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class FiniteAutomaton: def __init__(self, start_state, dump_state=''): self.start_state = start_state self.dump_state = dump_state self.table = {self.dump_state: {}} self.unresolved_composites = [] self.resolved_composites = [] self.composite_memo = {} self.is_updated = 1 def __setitem__(self, xxx_todo_changeme, x): (state, symbol) = xxx_todo_changeme self.table.setdefault(state, {})[symbol] = x self.is_updated = 1 def add_transition(self, state, symbol, *nexts): if len(nexts) == 1: c = nexts[0] else: for n in nexts: if n not in self.table: self.table[n] = {} c = self.new_composite(nexts) self[state, symbol] = c if c not in self.table: self.table[c] = {} def get_row_items(self, state): try: x = list(self.table[state].items()) except KeyError: return () ris = [] for k, v in x: if isinstance(v, CompositeState): for vi in v: ris.append((k, vi)) else: ris.append((k, v)) return ris def make_deterministic(self): # Resolve all unresolved composite states so we become deterministic while self.unresolved_composites: composites = self.unresolved_composites self.unresolved_composites = [] for c in composites: ds = {} l = [] for a in c: for k, v in self.get_row_items(a): ds.setdefault(k, []).append(v) for k, v in list(ds.items()): for a in c: if k not in self.table[a]: v.append(self.dump_state) break for k, v in list(ds.items()): self.add_transition(c, k, *v) def get_all_input_symbols(self): syms = {} for state, trans in list(self.table.items()): for k, v in trans: syms[k] = 1 return syms def get_all_states(self): return self.table def get_all_final_states(self): return {} def get_composites(self): if self.is_updated: self.make_deterministic() return list(self.composite_memo.values()) def get_transition_classes(self): # Get classes of states that have the same outgoing transitions tc = {} tck = {} for k, v in list(self.table.items()): trans = list(v.keys()) trans.sort() trans = tuple(trans) ks = tc.get(trans) if ks is None: ks = [] tc[trans] = ks ks.append(k) tck[k] = ks return tc, tck def get_minimized_dfa(self, finals): def markall(finals, tcv, table): def psrmark(l): for pq in l: if pq in PS: l1 = PS[pq] del PS[pq] if l1: psrmark(l1) PS = {} for Q in tcv: for ip, p in enumerate(Q): for q in Q[ip+1:]: if (p in finals) == (q in finals): PS[(p, q)] = () for pq in list(PS.keys()): p, q = pq dp = table[p] dq = table[q] # Now we know they contain the same symbols dps = [] for a in dp: dpa = dp[a] dqa = dq[a] if dpa is not dqa: dpadqa = (dpa, dqa) if dpadqa in PS: dps.append(dpadqa) else: dqadpa = (dqa, dpa) if dqadpa in PS: dps.append(dqadpa) else: l = PS[pq] del PS[pq] if l is not (): psrmark(l) break else: for dpadqa in dps: l = PS[dpadqa] if l is (): l = [pq] PS[dpadqa] = l else: l.append(pq) return PS def combine(QS, PQS): eqs = {} for Q in QS: for p in Q: eqs[p] = [p] for p, q in PQS: # # Combine to equivalence classes # # Now we know that p, q are combinable # ep = eqs[p] eq = eqs[q] if eq is not ep: if len(eq) > len(ep): eq, ep = ep, eq ep.extend(eq) for q in eq: eqs[q] = ep return eqs def finalize(eqs): csbyid = {} # Composite state by identity of atomic state list csbyas = {} # Composite state by atomic state i = 0 for eq in list(eqs.values()): ideq = id(eq) if ideq not in csbyid: c = 'MS%d' % i i += 1 csbyid[ideq] = eq[0], c for s in eq: csbyas[s] = c fsa = self.__class__(csbyas[self.start_state]) fsa.final_states = {} for cs0, cst in list(csbyid.values()): fsa.table[cst] = trans = {} for a, s in list(self.table[cs0].items()): trans[a] = csbyas[s] if cs0 in finals: fsa.final_states[cst] = 1 return fsa if self.is_updated: self.make_deterministic() tctck = self._tctck = self.get_transition_classes() self.is_updated = 0 else: tctck = self._tctck tc, tck = tctck tcv = list(tc.values()) PS = markall(finals, tcv, self.table) eqs = combine(tcv, PS) fsa = finalize(eqs) return fsa def new_composite(self, args): cs = CompositeState(list(dict([(arg, 1) for arg in args]).keys())) if len(cs) == 1: return args[0] try: return self.composite_memo[cs] except KeyError: self.composite_memo[cs] = cs self.unresolved_composites.append(cs) return cs def pp(self): ks = list(self.table.keys()) ks.sort() num = dict([(s, i) for i, s in enumerate(ks)]) for s in ks: k = self.table[s] print('%d: %s' % (num[s], s)) cs = list(k.keys()) cs.sort() for c in cs: v = k[c] print(' %r -> #%d: %s' % (c, num[v], v)) class CompositeState(tuple): pass