"""
SAT-Solvers via DIMACS Files
Sage supports calling SAT solvers using the popular DIMACS format. This module implements
infrastructure to make it easy to add new such interfaces and some example interfaces.
Currently, interfaces to **RSat** [RS]_ and **Glucose** [GL]_ are included by default.
.. note::
Our SAT solver interfaces are 1-based, i.e., literals start at 1. This is consistent with the
popular DIMACS format for SAT solving but not with Pythion's 0-based convention. However, this
also allows to construct clauses using simple integers.
AUTHORS:
- Martin Albrecht (2012): first version
Classes and Methods
-------------------
"""
import os, sys, subprocess, shlex
from sage.sat.solvers.satsolver import SatSolver
from sage.misc.misc import tmp_filename, get_verbose
from time import sleep
class DIMACS(SatSolver):
"""
Generic DIMACS Solver.
.. note::
Usually, users won't have to use this class directly but some
class which inherits from this class.
.. automethod:: __init__
.. automethod:: __call__
"""
command = ""
def __init__(self, command=None, filename=None, verbosity=0, **kwds):
"""
Construct a new generic DIMACS solver.
INPUT:
- ``command`` - a named format string with the command to
run. The string must contain {input} and may contain
{output} if the solvers writes the solution to an output
file. For example "sat-solver {input}" is a valid
command. If ``None`` then the class variable ``command`` is
used. (default: ``None``)
- ``filename`` - a filename to write clauses to in DIMACS
format, must be writable. If ``None`` a temporary filename
is chosen automatically. (default: ``None``)
- ``verbosity`` - a verbosity level, where zero means silent
and anything else means verbose output. (default: ``0``)
- ``**kwds`` - accepted for compatibility with other solves,
ignored.
TESTS::
sage: from sage.sat.solvers.dimacs import DIMACS
sage: DIMACS()
DIMACS Solver: ''
"""
if filename is None:
filename = tmp_filename()
self._headname = filename
self._verbosity = verbosity
if command is not None:
self._command = command
else:
self._command = self.__class__.command
self._tail = open(tmp_filename(),'w')
self._var = 0
self._lit = 0
def __repr__(self):
"""
TESTS::
sage: from sage.sat.solvers.dimacs import DIMACS
sage: DIMACS(command="iliketurtles {input}")
DIMACS Solver: 'iliketurtles {input}'
"""
return "DIMACS Solver: '%s'"%(self._command)
def __del__(self):
"""
TESTS::
sage: from sage.sat.solvers.dimacs import DIMACS
sage: d = DIMACS(command="iliketurtles {input}")
sage: del d
"""
if not self._tail.closed:
self._tail.close()
if os.path.exists(self._tail.name):
os.unlink(self._tail.name)
def var(self, decision=None):
"""
Return a *new* variable.
INPUT:
- ``decision`` - accepted for compatibility with other solvers, ignored.
EXAMPLE::
sage: from sage.sat.solvers.dimacs import DIMACS
sage: solver = DIMACS()
sage: solver.var()
1
"""
self._var+= 1
return self._var
def nvars(self):
"""
Return the number of variables.
EXAMPLE::
sage: from sage.sat.solvers.dimacs import DIMACS
sage: solver = DIMACS()
sage: solver.var()
1
sage: solver.var(decision=True)
2
sage: solver.nvars()
2
"""
return self._var
def add_clause(self, lits):
"""
Add a new clause to set of clauses.
INPUT:
- ``lits`` - a tuple of integers != 0
.. note::
If any element ``e`` in ``lits`` has ``abs(e)`` greater
than the number of variables generated so far, then new
variables are created automatically.
EXAMPLE::
sage: from sage.sat.solvers.dimacs import DIMACS
sage: solver = DIMACS()
sage: solver.var()
1
sage: solver.var(decision=True)
2
sage: solver.add_clause( (1, -2 , 3) )
sage: solver
DIMACS Solver: ''
"""
l = []
for lit in lits:
lit = int(lit)
while abs(lit) > self.nvars():
self.var()
l.append(str(lit))
l.append("0\n")
self._tail.write(" ".join(l) )
self._lit += 1
def write(self, filename=None):
"""
Write DIMACS file.
INPUT:
- ``filename`` - if ``None`` default filename specified at initialization is used for
writing to (default: ``None``)
EXAMPLE::
sage: from sage.sat.solvers.dimacs import DIMACS
sage: fn = tmp_filename()
sage: solver = DIMACS(filename=fn)
sage: solver.add_clause( (1, -2 , 3) )
sage: _ = solver.write()
sage: for line in open(fn).readlines():
... print line,
p cnf 3 1
1 -2 3 0
sage: from sage.sat.solvers.dimacs import DIMACS
sage: fn = tmp_filename()
sage: solver = DIMACS()
sage: solver.add_clause( (1, -2 , 3) )
sage: _ = solver.write(fn)
sage: for line in open(fn).readlines():
... print line,
p cnf 3 1
1 -2 3 0
"""
headname = self._headname if filename is None else filename
head = open(headname, "w")
head.truncate(0)
head.write("p cnf %d %d\n"%(self._var,self._lit))
head.close()
tail = self._tail
tail.close()
head = open(headname,"a")
tail = open(self._tail.name,"r")
head.write(tail.read())
tail.close()
head.close()
self._tail = open(self._tail.name,"a")
return headname
def clauses(self, filename=None):
"""
Return original clauses.
INPUT:
- ``filename`` - if not ``None`` clauses are written to ``filename`` in
DIMACS format (default: ``None``)
OUTPUT:
If ``filename`` is ``None`` then a list of ``lits, is_xor, rhs``
tuples is returned, where ``lits`` is a tuple of literals,
``is_xor`` is always ``False`` and ``rhs`` is always ``None``.
If ``filename`` points to a writable file, then the list of original
clauses is written to that file in DIMACS format.
EXAMPLE::
sage: from sage.sat.solvers.dimacs import DIMACS
sage: fn = tmp_filename()
sage: solver = DIMACS()
sage: solver.add_clause( (1, 2, 3) )
sage: solver.clauses()
[((1, 2, 3), False, None)]
sage: solver.add_clause( (1, 2, -3) )
sage: solver.clauses(fn)
sage: print open(fn).read()
p cnf 3 2
1 2 3 0
1 2 -3 0
<BLANKLINE>
"""
if filename is not None:
self.write(filename)
else:
tail = self._tail
tail.close()
tail = open(self._tail.name,"r")
clauses = []
for line in tail.readlines():
if line.startswith("p") or line.startswith("c"):
continue
clause = []
for lit in line.split(" "):
lit = int(lit)
if lit == 0:
break
clause.append(lit)
clauses.append( ( tuple(clause), False, None ) )
tail.close()
self._tail = open(self._tail.name, "a")
return clauses
@staticmethod
def render_dimacs(clauses, filename, nlits):
"""
Produce DIMACS file ``filename`` from ``clauses``.
INPUT:
- ``clauses`` - a list of clauses, either in simple format as a list of
literals or in extended format for CryptoMiniSat: a tuple of literals,
``is_xor`` and ``rhs``.
- ``filename`` - the file to write to
- ``nlits -- the number of literals appearing in ``clauses``
EXAMPLE::
sage: from sage.sat.solvers.dimacs import DIMACS
sage: fn = tmp_filename()
sage: solver = DIMACS()
sage: solver.add_clause( (1, 2, -3) )
sage: DIMACS.render_dimacs(solver.clauses(), fn, solver.nvars())
sage: print open(fn).read()
p cnf 3 1
1 2 -3 0
<BLANKLINE>
This is equivalent to::
sage: solver.clauses(fn)
sage: print open(fn).read()
p cnf 3 1
1 2 -3 0
<BLANKLINE>
This function also accepts a "simple" format::
sage: DIMACS.render_dimacs([ (1,2), (1,2,-3) ], fn, 3)
sage: print open(fn).read()
p cnf 3 2
1 2 0
1 2 -3 0
<BLANKLINE>
"""
fh = open(filename, "w")
fh.write("p cnf %d %d\n"%(nlits,len(clauses)))
for clause in clauses:
if len(clause) == 3 and clause[1] in (True, False) and clause[2] in (True,False,None):
lits, is_xor, rhs = clause
else:
lits, is_xor, rhs = clause, False, None
if is_xor:
closing = lits[-1] if rhs else -lits[-1]
fh.write("x" + " ".join(map(str, lits[:-1])) + " %d 0\n"%closing)
else:
fh.write(" ".join(map(str, lits)) + " 0\n")
fh.close()
def __call__(self, assumptions=None):
"""
Run 'command' and collect output.
INPUT:
- ``assumptions`` - ignored, accepted for compatibility with
other solvers (default: ``None``)
TESTS:
This class is not meant to be called directly::
sage: from sage.sat.solvers.dimacs import DIMACS
sage: fn = tmp_filename()
sage: solver = DIMACS(filename=fn)
sage: solver.add_clause( (1, -2 , 3) )
sage: solver()
Traceback (most recent call last):
...
ValueError: No SAT solver command selected.
"""
if assumptions is not None:
raise NotImplementedError("Assumptions are not supported for DIMACS based solvers.")
self.write()
output_filename = None
self._output = []
command = self._command.strip()
if not command:
raise ValueError("No SAT solver command selected.")
if "{output}" in command:
output_filename = tmp_filename()
command = command.format(input=self._headname, output=output_filename)
args = shlex.split(command)
try:
process = subprocess.Popen(args, stdout=subprocess.PIPE)
except OSError:
raise OSError("Could run '%s', perhaps you need to add your SAT solver to $PATH?"%(" ".join(args)))
try:
while process.poll() is None:
for line in iter(process.stdout.readline,''):
if get_verbose() or self._verbosity:
print line,
sys.stdout.flush()
self._output.append(line)
sleep(0.1)
if output_filename:
self._output.extend(open(output_filename).readlines())
except BaseException:
process.kill()
raise
class RSat(DIMACS):
"""
An instance of the RSat solver.
For information on RSat see: http://reasoning.cs.ucla.edu/rsat/
"""
command = "rsat {input} -v -s"
def __call__(self, assumptions=None):
"""
Solve this instance.
INPUT:
- ``assumptions`` - ignored, accepted for compatibility with
other solvers (default: ``None``)
OUTPUT:
- If this instance is SAT: A tuple of length ``nvars()+1``
where the ``i``-th entry holds an assignment for the
``i``-th variables (the ``0``-th entry is always ``None``).
- If this instance is UNSAT: ``False``
EXAMPLE::
sage: from sage.sat.boolean_polynomials import solve as solve_sat
sage: F,s = mq.SR(1,1,1,4,gf2=True,polybori=True).polynomial_system()
sage: solve_sat(F, solver=sage.sat.solvers.RSat) # not tested, requires RSat in PATH
"""
DIMACS.__call__(self)
s = [None] + [False for _ in range(self.nvars())]
for line in self._output:
if line.startswith("c"):
continue
if line.startswith("s"):
if "UNSAT" in line:
return False
if line.startswith("v"):
lits = map(int, line[2:-2].strip().split(" "))
for e in lits:
s[abs(e)] = e>0
return tuple(s)
class Glucose(DIMACS):
"""
An instance of the Glucose solver.
For information on Glucose see: http://www.lri.fr/~simon/?page=glucose
"""
command = "glucose_static -verb=2 {input} {output}"
def __call__(self, **kwds):
"""
Solve this instance.
INPUT:
- ``assumptions`` - ignored, accepted for compatibility with
other solvers (default: ``None``)
OUTPUT:
- If this instance is SAT: A tuple of length ``nvars()+1``
where the ``i``-th entry holds an assignment for the
``i``-th variables (the ``0``-th entry is always ``None``).
- If this instance is UNSAT: ``False``
EXAMPLE::
sage: from sage.sat.boolean_polynomials import solve as solve_sat
sage: F,s = mq.SR(1,1,1,4,gf2=True,polybori=True).polynomial_system()
sage: solve_sat(F, solver=sage.sat.solvers.Glucose) # not tested, requires Glucose in PATH
"""
DIMACS.__call__(self)
for line in self._output:
if line.startswith("c"):
continue
if line.startswith("s"):
if "UNSAT" in line:
return False
try:
s = map(int, line[:-2].strip().split(" "))
s = (None,) + tuple(e>0 for e in s)
return s
except ValueError:
pass
return False
