# -*- coding: utf-8 -*-
"""Finite languages and related automata manipulation
Finite languages manipulation
.. *Authors:* Rogério Reis & Nelma Moreira
.. *This is part of FAdo project* <http://fado.dcc.fc.up.pt
.. *Version:* 1.3.3
.. *Copyright*: 1999-2014 Rogério Reis & Nelma Moreira {rvr,nam}@dcc.fc.up.pt
.. This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA."""
import fa
from copy import copy
from common import *
import random
[docs]class FL(object):
"""Finite Language Class
:var Words: the elements of the language
:var Sigma: the alphabet"""
def __init__(self, wordsList=None, Sigma=None):
self.Words = set([])
if Sigma is None:
self.Sigma = set([])
else:
self.Sigma = Sigma
if wordsList is not None:
for w in wordsList:
if type(w) is Word:
self.addWord(w)
else:
self.addWord(Word(w))
def __str__(self):
l = "({"
for i in self.Words:
l += str(i) + ","
l = l[:-1] + "}, {"
for i in self.Sigma:
l += str(i)+","
l = l[:-1] + "})"
return l
def __repr__(self):
return "FL%s" % self.__str__()
def __len__(self):
return len(self.Words)
def __contains__(self, item):
return item in self.Words
[docs] def union(self, other):
"""union of FL: a | b
:param FL other: right hand operand
:rtype: FL
:raises FAdoGeneralError: if both arguments are not FL"""
return self.__or__(other)
def __or__(self, other):
if type(other) != type(self):
raise FAdoGeneralError("Incompatible objects")
new = FL()
new.Sigma = self.Sigma | other.Sigma
new.Words = self.Words | other.Words
return new
[docs] def intersection(self, other):
"""Intersection of FL: a & b
:param FL other: right hand operand
:raises FAdoGeneralError: if both arguments are not FL"""
return self.__and__(other)
def __iter__(self):
return iter(self.Words)
def __and__(self, other):
if type(other) != type(self):
raise FAdoGeneralError("Incompatible objects")
new = FL()
new.Sigma = self.Sigma | other.Sigma
new.Words = self.Words & other.Words
return new
[docs] def diff(self, other):
"""Difference of FL: a - b
:param FL other: right hand operand
:rtype: FL
:raises FAdoGeneralError: if both arguments are not FL"""
return self.__sub__(other)
def __sub__(self, other):
if type(other) != type(self):
raise FAdoGeneralError("Incompatible objects")
new = FL()
new.Sigma = self.Sigma | other.Sigma
new.Words = self.Words - other.Words
return new
[docs] def setSigma(self, Sigma, Strict=False):
"""Sets the alphabet of a FL
:param set Sigma: alphabet
:param bool Strict: behaviour
.. attention::
Unless Strict flag is set to True, alphabet can only be enlarged. The resulting alphabet is in fact the
union of the former alphabet with the new one. If flag is set to True, the alphabet is simply replaced."""
if Strict:
self.Sigma = Sigma
else:
self.Sigma = self.Sigma.union(Sigma)
[docs] def addWords(self, wList):
"""Adds a list of words to a FL
:param list wList: words to add"""
self.Words |= set(wList)
for w in wList:
if w.epsilonP():
continue
for c in w:
self.Sigma.add(c)
[docs] def addWord(self, word):
"""Adds a word to a FL
:type word: Word
:rtype: FL"""
if word in self:
return
self.Words.add(word)
if not word.epsilonP():
for c in word:
self.Sigma.add(c)
[docs] def suffixClosedP(self):
"""Tests if a language is suffix closed
:rtype: bool"""
wrds = list(copy(self.Words))
if Epsilon not in wrds:
return False
else:
wrds.remove(Epsilon)
wrds.sort(lambda x, y: len(x) - len(y))
while wrds:
w = wrds.pop()
for w1 in suffixes(w):
if w1 not in self.Words:
return False
else:
if w1 in wrds:
wrds.remove(w1)
return True
[docs] def filter(self, automata):
"""Separates a language in two other using a DFA of NFA as a filter
:param DFA|NFA automata: the automata to be used as a filter
:returns: the accepted/unaccepted pair of languages
:rtype: tuple of FL"""
a, b = (FL(), FL())
a.setSigma(self.Sigma)
b.setSigma(self.Sigma)
for w in self.Words:
if automata.evalWord(w):
a.addWords([w])
else:
b.addWords([w])
return a, b
[docs] def MADFA(self):
"""Generates the minimal acyclical DFA using specialized algorithm
.. versionadded:: 1.3.3
.. seealso:: Incremental Construction of Minimal Acyclic Finite-State Automata, J.Daciuk, S.Mihov, B.Watson and R.E.Watson
:rtype: ADFA"""
if self.Words == FL([Epsilon]).Words:
aut = ADFA()
i = aut.addState()
aut.setInitial(i)
aut.addFinal(i)
aut.setSigma(self.Sigma)
return aut
aut = ADFA()
i = aut.addState()
aut.setInitial(i)
aut.setSigma(self.Sigma)
register = set()
foo = sorted(list(self.Words))
for w in foo: # sorted(list(self.Words)):
(cPrefix, lState) = aut._common_prefix(w)
cSuffix = w[len(cPrefix):]
if aut.delta.get(lState, {}):
aut._replace_or_register(lState, register)
aut.addSuffix(lState, cSuffix)
aut._replace_or_register(i, register)
aut.Minimal = True
return aut
[docs] def trieFA(self):
"""Generates the trie automaton that recognises this language
:returns: the trie automaton
:rtype: ADFA"""
new = ADFA()
new.setSigma(copy(self.Sigma))
i = new.addState()
new.setInitial(i)
for w in self.Words:
if w.epsilonP():
new.addFinal(i)
else:
s = i
for c in w:
if c not in new.delta.get(s, []):
sn = new.addState()
new.addTransition(s, c, sn)
s = sn
else:
s = new.delta[s][c]
new.addFinal(s)
return new
[docs] def toDFA(self):
""" Generates a DFA recognizing the language
:rtype: ADFA
.. versionadded:: 1.2"""
return self.trieFA()
[docs] def toNFA(self):
"""Generates a NFA recognizing the language
:rtype: ANFA
.. versionadded:: 1.2"""
return self.toDFA().toANFA()
# noinspection PyUnboundLocalVariable
[docs] def multiLineAutomaton(self):
"""Generates the trivial linear ANFA equivalent to this language
:rtype: ANFA"""
new = ANFA()
s1 = None
new.setSigma(copy(self.Sigma))
for w in self.Words:
s = new.addState()
new.addInitial(s)
for c in w:
s1 = new.addState()
new.addTransition(s, c, s1)
s = s1
new.addFinal(s1)
return new
[docs]class DFCA(fa.DFA):
"""Deterministic Cover Automata class
.. inheritance-diagram:: DFCA"""
def __init__(self):
super(DFCA, self).__init__()
self.length = None
@property
def length(self):
"""
:return: size of the longest word
:rtype: int"""
return self.length
@length.setter
def length(self, value):
"""Setter
:param int value: size"""
self.length = value
@length.deleter
def length(self):
"""Length deleter"""
self.length = None
[docs]class AFA(object):
"""Base class for Acyclic Finite Automata
.. inheritance-diagram:: AFA
.. note::
This is just a container for some common methods. **Not to be used directly!!**"""
def __init__(self):
self.Dead = None
self.delta = dict()
self.Initial = None
self.States = []
self.Final = set()
[docs] @abstractmethod
def addState(self, _):
"""
:rtype: int"""
pass
@abstractmethod
def finalP(self, _):
pass
[docs] def setDeadState(self, sti):
"""Identifies the dead state
:param int sti: index of the dead state
.. attention::
nothing is done to ensure that the state given is legitimate
.. note::
without dead state identified, most of the methods for acyclic automata can not be applied"""
self.Dead = sti
[docs] def ensureDead(self):
"""Ensures that a state is defined as dead"""
try:
_ = self.Dead
except AttributeError:
x = self.addState(DeadName)
self.setDeadState(x)
[docs] def ordered(self):
"""Orders states names in its topological order
:returns: ordered list of state indexes
:rtype: list of int
.. note::
one could use the FA.toposort() method, but special care must be taken with the dead state for the
algorithms related with cover automata."""
def _dealS(st1):
if st1 not in torder:
torder.append(st1)
if st1 in self.delta.keys():
for k in self.delta[st1]:
for dest in forceIterable(self.delta[st1][k]):
if dest not in torder and dest != self.Dead:
queue.append(dest)
try:
dead = self.Dead
except AttributeError:
raise FAdoGeneralError("ADFA has not dead state identified")
torder, queue = [], []
_dealS(self.Initial)
while queue:
st = queue.pop()
_dealS(st)
torder.append(dead)
return torder
def _getRdelta(self):
"""
:returns: pair, map of number of sons map, of reverse conectivity
:rtype: dict"""
done = set()
deltaC, rdelta = {}, {}
notDone = set(forceIterable(self.Initial))
while notDone:
sts = uSet(notDone)
done.add(sts)
l = set()
for k in self.delta.get(sts, []):
for std in forceIterable(self.delta[sts][k]):
l.add(std)
rdelta.setdefault(std, set([])).add(sts)
if std not in done:
notDone.add(std)
deltaC[sts] = len(l)
notDone.remove(sts)
for s in forceIterable(self.Initial):
if s not in rdelta:
rdelta[s] = set()
return deltaC, rdelta
[docs] def directRank(self):
"""Compute rank function
:return: ranf map
:rtype: dict"""
r, _ = self.evalRank()
n = {}
for x in r:
for i in r[x]:
n[i] = x
return n
[docs] def evalRank(self):
"""Evaluates the rank map of a automaton
:return: pair of sets of states by rank map, reverse delta accessability map
:rtype: tuple"""
(deltaC, rdelta) = self._getRdelta()
rank, deltai = {}, {}
for s in xrange(len(self.States)):
deltai.setdefault(deltaC[s], set([])).add(s)
i = -1
notDone = copy(range(len(self.States)))
deltaC[self.Dead] = 0
deltai[1].remove(self.Dead)
deltai[0] = {self.Dead}
rdelta[self.Dead].remove(self.Dead)
while notDone:
rank[i] = deepcopy(deltai[0])
deltai[0] = set()
for s in rank[i]:
for s1 in rdelta[s]:
l = deltaC[s1]
deltaC[s1] = l - 1
deltai[l].remove(s1)
deltai.setdefault(l - 1, set()).add(s1)
notDone.remove(s)
i += 1
return rank, rdelta
[docs] def getLeaves(self):
"""The set of leaves, i.e. final states for last symbols of language words
:return: set of leaves
:rtype: set"""
# noinspection PyUnresolvedReferences
def _last(s1):
queue, done = {s1}, set()
while queue:
q = queue.pop()
done.add(q)
for k in self.delta.get(q, {}):
for s1 in forceIterable(self.delta[q][k]):
if self.finalP(s1):
return False
elif s1 not in done:
queue.add(s1)
return True
leaves = set()
for s in self.Final:
if _last(s):
leaves.add(self.States[s])
return leaves
[docs]class ADFA(fa.DFA, AFA):
"""Acyclic Deterministic Finite Automata class
.. inheritance-diagram:: ADFA
.. versionchanged:: 1.3.3
"""
def __init__(self):
fa.DFA.__init__(self)
AFA.__init__(self)
self.Minimal = False
def __repr__(self):
return 'ADFA({0:s})'.format(self.__str__())
[docs] def complete(self, dead=None):
"""Make the ADFA complete
:param int dead: a state to be identified as dead state if one was not identified yet
:rtype: ADFA
.. attention::
The object is modified in place
.. versionchanged:: 1.3.3"""
if dead is not None:
self.Dead = dead
else:
try:
if self.Dead is None:
raise AttributeError
else:
_ = self.Dead
except AttributeError:
foo = self.addState(DeadName)
self.Dead = foo
for st in range(len(self.States)):
for k in self.Sigma:
if k not in self.delta.get(st, {}).keys():
self.addTransition(st, k, self.Dead)
self.Minimal = False
return self
[docs] def dup(self):
"""Duplicate the basic structure into a new ADFA. Basically a copy.deep.
:rtype: ADFA"""
return deepcopy(self)
def __invert__(self):
""" Complement of a ADFA is a DFA
:return:DFA
"""
aut = self.forceToDFA()
return ~aut
[docs] def minimalP(self, method=None):
"""Tests if the DFA is minimal
:param method: minimization algorithm (here void)
:rtype: bool
.. versionchanged:: 1.3.3"""
if self.Minimal:
return True
foo = self.minimal()
if self.completeP():
foo.complete()
answ = len(foo) == len(self)
if answ:
self.Minimal = True
return answ
[docs] def forceToDFA(self):
""" Conversion to DFA
:rtype: DFA"""
new = fa.DFA()
new.States = deepcopy(self.States)
new.Sigma = deepcopy(self.Sigma)
new.Initial = self.Initial
new.Final = copy(self.Final)
for s in self.delta:
for c in self.delta[s]:
new.addTransition(s, c, self.delta[s][c])
return new
[docs] def forceToDFCA(self):
""" Conversion to DFCA
:rtype: DFA"""
new = fa.DFA()
new.States = deepcopy(self.States)
new.Sigma = deepcopy(self.Sigma)
new.Initial = self.Initial
new.Final = copy(self.Final)
for s in self.delta:
for c in self.delta[s]:
new.addTransition(s, c, self.delta[s][c])
return new
[docs] def wordGenerator(self):
"""Creates a random word generator
:return: the random word generator
:rtype: RndWGen
.. versionadded:: 1.2"""
return RndWGen(self)
[docs] def possibleToReverse(self):
"""Tests if language is reversible
.. versionadded:: 1.3.3"""
return True
[docs] def minimal(self):
"""Finds the minimal equivalent ADFA
.. seealso:: [TCS 92 pp 181-189] Minimisation of acyclic deterministic automata in linear time, Dominique Revuz
.. versionchanged:: 1.3.3
:returns: the minimal equivalent ADFA
:rtype: ADFA"""
def _getListDelta(ss):
"""returns [([sons,final?],s) for s in ss].sort"""
l = []
for s in ss:
dl = [new.delta[s][k] for k in new.Sigma]
dl.append(s in new.Final)
l.append((dl, s))
l.sort()
return l
def _collapse(r1, r2):
"""redirects all transitions going to r2 to r1 and adds r2 to toBeDeleted"""
for s in rdelta[r2]:
for k in new.delta[s]:
if new.delta[s][k] == r2:
new.delta[s][k] = r1
toBeDeleted.append(r2)
if len(self.States) == 1:
return self
new = deepcopy(self)
new.trim()
new.complete()
if new.Dead is None:
deadName = None
else:
deadName = new.States[new.Dead]
rank, rdelta = new.evalRank()
toBeDeleted = []
maxr = len(rank) - 2
for r in xrange(maxr + 1):
ls = _getListDelta(rank[r])
(d0, s0) = ls[0]
j = 1
while j < len(ls):
(d1, s1) = ls[j]
if d0 == d1:
_collapse(s0, s1)
else:
(d0, s0) = (d1, s1)
j += 1
new.deleteStates(toBeDeleted)
if deadName is not None:
new.Dead = new.stateIndex(deadName)
new.Minimal = True
return new
[docs] def minReversible(self):
"""Returns the minimal reversible equivalent automaton
:rtype: ADFA"""
new = self.dup()
new.evalRank()
[docs] def statePairEquiv(self, s1, s2):
"""Tests if two states of a ADFA are equivalent
:param int s1: state1
:param int s2: state2
:rtype: bool
.. versionadded:: 1.3.3"""
if not self.same_nullability(s1, s2):
return False
else:
return self.delta.get(s1, {}) == self.delta.get(s2, {})
[docs] def addSuffix(self, st, w):
"""Adds a suffix starting in st
:param int st: state
:param Word w: suffix
.. versionadded:: 1.3.3
.. attention:: in place transformation"""
s1 = st
for c in w:
s2 = self.addState()
self.addTransition(s1, c, s2)
s1 = s2
self.addFinal(s1)
def _last_child(self, s):
"""to be used by xxx of FL.MADFA
:param int s: state index
:returns: pair state index / symbol
.. versionadded:: 1.3.3"""
for c in sorted(list(self.Sigma)).__reversed__():
if c in self.delta.get(s, {}):
return self.delta[s][c], c
raise FAdoGeneralError("Something unexpected in _last_child({:d})".format(s))
def _replace_or_register(self, s, r):
"""to be used by xxx of FL.MADFA
:param int s: state
:param Set r: register (inherited from context)
.. versionadded:: 1.3.3"""
(child, c) = self._last_child(s)
if self.delta.get(child, {}):
self._replace_or_register(child, r)
for q in r:
if self.statePairEquiv(q, child):
self.delta[s][c] = q
self.deleteState(child)
return
r.add(child)
def _common_prefix(self, wrd):
"""The longest prefix of w that can be read in the ADFA and the correspondent state
:param Word wrd: word"""
pref = Word()
q = self.Initial
for s in wrd:
if s in self.delta.get(q, {}):
pref.append(s)
q = self.delta[q][s]
else:
break
return pref, q
def _addWordToMinimal(self, w):
"""Incremental minimization algorithm
:param Word w: word
.. attention:: in place transformation
.. versionadded:: 1.3.3
.. seealso:: Incremental Construction of Minimal Acyclic Finite-State Automata, J.Daciuk, S.Mihov,
B.Watson and R.E.Watson"""
def _transverseNonConfluence(wrd):
inCount = dict()
for s in range(len(self.States)):
for c in self.delta.get(s, {}):
for s1 in self.delta[s][c]:
inCount[s1] = inCount.get(s1, 0) + 1
q1 = self.Initial
visited1 = [q1]
for ii, sym in enumerate(wrd):
if sym not in self.delta.get(q1, {}) or inCount[self.delta[q1][sym]] > 1:
# here there was a reference to s self.delta.get(s, {}) that must be wrong!
return q1, ii
q1 = self.delta[q1][sym]
visited1.append(q1)
def _cloneConfluence(st, wrd, ind):
q1 = st
for ii, sym in enumerate(wrd[ind:]):
if sym not in self.delta.get(q1, {}):
return q1, ii + ind
qn = self.delta[q1][sym]
sn = self.addState()
for c1 in self.delta.get(qn, {}):
self.delta.setdefault(sn, {})[c1] = self.delta[qn][c1]
if self.finalP(qn):
self.addFinal(sn)
self.addTransition(q1, sym, sn)
q1 = sn
visited.append(q1)
def _replOrReg(st, wrd):
if len(w) != 0:
self.addTransition(q, wrd[0], _replOrReg(self.delta[st][wrd[0]], wrd[1:]))
else:
for c in register:
if self.statePairEquiv(c, q):
self.deleteState(q)
return c
register.add(q)
def _addSuffix(st, wrd):
s = st
for c in wrd:
sn = self.addState()
self.addTransition(s, c, sn)
s = sn
self.addFinal(s)
register = set()
visited = []
q, i = _transverseNonConfluence(w)
f = q
register.remove(q)
j = i
q, i = _cloneConfluence(q, w, i)
_addSuffix(q, w[i:])
if j < len(w):
self.delta[f][w[j]] = _replOrReg(self.delta[f][w[j]], w[j+1:])
[docs] def dissMin(self, witnesses=None):
"""Evaluates the minimal dissimilarity language
:param dict witnesses: optional witness dictionay
:rtype: FL
.. versionadded:: 1.2.1"""
new = self.minimal()
sz = len(new.States)
todo = [(i, j) for i in range(sz) for j in range(i)]
mD = FL(Sigma=new.Sigma)
lvl = new.level()
rnk = new.directRank()
l = max([rnk[x] for x in rnk])
Li = []
for (i, j) in todo:
if self.finalP(i) ^ self.finalP(j):
if witnesses is not None:
witnesses[(i, j)] = Word(Epsilon)
Li.append((i, j))
mD.addWord(Word(Epsilon))
delFromList(todo, Li)
words = self.words()
for w in words:
if len(w) >= l or not todo:
break
Li = []
for (i, j) in todo:
if (lvl[i] + len(w) > l) or (lvl[j] + len(w) > l):
Li.append((i, j))
elif self.evalWordP(w, i) ^ self.evalWordP(w, j):
mD.addWord(w)
if witnesses is not None:
witnesses[(i, j)] = w
Li.append((i, j))
delFromList(todo, Li)
return mD
[docs] def diss(self):
""" Evaluates the dissimilarity language
:rtype: FL
.. versionadded:: 1.2.1"""
new = self.minimal()
n = len(new.States)
mD = FL(Sigma=new.Sigma)
lvl = new.level()
rnk = new.directRank()
l = max([rnk[x] for x in rnk])
if len(new.Final) != n:
mD.addWord(Word(Epsilon))
words = self.words()
for w in words:
lw = len(w)
if lw >= l:
break
skip = False
for i in range(n):
if skip:
break
for j in range(i):
if (lvl[i] + lw <= l) and (lvl[j] + lw <= l) and (self.evalWordP(w, i) ^ self.evalWordP(w, j)):
mD.addWord(w)
skip = True
break
return mD
[docs] def level(self):
"""Computes the level for each state
:returns: levels of states
:rtype: dict
.. versionadded:: 0.9.8"""
lvl = {}
done, alvl = set(), [self.Initial]
l = 0
while alvl:
nlvl = set()
for i in alvl:
lvl[i] = l
done.add(i)
for c in self.delta[i]:
j = self.delta[i][c]
if j not in done and j not in alvl:
nlvl.add(j)
l += 1
alvl = copy(nlvl)
return lvl
def _gap(self, l, lvl):
"""Computes the gap value for each pair of states.
The automata is supposed to have its states named numerically in such way that the initial is zero
:param int l: length of the longest word
:param dict lvl: level of each state
:returns: gap function
:rtype: dict"""
def _range(r, s):
return l - max(lvl[r], lvl[s])
gp = {}
n = len(self.States) - 1
for i in range(n):
gp[(self.stateIndex(i), self.stateIndex(n))] = l
if lvl[self.stateIndex(n)] <= l:
for i in self.Final:
gp[(i, self.stateIndex(n))] = 0
for i in range(n):
for j in range(i + 1, n):
if not self.same_nullability(self.stateIndex(i), self.stateIndex(j)):
gp[(self.stateIndex(i), self.stateIndex(j))] = 0
else:
gp[(self.stateIndex(i), self.stateIndex(j))] = l
for i in range(n - 2, -1, -1):
for j in range(n, i, -1):
for c in self.Sigma:
i1, j1 = self.delta[self.stateIndex(i)][c], self.delta[self.stateIndex(j)][c]
if i1 != j1:
if int(self.States[i1]) < int(self.States[j1]):
g = gp[(i1, j1)]
else:
g = gp[(j1, i1)]
if g + 1 <= _range(self.stateIndex(i), self.stateIndex(j)):
gp[(self.stateIndex(i), self.stateIndex(j))] = min(gp[(self.stateIndex(i),
self.stateIndex(j))], g + 1)
return gp
[docs] def minDFCA(self):
"""Generates a minimal deterministic cover automata from a DFA
:rtype: DFCA
.. versionadded:: 0.9.8
.. seealso::
Cezar Campeanu, Andrei Päun, and Sheng Yu, An efficient algorithm for constructing minimal cover
automata for finite languages, IJFCS"""
new = self.dup().minimal()
if not self.completeP():
new.complete()
rank = new.directRank()
irank = dict((v, [k for (k, xx) in filter(lambda (key, value): value == v, rank.items())])
for v in set(rank.values()))
l = rank[new.Initial]
lvl = new.level()
foo = [x for x in irank]
foo.sort(reverse=True)
lnames = [None for _ in new.States]
newname = 0
for i in foo:
for j in irank[i]:
lnames[j] = newname
newname += 1
new.States = lnames
g = new._gap(l, lvl)
P = [False for _ in new.States]
toMerge = []
for i in range(len(new.States) - 1):
if not P[i]:
for j in range(i + 1, len(new.States)):
if not P[j] and g[(new.stateIndex(i), new.stateIndex(j))] == l:
toMerge.append((i, j))
P[j] = True
for (a, b) in toMerge:
new.mergeStates(new.stateIndex(b), new.stateIndex(a))
new.trim()
new = new.forceToDFCA()
new.length = l
return new
[docs] def trim(self):
"""Remove states that do not lead to a final state, or, inclusively, that can't be reached from the initial
state. Only useful states remain.
.. attention:: in place transformation"""
fa.OFA.trim(self)
try:
del self.Dead
except AttributeError:
pass
return self
[docs] def toANFA(self):
"""Converts the ADFA in a equivalent ANFA
:rtype: ANFA"""
new = ANFA()
new.setSigma(copy(self.Sigma))
new.States = copy(self.States)
for s in xrange(len(self.States)):
for k in self.delta.get(s, {}):
new.addTransition(s, k, self.delta[s][k])
new.addInitial(self.Initial)
for s in self.Final:
new.addFinal(s)
return new
[docs] def toNFA(self):
"""Converts the ADFA in a equivalent NFA
:rtype: ANFA
.. versionadded:: 1.2"""
return self.toANFA()
[docs]class RndWGen(object):
"""Word random generator class
.. versionadded:: 1.2"""
def __init__(self, aut):
"""
:param aut: automata recognizing the language
:type aut: ADFA """
self.Sigma = list(aut.Sigma)
self.table = dict()
self.aut = aut.minimal()
rank, _ = self.aut.evalRank()
self.aut._compute_delta_inv()
deltai = self.aut.delta_inv
mrank = max(rank)
for i in range(0, mrank + 1):
for s in rank[i]:
self.table.setdefault(s, {})
if self.aut.finalP(s):
final = 1
else:
final = 0
self.table[s][None] = sum([self.table[s].get(c, 0) for c in self.Sigma])
for c in self.Sigma:
rs = deltai[s].get(c, [])
for r in rs:
self.table.setdefault(r, {})
self.table[r][c] = self.table[s][None] + final
@staticmethod
def _rndChoose(l):
sm = sum(l)
r = random.randint(1, sm)
for i, j in enumerate(l):
if r <= j:
return i
else:
r -= j
[docs] def next(self):
"""Next word
:return: a new random word"""
word = Word()
s = self.aut.Initial
while True:
if self.aut.finalP(s) and random.randint(1, self.table[s][None] + 1) == 1:
return word
i = self._rndChoose([self.table[s].get(c, 0) for c in self.Sigma])
word.append(self.Sigma[i])
s = self.aut.delta[s][self.Sigma[i]]
# noinspection PyUnresolvedReferences
[docs]class ANFA(fa.NFA, AFA):
"""Acyclic Nondeterministic Finite Automata class
.. inheritance-diagram:: ANFA"""
[docs] def moveFinal(self, st, stf):
"""Unsets a set as final transfering transition to another final
:param int st: the state to be 'moved'
:param int stf: the destination final state
.. note::
stf must be a 'last' final state, i.e., must have no out transitions to anywhere but to a possible dead
state
.. attention:: the object is modified in place"""
(rdelta, _) = self._getRdelta()
for s in rdelta[st]:
l = []
for k in self.delta[s]:
if st in self.delta[s][k]:
l.append(k)
for k in l:
self.addTransition(s, k, stf)
self.delFinal(s)
[docs] def mergeStates(self, s1, s2):
"""Merge state s2 into state s1
:param int s1: state
:param int s2: state
.. note::
no attempt is made to check if the merging preserves the language of teh automaton
.. attention:: the object is modified in place"""
(_, rdelta) = self._getRdelta()
for s in rdelta[s2]:
l = []
for k in self.delta[s]:
if s2 in self.delta[s][k]:
l.append(k)
for k in l:
self.delta[s][k].remove(s2)
self.addTransition(s, k, s1)
for k in self.delta.get(s2, {}):
for ss in self.delta[s2][k]:
self.delta.setdefault(s1, {}).setdefault(k, set()).add(ss)
self.deleteState(s2)
[docs] def mergeLeaves(self):
"""Merge leaves
.. attention:: object is modified in place"""
l = self.getLeaves()
if len(l):
s0n = l.pop()
while l:
s0 = self.stateIndex(s0n)
s = self.stateIndex(l.pop())
self.mergeStates(s0, s)
[docs] def mergeInitial(self):
"""Merge initial states
.. attention:: object is modified in place"""
l = copy(self.Initial)
s0 = self.stateIndex(l.pop())
while l:
s = self.stateIndex(l.pop())
self.mergeStates(s0, s)
[docs]def sigmaInitialSegment(Sigma, l, exact=False):
"""Generates the ADFA recognizing Sigma^i for i<=l
:param set Sigma: the alphabet
:param int l: length
:param bool exact: only the words with exactly that length?
:returns: the automaton
:rtype: ADFA"""
new = ADFA()
new.setSigma(Sigma)
s = new.addState()
if not exact:
new.addFinal(s)
new.setInitial(s)
for i in range(l):
s1 = new.addState()
if not exact or i == l - 1:
new.addFinal(s1)
for k in Sigma:
new.addTransition(s, k, s1)
s = s1
return new
# noinspection PyUnboundLocalVariable
[docs]def genRndTrieBalanced(maxL, Sigma, safe=True):
"""Generates a random trie automaton for a binary language of balanced words of a given leght for max word
:param int maxL: length of the max word
:param set Sigma: alphabet to be used
:param bool safe: should a word of size maxl be present in every language?
:return: the generated trie automaton
:rtype: ADFA"""
def _genEnsurance(m, alphabet):
l = len(alphabet)
fair = m / l
if m % l == 0:
odd = 0
else:
odd = 1
pool = copy(alphabet)
c = {}
sl = []
while len(sl) < m:
s1 = random.choice(pool)
c[s1] = c.get(s1, 0) + 1
if c[s1] == fair + odd:
pool.remove(s1)
sl.append(s1)
return sl
def _legal(cont):
l = [cont[k1] for k1 in cont]
return max(l) - min(l) <= 1
def _descend(s1, ens, safe1, m, cont):
sons = 0
if not safe1:
if _legal(cont):
final = random.randint(0, 1)
else:
final = 0
# noinspection PyUnboundLocalVariable
if safe1:
trie.addFinal(s1)
final = 1
elif final == 1:
trie.addFinal(s1)
if m != 0:
if safe1:
ks = ens.pop()
else:
ks = None
for k1 in trie.Sigma:
ss = trie.addState()
trie.addTransition(s1, k1, ss)
cont[k1] = cont.get(k1, 0) + 1
if _descend(ss, ens, k1 == ks, m - 1, cont):
sons += 1
cont[k1] -= 1
if sons == 0 and final == 0:
trie.deleteState(s1)
return False
else:
return True
if safe:
ensurance = _genEnsurance(maxL, Sigma)
else:
ensurance = None
trie = ADFA()
trie.setSigma(Sigma)
s = trie.addState()
trie.setInitial(s)
contab = {}
for k in Sigma:
contab[k] = 0
_descend(s, ensurance, safe, maxL, contab)
if random.randint(0, 1) == 1:
trie.delFinal(s)
return trie
# noinspection PyUnboundLocalVariable
[docs]def genRndTrieUnbalanced(maxL, Sigma, ratio, safe=True):
"""Generates a random trie automaton for a binary language of balanced words of a given length for max word
:param int maxL: length of the max word
:param set Sigma: alphabet to be used
:param int ratio: the ratio of the unbalance
:param bool safe: should a word of size maxl be present in every language?
:return: the generated trie automaton
:rtype: ADFA"""
def _genEnsurance(m, alphabet):
chief = uSet(alphabet)
fair = m / (ratio + 1)
pool = list(copy(alphabet))
c = {}
sl = []
while len(sl) < m:
s1 = random.choice(pool)
c[s1] = c.get(s1, 0) + 1
if len(sl) - c.get(chief, 0) == fair:
pool = [chief]
sl.append(s1)
return sl
def _legal(cont):
l = [cont[k1] for k1 in cont]
return (ratio + 1) * cont[uSet(Sigma)] >= sum(l)
# noinspection PyUnboundLocalVariable
def _descend(s1, ens, safe1, m, cont):
sons = 0
if not safe1:
if _legal(cont):
final = random.randint(0, 1)
else:
final = 0
if safe1:
trie.addFinal(s1)
final = 1
elif final == 1:
trie.addFinal(s1)
if m:
if safe1:
ks = ens.pop()
else:
ks = None
for k1 in trie.Sigma:
ss = trie.addState()
trie.addTransition(s1, k1, ss)
cont[k1] = cont.get(k1, 0) + 1
if _descend(ss, ens, k1 == ks, m - 1, cont):
sons += 1
cont[k1] -= 1
if sons == 0 and final == 0:
trie.deleteState(s1)
return False
else:
return True
if safe:
ensurance = _genEnsurance(maxL, Sigma)
else:
ensurance = None
trie = ADFA()
trie.setSigma(Sigma)
s = trie.addState()
trie.setInitial(s)
contab = {}
for k in Sigma:
contab[k] = 0
_descend(s, ensurance, safe, maxL, contab)
if random.randint(0, 1) == 1:
trie.delFinal(s)
return trie
# noinspection PyUnboundLocalVariable
[docs]def genRandomTrie(maxL, Sigma, safe=True):
"""Generates a random trie automaton for a finite language with a given length for max word
:param int maxL: length of the max word
:param set Sigma: alphabet to be used
:param bool safe: should a word of size maxl be present in every language?
:return: the generated trie automaton
:rtype: ADFA"""
def _genEnsurance(m, alphabet):
l = len(alphabet)
sl = list(alphabet)
return [sl[random.randint(0, l - 1)] for _ in xrange(m)]
# noinspection PyUnboundLocalVariable
def _descend(s1, ens, safe1, m):
sons = 0
final = None
if not safe1:
final = random.randint(0, 1)
if safe1:
trie.addFinal(s1)
final = 1
elif final == 1:
trie.addFinal(s1)
if m:
if safe1:
ks = ens.pop()
else:
ks = None
for k in trie.Sigma:
ss = trie.addState()
trie.addTransition(s1, k, ss)
if _descend(ss, ens, k == ks, m - 1):
sons += 1
if sons == 0 and final == 0:
trie.deleteState(s1)
return False
else:
return True
if safe:
ensurance = _genEnsurance(maxL, Sigma)
else:
ensurance = None
trie = ADFA()
trie.setSigma(Sigma)
s = trie.addState()
trie.setInitial(s)
_descend(s, ensurance, safe, maxL)
if random.randint(0, 1) == 1:
trie.delFinal(s)
return trie
# noinspection PyUnboundLocalVariable
[docs]def genRndTriePrefix(maxL, Sigma, ClosedP=False, safe=True):
"""Generates a random trie automaton for a finite (either prefix free or prefix closed) language with a given
length for max word
:param int maxL: length of the max word
:param set Sigma: alphabet to be used
:param bool ClosedP: should it be a prefix closed language?
:param bool safe: should a word of size maxl be present in every language?
:return: the generated trie automaton
:rtype: ADFA"""
def _genEnsurance(m, alphabet):
l = len(alphabet)
sl = list(alphabet)
return [sl[random.randint(0, l - 1)] for _ in xrange(m)]
def _descend(s1, ens, saf, m):
sons = ClosedP
if m is 0:
final = random.randint(0, 1)
if saf or final == 1:
trie.addFinal(s1)
return True
else:
return False
else:
if saf is True:
ks = ens.pop()
else:
ks = None
for k in trie.Sigma:
ss = trie.addState()
trie.addTransition(s1, k, ss)
r = _descend(ss, ens, k == ks, m - 1)
if not ClosedP:
sons |= r
else:
sons &= 1
if not ClosedP:
if not sons:
final = random.randint(0, 1)
if final == 1:
trie.addFinal(s1)
return True
else:
return False
else:
return True
else:
if not sons:
final = random.randint(0, 1)
if final == 1:
trie.addFinal(s1)
return True
else:
return False
else:
trie.addFinal(s1)
return True
ensurance = None
if safe:
ensurance = _genEnsurance(maxL, Sigma)
trie = ADFA()
trie.setSigma(Sigma)
s = trie.addState()
trie.setInitial(s)
_descend(s, ensurance, safe, maxL)
return trie
[docs]def DFAtoADFA(aut):
"""Transforms an acyclic DFA into a ADFA
:param DFA aut: the automaton to be transformed
:raises notAcyclic: if the DFA is not acyclic
:returns: the converted automaton
:rtype: ADFA"""
new = deepcopy(aut)
new.trim()
if not new.acyclicP(True):
raise notAcyclic()
afa = ADFA()
afa.States = copy(new.States)
afa.Sigma = copy(new.Sigma)
afa.Initial = new.Initial
afa.delta = copy(new.delta)
afa.Final = copy(new.Final)
afa.complete()
return afa
[docs]def stringToADFA(s):
"""Convert a canonical string representation of a ADFA to a ADFA
:param list s: the string in its canonical order
:returns: the ADFA
:rtype: ADFA
.. seealso::
Marco Almeida, Nelma Moreira, and Rogério Reis. Exact generation of minimal acyclic deterministic finite
automata. International Journal of Foundations of Computer Science, 19(4):751-765, August 2008.
"""
k = len(s[0]) - 1
new = ADFA()
new.setSigma([str(c) for c in range(k)])
for st, sts in enumerate(s):
new.addState(str(st))
for c, s1 in enumerate(sts[:-1]):
new.addTransition(st, str(c), s1)
if sts[-1]:
new.addFinal(st)
new.setInitial(len(s) - 1)
return new