mirror of
https://git.cs.ou.nl/joshua.moerman/mealy-decompose.git
synced 2025-04-29 17:57:44 +02:00
335 lines
9.9 KiB
Python
335 lines
9.9 KiB
Python
# Copyright 2024-2025 Joshua Moerman, Open Universiteit. All rights reserved
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# SPDX-License-Identifier: EUPL-1.2
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from pysat.solvers import Solver
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from pysat.card import CardEnc
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from pysat.formula import IDPool
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from pysat.formula import CNF
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import math
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import argparse
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parser = argparse.ArgumentParser(description='Decomposes a FSM into smaller components by remapping its outputs. Uses a SAT solver.')
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parser.add_argument('-c', '--components', type=int, default=2, help='number of components')
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parser.add_argument('-n', '--total-size', type=int, help='total number of states of the components')
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parser.add_argument('--add-state-trans', default=False, action='store_true', help='adds state transitivity constraints')
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parser.add_argument('-v', '--verbose', default=False, action='store_true', help='prints more info')
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parser.add_argument('filename', help='path to .dot file')
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args = parser.parse_args()
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# als de de total_size te laag is => UNSAT => duurt lang
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c = args.components
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total_size = args.total_size
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assert c >= 1 # c = 1 is zinloos, maar zou moeten werken
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assert total_size >= c # elk component heeft tenminste 1 state
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###################################
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# .dot file parser (heuristic)
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class FSM:
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def __init__(self, initial_state, states, inputs, outputs, transition_map, output_map):
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self.initial_state = initial_state
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self.states = states
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self.inputs = inputs
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self.outputs = outputs
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self.transition_map = transition_map
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self.output_map = output_map
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def __str__(self):
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return f'FSM({self.initial_state}, {self.states}, {self.inputs}, {self.outputs}, {self.transition_map}, {self.output_map})'
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def transition(self, s, a):
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return self.transition_map[(s, a)]
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def output(self, s, a):
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return self.output_map[(s, a)]
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def parse_dot_file(lines):
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def parse_transition(line):
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(l, _, r) = line.partition('->')
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s = l.strip()
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(l, _, r) = r.partition('[label="')
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t = l.strip()
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(l, _, _) = r.partition('"]')
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(i, _, o) = l.partition('/')
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return (s, i, o, t)
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initial_state = None
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states, inputs, outputs = set(), set(), set()
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transition_map, output_map = {}, {}
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for line in lines:
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(s, i, o, t) = parse_transition(line)
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if s and i and o and t:
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states.add(s)
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inputs.add(i)
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outputs.add(o)
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states.add(t)
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transition_map[(s, i)] = t
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output_map[(s, i)] = o
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if not initial_state:
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initial_state = s
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assert initial_state in states
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assert len(transition_map) == len(states) * len(inputs)
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assert len(output_map) == len(states) * len(inputs)
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return FSM(initial_state, states, inputs, outputs, transition_map, output_map)
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with open(args.filename) as file:
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machine = parse_dot_file(file)
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if args.verbose:
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print(machine)
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print(f'Initial size: {len(machine.states)}')
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###################################
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# Utility functions
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def print_table(cell, rs, cs):
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first_col_size = max([len(str(r)) for r in rs])
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col_size = 1 + max([len(str(c)) for c in cs] + [len(cell(r, c)) for c in cs for r in rs])
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print(''.rjust(first_col_size), end='')
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for c in cs:
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print(str(c).rjust(col_size), end='')
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print('')
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for r in rs:
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print(str(r).rjust(first_col_size), end='')
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for c in cs:
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print(cell(r, c).rjust(col_size), end='')
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print('')
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class Progress:
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def __init__(self, name, guess):
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self.reset(name, guess, show=False)
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def reset(self, name, guess, show=True):
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self.name = name
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self.guess = math.ceil(guess)
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self.count = 0
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self.percentage = None
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if show:
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print(name)
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def add(self, n=1):
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self.count += n
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percentage = math.floor(100 * self.count / self.guess)
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if percentage != self.percentage:
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self.percentage = percentage
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print(f'{self.percentage}%', end='', flush=True)
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print('\r', end='')
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progress = Progress('', 1)
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########################
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# Encodering naar logica
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print('Start encoding')
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os = list(machine.outputs) # outputs
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rids = [i for i in range(c)] # components
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vpool = IDPool()
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cnf = CNF()
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# Een hulp variabele voor False en True, maakt de andere variabelen eenvoudiger
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def var_const(b):
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return vpool.id(('const', b))
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cnf.append([var_const(True)])
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cnf.append([-var_const(False)])
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# Voor elke relatie en elke twee elementen o1 en o2, is er een variabele die
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# aangeeft of o1 en o2 gerelateerd zijn. Er is 1 variabele voor xRy en yRx, dus
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# symmetrie is al ingebouwd. Reflexiviteit is ook ingebouwd.
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def var_rel(rid, o1, o2):
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if o1 == o2:
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return var_const(True)
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[so1, so2] = sorted([o1, o2])
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return vpool.id(('rel', rid, so1, so2))
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# De relatie op outputs geeft een relaties op states. Deze relatie moet ook een
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# bisimulatie zijn.
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def var_state_rel(rid, s1, s2):
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if s1 == s2:
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return var_const(True)
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[ss1, ss2] = sorted([s1, s2])
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return vpool.id(('state_rel', rid, ss1, ss2))
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# Voor elke relatie, en elke equivalentie-klasse, kiezen we precies 1 state
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# als representant. Deze variabele geeft aan welk element.
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def var_state_rep(rid, s):
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return vpool.id(('state_rep', rid, s))
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# Contraints zodat de relatie een equivalentie relatie is. We hoeven alleen
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# maar transitiviteit te encoderen, want refl en symm zijn ingebouwd in de var.
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progress.reset('transitivity (o)', guess=len(rids) * len(os) ** 3)
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for rid in rids:
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for xo in os:
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for yo in os:
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for zo in os:
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# als xo R yo en yo R zo dan xo R zo
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cnf.append([-var_rel(rid, xo, yo), -var_rel(rid, yo, zo), var_rel(rid, xo, zo)])
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progress.add()
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if args.add_state_trans:
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progress.reset('transitivity (s)', guess=len(rids) * len(machine.states) ** 3)
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for rid in rids:
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for sx in machine.states:
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for sy in machine.states:
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for sz in machine.states:
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# als sx R sy en sy R sz dan sx R sz
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cnf.append([-var_state_rel(rid, sx, sy), -var_state_rel(rid, sy, sz), var_state_rel(rid, sx, sz)])
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progress.add()
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# Constraint zodat de relaties samen alle elementen kunnen onderscheiden.
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# (Aka: the bijbehorende quotienten zijn joint-injective.)
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progress.reset('injectivity', guess=len(os) * (len(os) - 1) / 2)
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for xi, xo in enumerate(os):
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for yo in os[xi + 1 :]:
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# Tenminste een rid moet een verschil maken
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cnf.append([-var_rel(rid, xo, yo) for rid in rids])
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progress.add()
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# sx ~ sy => for each input: (1) outputs equivalent AND (2) successors related
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# Momenteel hebben we niet de inverse implicatie, is misschien ook niet nodig?
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progress.reset('bisimulation modulo rel', guess=len(rids) * len(machine.states) * len(machine.states) * len(machine.inputs))
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for rid in rids:
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for sx in machine.states:
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for sy in machine.states:
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for i in machine.inputs:
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# sx ~ sy => output(sx, i) ~ output(sy, i)
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ox = machine.output(sx, i)
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oy = machine.output(sy, i)
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cnf.append([-var_state_rel(rid, sx, sy), var_rel(rid, ox, oy)])
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# sx ~ sy => delta(sx, i) ~ delta(sy, i)
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tx = machine.transition(sx, i)
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ty = machine.transition(sy, i)
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cnf.append([-var_state_rel(rid, sx, sy), var_state_rel(rid, tx, ty)])
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progress.add()
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# De constraints die zorgen dat representanten ook echt representanten zijn.
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states = list(machine.states)
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progress.reset('representatives', guess=len(rids) * len(states))
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for rid in rids:
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for ix, sx in enumerate(states):
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# Belangrijkste: een element is een representant, of equivalent met een
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# eerder element. We forceren hiermee dat de solver representanten moet
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# kiezen (voor aan de lijst).
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cnf.append([var_state_rep(rid, sx)] + [var_state_rel(rid, sx, sy) for sy in states[:ix]])
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for sy in states[:ix]:
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# rx en ry kunnen niet beide een representant zijn, tenzij ze
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# niet gerelateerd zijn.
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cnf.append([-var_state_rep(rid, sx), -var_state_rep(rid, sy), -var_state_rel(rid, sx, sy)])
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progress.add()
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# Tot slot willen we weinig representanten. Dit doen we met een "atmost"
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# formule. Idealiter zoeken we naar de total_size, maar die staat nu vast.
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print('size constraints')
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cnf_optim = CardEnc.atmost([var_state_rep(rid, sx) for rid in rids for sx in machine.states], total_size, vpool=vpool)
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cnf.extend(cnf_optim)
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def print_eqrel(rel, xs):
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print_table(lambda r, c: 'Y' if rel(r, c) else '·', xs, xs)
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##################################
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# Probleem oplossen met solver :-)
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print('Start solving')
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print('- copying formula')
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with Solver(bootstrap_with=cnf) as solver:
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print('- actual solve')
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sat = solver.solve()
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print('===============')
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if not sat:
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print('unsat :-(')
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exit()
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print('sat :-)')
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# Even omzetten in een makkelijkere data structuur
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print('- get model')
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m = solver.get_model()
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model = {}
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for l in m:
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model[abs(l)] = l > 0
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if args.verbose:
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for rid in rids:
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print(f'Relation {rid}:')
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print_eqrel(lambda x, y: model[var_rel(rid, x, y)], os)
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for rid in rids:
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print(f'State relation {rid}:')
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print_eqrel(lambda x, y: model[var_state_rel(rid, x, y)], machine.states)
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# print equivalence classes
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count = 0
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for rid in rids:
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if args.verbose:
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print(f'component {rid}')
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# Eerst verzamelen we de representanten
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for s in machine.states:
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if model[var_state_rep(rid, s)]:
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count += 1
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if args.verbose:
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print(f'- representative state {s}')
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# count moet gelijk zijn aan cost (of kleiner)
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print(f'Reduced size = {count}')
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projections = {}
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for rid in rids:
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local_outputs = machine.outputs.copy()
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projections[rid] = {}
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count = 0
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while local_outputs:
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repr = local_outputs.pop()
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if repr in projections[rid]:
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continue
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projections[rid][repr] = f'cls_{rid}_{count}'
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others = False
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for o in local_outputs:
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if model[var_rel(rid, o, repr)]:
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others = True
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projections[rid][o] = f'cls_{rid}_{count}'
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if not others:
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projections[rid][repr] = f'{repr}'
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count += 1
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print('===============')
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print('Output mapping:')
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print_table(lambda o, rid: projections[rid][o], machine.outputs, rids)
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