pycryptosat 5.11.1

Bindings to CryptoMiniSat, an advanced SAT solver

pycryptosat: bindings to the CryptoMiniSat SAT solver

This directory provides Python bindings to CryptoMiniSat on the C++ level, i.e. when importing pycryptosat, the CryptoMiniSat solver becomes part of the Python process itself.

Compiling

The pycryptosat python package compiles separately from the CryptoMiniSat library, so if you have special flags included with CryptoMiniSat, it will NOT be reflected in the python package.

In order to compile, install the python developer tools:

apt-get install python-dev

Then run

python -m build

Usage

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 variable 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:

• time_limit: the time limit (integer)
• confl_limit: the propagation limit (integer)
• verbose: the verbosity level (integer)

Both time_limit and confl_limit set a budget to the solver. The former is based on time elapsed while the former is based on number of conflicts met during search. If the solver runs out of budget, it returns with (None, None). If both limits are used, the solver will terminate whenever one of the limits are hit (whichever first). Warning: Results from time_limit may differ from run to run, depending on compute load, etc. Use confl_limit for more reproducible runs.

Example

Let us consider the following clauses, represented using the DIMACS cnf <http://en.wikipedia.org/wiki/Conjunctive_normal_form>_ 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 (x\ :sub:1 or not x\ :sub:5 or x\ :sub:4). Note that the variable x\ :sub:2 is not used in any of the clauses, which means that for each solution with x\ :sub:2 = True, we must also have a solution with x\ :sub:2 = 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 i\ :sup:th variable::

>>> import pycryptosat
>>> solver = pycryptosat.Solver()
>>> solver.add_clause([1, -5, 4])
>>> solver.add_clause([-1, 5, 3, 4])
>>> solver.add_clause([-3, -4])
>>> solver.solve()
(True, (None, True, False, False, True, True))

This solution translates to: x\ :sub:1 = x\ :sub:4 = x\ :sub:5 = True, x\ :sub:2 = x\ :sub:3 = False