#!/usr/bin/env python
#-*- coding:utf-8 -*-
##
## lbx.py
##
## Created on: Jan 9, 2017
## Author: Alexey S. Ignatiev
## E-mail: aignatiev@ciencias.ulisboa.pt
##
"""
===============
List of classes
===============
.. autosummary::
:nosignatures:
LBX
==================
Module description
==================
This module implements a prototype of the LBX algorithm for the computation
of a *minimal correction subset* (MCS) and/or MCS enumeration. The LBX
abbreviation stands for *literal-based MCS extraction* algorithm, which was
proposed in [1]_. Note that this prototype does not follow the original
low-level implementation of the corresponding MCS extractor available
`online <https://reason.di.fc.ul.pt/wiki/doku.php?id=lbx>`_ (compared to
our prototype, the low-level implementation has a number of additional
heuristics used). However, it implements the LBX algorithm for partial
MaxSAT formulas, as described in [1]_.
.. [1] Carlos Mencia, Alessandro Previti, Joao Marques-Silva.
*Literal-Based MCS Extraction*. IJCAI 2015. pp. 1973-1979
The implementation can be used as an executable (the list of available
command-line options can be shown using ``lbx.py -h``) in the following
way:
::
$ xzcat formula.wcnf.xz
p wcnf 3 6 4
1 1 0
1 2 0
1 3 0
4 -1 -2 0
4 -1 -3 0
4 -2 -3 0
$ lbx.py -d -e all -s glucose3 -vv formula.wcnf.xz
c MCS: 1 3 0
c cost: 2
c MCS: 2 3 0
c cost: 2
c MCS: 1 2 0
c cost: 2
c oracle time: 0.0002
Alternatively, the algorithm can be accessed and invoked through the
standard ``import`` interface of Python, e.g.
.. code-block:: python
>>> from pysat.examples.lbx import LBX
>>> from pysat.formula import WCNF
>>>
>>> wcnf = WCNF(from_file='formula.wcnf.xz')
>>>
>>> lbx = LBX(wcnf, use_cld=True, solver_name='g3')
>>> for mcs in lbx.enumerate():
... lbx.block(mcs)
... print(mcs)
[1, 3]
[2, 3]
[1, 2]
==============
Module details
==============
"""
#
#==============================================================================
from __future__ import print_function
import collections
import getopt
from math import copysign
import os
from pysat.formula import CNFPlus, WCNFPlus
from pysat.solvers import Solver, SolverNames
import re
from six.moves import range
import sys
#
#==============================================================================
class LBX(object):
"""
LBX-like algorithm for computing MCSes. Given an unsatisfiable partial
CNF formula, i.e. formula in the :class:`.WCNF` format, this class can
be used to compute a given number of MCSes of the formula. The
implementation follows the LBX algorithm description in [1]_. It can
use any SAT solver available in PySAT. Additionally, the "clause
:math:`D`" heuristic can be used when enumerating MCSes.
The default SAT solver to use is ``m22`` (see :class:`.SolverNames`).
The "clause :math:`D`" heuristic is disabled by default, i.e.
``use_cld`` is set to ``False``. Internal SAT solver's timer is also
disabled by default, i.e. ``use_timer`` is ``False``.
:param formula: unsatisfiable partial CNF formula
:param use_cld: whether or not to use "clause :math:`D`"
:param solver_name: SAT oracle name
:param use_timer: whether or not to use SAT solver's timer
:type formula: :class:`.WCNF`
:type use_cld: bool
:type solver_name: str
:type use_timer: bool
"""
def __init__(self, formula, use_cld=False, solver_name='m22', use_timer=False):
"""
Constructor.
"""
# bootstrapping the solver with hard clauses
self.oracle = Solver(name=solver_name, bootstrap_with=formula.hard,
use_timer=use_timer)
self.solver = solver_name
# adding native cardinality constraints (if any) as hard clauses
# this can be done only if the Minicard solver is in use
if isinstance(formula, WCNFPlus) and formula.atms:
assert solver_name in SolverNames.minicard, \
'Only Minicard supports native cardinality constraints. Make sure you use the right type of formula.'
for atm in formula.atms:
self.oracle.add_atmost(*atm)
self.topv = formula.nv # top variable id
self.soft = formula.soft
self.sels = []
self.ucld = use_cld
# mappings between internal and external variables
VariableMap = collections.namedtuple('VariableMap', ['e2i', 'i2e'])
self.vmap = VariableMap(e2i={}, i2e={})
# at this point internal and external variables are the same
for v in range(1, formula.nv + 1):
self.vmap.e2i[v] = v
self.vmap.i2e[v] = v
for cl in self.soft:
sel = cl[0]
if len(cl) > 1 or cl[0] < 0:
self.topv += 1
sel = self.topv
self.oracle.add_clause(cl + [-sel])
self.sels.append(sel)
def __del__(self):
"""
Destructor.
"""
self.delete()
def __enter__(self):
"""
'with' constructor.
"""
return self
def __exit__(self, exc_type, exc_value, traceback):
"""
'with' destructor.
"""
self.delete()
def delete(self):
"""
Explicit destructor of the internal SAT oracle.
"""
if self.oracle:
self.oracle.delete()
self.oracle = None
def add_clause(self, clause, soft=False):
"""
The method for adding a new hard of soft clause to the problem
formula. Although the input formula is to be specified as an
argument of the constructor of :class:`LBX`, adding clauses may be
helpful when *enumerating* MCSes of the formula. This way, the
clauses are added incrementally, i.e. *on the fly*.
The clause to add can be any iterable over integer literals. The
additional Boolean parameter ``soft`` can be set to ``True``
meaning the the clause being added is soft (note that parameter
``soft`` is set to ``False`` by default).
:param clause: a clause to add
:param soft: whether or not the clause is soft
:type clause: iterable(int)
:type soft: bool
"""
# first, map external literals to internal literals
# introduce new variables if necessary
cl = list(map(lambda l: self._map_extlit(l), clause if not len(clause) == 2 or not type(clause[0]) == list else clause[0]))
if not soft:
if not len(clause) == 2 or not type(clause[0]) == list:
# the clause is hard, and so we simply add it to the SAT oracle
self.oracle.add_clause(cl)
else:
# this should be a native cardinality constraint,
# which can be used only together with Minicard
assert self.solver in SolverNames.minicard, \
'Only Minicard supports native cardinality constraints.'
self.oracle.add_atmost(cl, clause[1])
else:
self.soft.append(cl)
# soft clauses should be augmented with a selector
sel = cl[0]
if len(cl) > 1 or cl[0] < 0:
self.topv += 1
sel = self.topv
self.oracle.add_clause(cl + [-sel])
self.sels.append(sel)
def compute(self):
"""
Compute and return one solution. This method checks whether the
hard part of the formula is satisfiable, i.e. an MCS can be
extracted. If the formula is satisfiable, the model computed by the
SAT call is used as an *over-approximation* of the MCS in the
method :func:`_compute` invoked here, which implements the LBX
algorithm.
An MCS is reported as a list of integers, each representing a soft
clause index (the smallest index is ``1``).
:rtype: list(int)
"""
self.setd = []
self.satc = [False for cl in self.soft] # satisfied clauses
self.solution = None
self.bb_assumps = [] # backbone assumptions
self.ss_assumps = [] # satisfied soft clause assumptions
if self.oracle.solve():
# hard part is satisfiable => there is a solution
self._filter_satisfied(update_setd=True)
self._compute()
self.solution = list(map(lambda i: i + 1, filter(lambda i: not self.satc[i], range(len(self.soft)))))
return self.solution
def enumerate(self):
"""
This method iterates through MCSes enumerating them until the
formula has no more MCSes. The method iteratively invokes
:func:`compute`. Note that the method does not block the MCSes
computed - this should be explicitly done by a user.
"""
done = False
while not done:
mcs = self.compute()
if mcs != None:
yield mcs
else:
done = True
def block(self, mcs):
"""
Block a (previously computed) MCS. The MCS should be given as an
iterable of integers. Note that this method is not automatically
invoked from :func:`enumerate` because a user may want to block
some of the MCSes conditionally depending on the needs. For
example, one may want to compute disjoint MCSes only in which case
this standard blocking is not appropriate.
:param mcs: an MCS to block
:type mcs: iterable(int)
"""
self.oracle.add_clause([self.sels[cl_id - 1] for cl_id in mcs])
def _satisfied(self, cl, model):
"""
Given a clause (as an iterable of integers) and an assignment (as a
list of integers), this method checks whether or not the assignment
satisfies the clause. This is done by a simple clause traversal.
The method is invoked from :func:`_filter_satisfied`.
:param cl: a clause to check
:param model: an assignment
:type cl: iterable(int)
:type model: list(int)
:rtype: bool
"""
for l in cl:
if len(model) < abs(l) or model[abs(l) - 1] == l:
# either literal is unassigned or satisfied by the model
return True
return False
def _filter_satisfied(self, update_setd=False):
"""
This method extracts a model provided by the previous call to a SAT
oracle and iterates over all soft clauses checking if each of is
satisfied by the model. Satisfied clauses are marked accordingly
while the literals of the unsatisfied clauses are kept in a list
called ``setd``, which is then used to refine the correction set
(see :func:`_compute`, and :func:`do_cld_check`).
Optional Boolean parameter ``update_setd`` enforces the method to
update variable ``self.setd``. If this parameter is set to
``False``, the method only updates the list of satisfied clauses,
which is an under-approximation of a *maximal satisfiable subset*
(MSS).
:param update_setd: whether or not to update setd
:type update_setd: bool
"""
model = self.oracle.get_model()
setd = set()
for i, cl in enumerate(self.soft):
if not self.satc[i]:
if self._satisfied(cl, model):
self.satc[i] = True
self.ss_assumps.append(self.sels[i])
else:
setd = setd.union(set(cl))
if update_setd:
self.setd = sorted(setd)
def _compute(self):
"""
The main method of the class, which computes an MCS given its
over-approximation. The over-approximation is defined by a model
for the hard part of the formula obtained in :func:`compute`.
The method is essentially a simple loop going over all literals
unsatisfied by the previous model, i.e. the literals of
``self.setd`` and checking which literals can be satisfied. This
process can be seen a refinement of the over-approximation of the
MCS. The algorithm follows the pseudo-code of the LBX algorithm
presented in [1]_.
Additionally, if :class:`LBX` was constructed with the requirement
to make "clause :math:`D`" calls, the method calls
:func:`do_cld_check` at every iteration of the loop using the
literals of ``self.setd`` not yet checked, as the contents of
"clause :math:`D`".
"""
# unless clause D checks are used, test one literal at a time
# and add it either to satisfied of backbone assumptions
i = 0
while i < len(self.setd):
if self.ucld:
self.do_cld_check(self.setd[i:])
i = 0
if self.setd: # if may be empty after the clause D check
if self.oracle.solve(assumptions=self.ss_assumps + self.bb_assumps + [self.setd[i]]):
# filtering satisfied clauses
self._filter_satisfied()
else:
# current literal is backbone
self.bb_assumps.append(-self.setd[i])
i += 1
def do_cld_check(self, cld):
"""
Do the "clause :math:`D`" check. This method receives a list of
literals, which serves a "clause :math:`D`" [2]_, and checks
whether the formula conjoined with :math:`D` is satisfiable.
.. [2] Joao Marques-Silva, Federico Heras, Mikolas Janota,
Alessandro Previti, Anton Belov. *On Computing Minimal
Correction Subsets*. IJCAI 2013. pp. 615-622
If clause :math:`D` cannot be satisfied together with the formula,
then negations of all of its literals are backbones of the formula
and the LBX algorithm can stop. Otherwise, the literals satisfied
by the new model refine the MCS further.
Every time the method is called, a new fresh selector variable
:math:`s` is introduced, which augments the current clause
:math:`D`. The SAT oracle then checks if clause :math:`(D \\vee
\\neg{s})` can be satisfied together with the internal formula.
The :math:`D` clause is then disabled by adding a hard clause
:math:`(\\neg{s})`.
:param cld: clause :math:`D` to check
:type cld: list(int)
"""
# adding a selector literal to clause D
# selector literals for clauses D currently
# cannot be reused, but this may change later
self.topv += 1
sel = self.topv
cld.append(-sel)
# adding clause D
self.oracle.add_clause(cld)
if self.oracle.solve(assumptions=self.ss_assumps + self.bb_assumps + [sel]):
# filtering satisfied
self._filter_satisfied(update_setd=True)
else:
# clause D is unsatisfiable => all literals are backbones
self.bb_assumps.extend([-l for l in cld[:-1]])
self.setd = []
# deactivating clause D
self.oracle.add_clause([-sel])
def _map_extlit(self, l):
"""
Map an external variable to an internal one if necessary.
This method is used when new clauses are added to the formula
incrementally, which may result in introducing new variables
clashing with the previously used *clause selectors*. The method
makes sure no clash occurs, i.e. it maps the original variables
used in the new problem clauses to the newly introduced auxiliary
variables (see :func:`add_clause`).
Given an integer literal, a fresh literal is returned. The returned
integer has the same sign as the input literal.
:param l: literal to map
:type l: int
:rtype: int
"""
v = abs(l)
if v in self.vmap.e2i:
return int(copysign(self.vmap.e2i[v], l))
else:
self.topv += 1
self.vmap.e2i[v] = self.topv
self.vmap.i2e[self.topv] = v
return int(copysign(self.topv, l))
def oracle_time(self):
"""
Report the total SAT solving time.
"""
return self.oracle.time_accum()
#
#==============================================================================
def parse_options():
"""
Parses command-line options.
"""
try:
opts, args = getopt.getopt(sys.argv[1:],
'de:hs:v',
['dcalls',
'enum=',
'help',
'solver=',
'verbose'])
except getopt.GetoptError as err:
sys.stderr.write(str(err).capitalize() + '\n')
usage()
sys.exit(1)
dcalls = False
to_enum = 1
solver = 'm22'
verbose = 0
for opt, arg in opts:
if opt in ('-d', '--dcalls'):
dcalls = True
elif opt in ('-e', '--enum'):
to_enum = str(arg)
if to_enum != 'all':
to_enum = int(to_enum)
elif opt in ('-h', '--help'):
usage()
sys.exit(0)
elif opt in ('-s', '--solver'):
solver = str(arg)
elif opt in ('-v', '--verbose'):
verbose += 1
else:
assert False, 'Unhandled option: {0} {1}'.format(opt, arg)
return dcalls, to_enum, solver, verbose, args
#
#==============================================================================
def usage():
"""
Prints help message.
"""
print('Usage:', os.path.basename(sys.argv[0]), '[options] file')
print('Options:')
print(' -d, --dcalls Try to bootstrap algorithm')
print(' -e, --enum=<string> How many solutions to compute')
print(' Available values: [1 .. all] (default: 1)')
print(' -h, --help')
print(' -s, --solver SAT solver to use')
print(' Available values: g3, g4, lgl, mcb, mcm, mpl, m22, mc, mgh (default = m22)')
print(' -v, --verbose Be verbose')
#
#==============================================================================
if __name__ == '__main__':
dcalls, to_enum, solver, verbose, files = parse_options()
if type(to_enum) == str:
to_enum = 0
if files:
# reading standard CNF, WCNF, or (W)CNF+
if re.search('cnf[p|+]?(\.(gz|bz2|lzma|xz))?$', files[0]):
if re.search('\.wcnf[p|+]?(\.(gz|bz2|lzma|xz))?$', files[0]):
formula = WCNFPlus(from_file=files[0])
else: # expecting '*.cnf[,p,+].*'
formula = CNFPlus(from_file=files[0]).weighted()
with LBX(formula, use_cld=dcalls, solver_name=solver, use_timer=True) as mcsls:
for i, mcs in enumerate(mcsls.enumerate()):
if verbose:
print('c MCS:', ' '.join([str(cl_id) for cl_id in mcs]), '0')
if verbose > 1:
cost = sum([formula.wght[cl_id - 1] for cl_id in mcs])
print('c cost:', cost)
if to_enum and i + 1 == to_enum:
break
mcsls.block(mcs)
print('c oracle time: {0:.4f}'.format(mcsls.oracle_time()))
