def image(source, aut):
bdd = aut.bdd
n = len(aut.players)
ivar = '_i'
pre = bdd.false
for i, p in aut.turns.iteritems():
assert i < n, (i, n)
assert p in aut.players, (p, aut.players)
ip = (i + 1) % n
(action,) = aut.action[p]
qvars = aut.prime[p]
u = symbolic.cofactor(source, ivar, i, bdd, aut.vars)
u = bdd.apply('and', action, u)
u = bdd.quantify(u, qvars, forall=False)
u = _bdd.rename(u, bdd, aut.unprime[p])
s = '{ivar} = {ip}'.format(ivar=ivar, ip=ip)
turn = aut.add_expr(s)
u = bdd.apply('and', turn, u)
pre = bdd.apply('or', pre, u)
return pre
def image(source, aut):
bdd = aut.bdd
n = len(aut.players)
ivar = '_i'
pre = bdd.false
for i, p in aut.turns.items():
assert i < n, (i, n)
assert p in aut.players, (p, aut.players)
ip = (i + 1) % n
(action, ) = aut.action[p]
qvars = aut.prime[p]
u = symbolic.cofactor(source, ivar, i, bdd, aut.vars)
u = bdd.apply('and', action, u)
u = bdd.quantify(u, qvars, forall=False)
u = _bdd.rename(u, bdd, aut.unprime[p])
s = '{ivar} = {ip}'.format(ivar=ivar, ip=ip)
turn = aut.add_expr(s)
u = bdd.apply('and', turn, u)
pre = bdd.apply('or', pre, u)
return pre
def ue_preimage(target, team, aut):
bdd = aut.bdd
n = len(aut.players)
ivar = '_i'
pre = bdd.false
for i, p in aut.turns.iteritems():
assert i < n, (i, n)
assert p in aut.players, (p, aut.players)
ip = (i + 1) % n
u = symbolic.cofactor(target, ivar, ip, bdd, aut.vars)
u = _bdd.rename(u, bdd, aut.prime[p])
(action,) = aut.action[p]
if p not in team:
u = bdd.apply('not', u)
u = bdd.apply('and', action, u)
u = bdd.quantify(u, aut.unprime[p], forall=False)
if p not in team:
u = bdd.apply('not', u)
s = '{ivar} = {i}'.format(ivar=ivar, i=i)
turn = aut.add_expr(s)
u = bdd.apply('and', turn, u)
pre = bdd.apply('or', pre, u)
return pre
def preimage(target, aut):
"""Predecessors with interleaving repr."""
bdd = aut.bdd
n = len(aut.players)
ivar = '_i'
# needed to force extra steps outside
pre = bdd.false
for i, p in aut.turns.iteritems():
assert i < n, (i, n)
assert p in aut.players, (p, aut.players)
ip = (i + 1) % n
u = symbolic.cofactor(target, ivar, ip, bdd, aut.vars)
(action,) = aut.action[p]
u = _bdd.rename(u, bdd, aut.prime[p])
u = bdd.apply('and', action, u)
qvars = aut.unprime[p]
u = bdd.quantify(u, qvars, forall=False)
s = '{ivar} = {i}'.format(ivar=ivar, i=i)
turn = aut.add_expr(s)
u = bdd.apply('and', turn, u)
# TODO: revisit the index behavior
pre = bdd.apply('or', pre, u)
return pre
def ue_preimage(target, team, aut):
bdd = aut.bdd
n = len(aut.players)
ivar = '_i'
pre = bdd.false
for i, p in aut.turns.items():
assert i < n, (i, n)
assert p in aut.players, (p, aut.players)
ip = (i + 1) % n
u = symbolic.cofactor(target, ivar, ip, bdd, aut.vars)
u = _bdd.rename(u, bdd, aut.prime[p])
(action, ) = aut.action[p]
if p not in team:
u = bdd.apply('not', u)
u = bdd.apply('and', action, u)
u = bdd.quantify(u, aut.unprime[p], forall=False)
if p not in team:
u = bdd.apply('not', u)
s = '{ivar} = {i}'.format(ivar=ivar, i=i)
turn = aut.add_expr(s)
u = bdd.apply('and', turn, u)
pre = bdd.apply('or', pre, u)
return pre
def preimage(target, aut):
"""Predecessors with interleaving repr."""
bdd = aut.bdd
n = len(aut.players)
ivar = '_i'
# needed to force extra steps outside
pre = bdd.false
for i, p in aut.turns.items():
assert i < n, (i, n)
assert p in aut.players, (p, aut.players)
ip = (i + 1) % n
u = symbolic.cofactor(target, ivar, ip, bdd, aut.vars)
(action, ) = aut.action[p]
u = _bdd.rename(u, bdd, aut.prime[p])
u = bdd.apply('and', action, u)
qvars = aut.unprime[p]
u = bdd.quantify(u, qvars, forall=False)
s = '{ivar} = {i}'.format(ivar=ivar, i=i)
turn = aut.add_expr(s)
u = bdd.apply('and', turn, u)
# TODO: revisit the index behavior
pre = bdd.apply('or', pre, u)
return pre
