def atleast(cls,
lits,
bound=1,
top_id=None,
vpool=None,
encoding=EncType.seqcounter):
"""
This method can be used for creating a CNF encoding of an AtLeastK
constraint, i.e. of :math:`\sum_{i=1}^{n}{x_i}\geq k`. The method
takes 1 mandatory argument ``lits`` and 3 default arguments can be
specified: ``bound``, ``top_id``, ``vpool``, and ``encoding``.
:param lits: a list of literals in the sum.
:param bound: the value of bound :math:`k`.
:param top_id: top variable identifier used so far.
:param vpool: variable pool for counting the number of variables.
:param encoding: identifier of the encoding to use.
:type lits: iterable(int)
:type bound: int
:type top_id: integer or None
:type vpool: :class:`.IDPool`
:type encoding: integer
Parameter ``top_id`` serves to increase integer identifiers of
auxiliary variables introduced during the encoding process. This
is helpful when augmenting an existing CNF formula with the new
cardinality encoding to make sure there is no collision between
identifiers of the variables. If specified, the identifiers of the
first auxiliary variable will be ``top_id+1``.
Instead of ``top_id``, one may want to use a pool of variable
identifiers ``vpool``, which is automatically updated during the
method call. In many circumstances, this is more convenient than
using ``top_id``. Also note that parameters ``top_id`` and
``vpool`` **cannot** be specified *simultaneusly*.
The default value of ``encoding`` is :attr:`Enctype.seqcounter`.
The method *translates* the AtLeast constraint into an AtMost
constraint by *negating* the literals of ``lits``, creating a new
bound :math:`n-k` and invoking :meth:`CardEnc.atmost` with the
modified list of literals and the new bound.
:raises CardEnc.NoSuchEncodingError: if encoding does not exist.
:rtype: a :class:`.CNFPlus` object where the new \
clauses (or the new native atmost constraint) are stored.
"""
if encoding < 0 or encoding > 9:
raise (NoSuchEncodingError(encoding))
assert not top_id or not vpool, \
'Use either a top id or a pool of variables but not both.'
# we are going to return this formula
ret = CNFPlus()
# if the list of literals is empty, return empty formula
if not lits:
return ret
# obtaining the top id from the variable pool
if vpool:
top_id = vpool.top
if not top_id:
top_id = max(map(lambda x: abs(x), lits))
# Minicard's native representation is handled separately
if encoding == 9:
ret.atmosts, ret.nv = [([-l for l in lits], len(lits) - bound)
], top_id
return ret
# saving default SIGINT handler
def_sigint_handler = signal.signal(signal.SIGINT, signal.SIG_DFL)
res = pycard.encode_atleast(lits, bound, top_id, encoding)
# recovering default SIGINT handler
def_sigint_handler = signal.signal(signal.SIGINT, def_sigint_handler)
if res:
ret.clauses, ret.nv = res
# updating vpool if necessary
if vpool:
if vpool._occupied and vpool.top <= vpool._occupied[0][0] <= ret.nv:
cls._update_vids(ret, vpool)
else:
vpool.top = ret.nv - 1
vpool._next()
return ret
def atleast(cls, lits, bound=1, top_id=None, encoding=EncType.seqcounter):
"""
This method can be used for creating a CNF encoding of an AtLeastK
constraint, i.e. of :math:`\sum_{i=1}^{n}{x_i}\geq k`. The method
takes 1 mandatory argument ``lits`` and 3 default arguments can be
specified: ``bound``, ``top_id``, and ``encoding``.
:param lits: a list of literals in the sum.
:param bound: the value of bound :math:`k`.
:param top_id: top variable identifier used so far.
:param encoding: identifier of the encoding to use.
:type lits: iterable(int)
:type bound: int
:type top_id: integer or None
:type encoding: integer
Parameter ``top_id`` serves to increase integer identifiers of
auxiliary variables introduced during the encoding process. This is
helpful when augmenting an existing CNF formula with the new
cardinality encoding to make sure there is no collision between
identifiers of the variables. If specified the identifiers of the
first auxiliary variable will be ``top_id+1``.
The default value of ``encoding`` is :attr:`Enctype.seqcounter`.
The method *translates* the AtLeast constraint into an AtMost
constraint by *negating* the literals of ``lits``, creating a new
bound :math:`n-k` and invoking :meth:`CardEnc.atmost` with the
modified list of literals and the new bound.
:raises CardEnc.NoSuchEncodingError: if encoding does not exist.
:rtype: a :class:`.CNFPlus` object where the new \
clauses (or the new native atmost constraint) are stored.
"""
if encoding < 0 or encoding > 9:
raise (NoSuchEncodingError(encoding))
# we are going to return this formula
ret = CNFPlus()
# if the list of literals is empty, return empty formula
if not lits:
return ret
if not top_id:
top_id = max(map(lambda x: abs(x), lits))
# Minicard's native representation is handled separately
if encoding == 9:
ret.atmosts, ret.nv = [([-l for l in lits], len(lits) - bound)
], top_id
return ret
# saving default SIGINT handler
def_sigint_handler = signal.signal(signal.SIGINT, signal.SIG_DFL)
res = pycard.encode_atleast(lits, bound, top_id, encoding)
# recovering default SIGINT handler
def_sigint_handler = signal.signal(signal.SIGINT, def_sigint_handler)
if res:
ret.clauses, ret.nv = res
return ret