limit
argument sets a kind of time-out limit to the solver. If
the solver runs out of time, it returns with (None, None)
.
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 pycryptosat >>> solver = pycryptosat.Solver() >>> solver.add_clause([1, -5, 4]) >>> solver.add_clause([-1, 5, 3, 4]) >>> solver.add_clause([-3, -4]]) >>> pycryptosat.solve() (True, (None, True, False, False, True, True))
This solution translates to: x1 = x4 = x5 = True, x2 = x3 = False