Additional optimisation of components

other/decompose_fsm_optimise.py

@@ -11,28 +11,36 @@ import argparse
 # Stap 2: python3 decompose_fsm.py -h
 
 keep_log = True
+record_file = './results/log.txt' if keep_log else None
+
+filename = None
 
 
 def main():
-  record_file = './results/log.txt' if keep_log else None
-
   parser = argparse.ArgumentParser(description='Decomposes a FSM into smaller components by remapping its outputs. Uses a SAT solver.')
   parser.add_argument('-c', '--components', type=int, default=2, help='number of components')
   parser.add_argument('-w', '--weak', default=False, action='store_true', help='look for weak decomposition')
   parser.add_argument('--add-state-trans', default=False, action='store_true', help='adds state transitivity constraints')
-  parser.add_argument('-v', '--verbose', default=False, action='store_true', help='prints more info')
   parser.add_argument('-t', '--timeout', type=int, default=None, help='timeout (in seconds)')
   parser.add_argument('filename', help='path to .dot file')
   args = parser.parse_args()
 
+  global filename
+  filename = args.filename
+
   # Aantal componenten. c = 1 is zinloos, maar zou moeten werken
   c = args.components
   assert c >= 1
 
   with open(args.filename) as file:
     machine = parse_dot_file(file)
-    if args.verbose:
+
-      print(machine)
+  # Als er maar 1 state is, valt er niks te ontbinden, maar het script zou niet
+  # moeten crashen. Het aantal outputs moet minstens 3 zijn voor een zinvolle
+  # decompositie.
+  assert len(machine.states) >= 1
+  assert len(machine.inputs) >= 1
+  assert len(machine.outputs) >= 1
 
   print(f'Input FSM: {len(machine.states)} states, {len(machine.inputs)} inputs, and {len(machine.outputs)} outputs')
 
@@ -48,7 +56,7 @@ def main():
     signal.signal(signal.SIGALRM, timeout_handler)
     signal.alarm(args.timeout)
 
-  encoder = Encoder(machine, args, record_file=record_file)
+  with Encoder(machine, c, args.weak, add_state_trans=args.add_state_trans, record_file=record_file) as encoder:
     encoder.solve()
 
 
@@ -134,10 +142,10 @@ def print_eqrel(rel, xs):
 
 
 class Progress:
-  def __init__(self, name, guess):
+  def __init__(self, name: str, guess: int):
     self.reset(name, guess, show=False)
 
-  def reset(self, name, guess, show=True):
+  def reset(self, name: str, guess: int, show: bool = True):
     self.name = name
     self.guess = math.ceil(guess)
     self.count = 0
@@ -146,7 +154,7 @@ class Progress:
     if show:
       print(name)
 
-  def add(self, n=1):
+  def add(self, n: int = 1):
     self.count += n
     percentage = math.floor(100 * self.count / self.guess)
 
@@ -159,21 +167,40 @@ class Progress:
 ###################################
 # Main logic
 class Encoder:
-  def __init__(self, machine, args, record_file=None, progress=None):
+  def __init__(self, machine: FSM, components: int = 2, weak: bool = False, add_state_trans: bool = False, record_file: str = None, progress: Progress = None):
     self.machine = machine
-    self.args = args
+    self.c = components
+    self.weak = weak
     self.record_file = record_file
     self.progress = progress if progress else Progress('', 1)
 
-    self.c = self.args.components
+    # optionally add state transitivity constraints. This is not necessary for
+    # the decomposition and it is cubic in the number of states, so it's off
+    # by default.
+    self.add_state_trans = add_state_trans
+
     self.N = len(self.machine.states)
-    self.os = list(machine.outputs)  # outputs
+    self.rids = [i for i in range(self.c)]
-    self.rids = [i for i in range(self.c)]  # components
     self.vpool = IDPool()
     self.solver = Solver()
 
+  def __enter__(self):
+    self.solver = Solver()
+    self.solver.__enter__()
+
     self.encode()
 
+    if self.weak:
+      self.encode_weak_size_constraints()
+    else:
+      self.encode_strict_size_constraints()
+    assert hasattr(self, 'rhs')
+
+    return self
+
+  def __exit__(self, *args):
+    return self.solver.__exit__(*args)
+
   def add_clause(self, cls, no_return=True):
     self.solver.add_clause(cls, no_return)
 
@@ -181,34 +208,37 @@ class Encoder:
     self.solver.append_formula(clss, no_return)
 
   # Een hulp variabele voor False en True, maakt de andere variabelen eenvoudiger
-  def var_const(self, b):
+  def var_const(self, b) -> int:
     return self.vpool.id(('const', b))
 
-  # Voor elke relatie en elke twee elementen o1 en o2, is er een variabele die
+  # Een variabele die aangeeft of x en y gerelateerd zijn. Deze variabele is
-  # aangeeft of o1 en o2 gerelateerd zijn. Er is 1 variabele voor xRy en yRx, dus
+  # symmetrisch en reflexief. De id is een object die de relatie identificeert.
-  # symmetrie is al ingebouwd. Reflexiviteit is ook ingebouwd.
+  # Zo kunnen we meerdere relaties encoderen.
-  def var_rel(self, rid, o1, o2):
+  def var_rel_abs(self, id, x, y) -> int:
-    if o1 == o2:
+    if x == y:
       return self.var_const(True)
 
-    [so1, so2] = sorted([o1, o2])
+    [sx, sy] = sorted([x, y])
-    return self.vpool.id(('rel', rid, so1, so2))
+    return self.vpool.id(('r', id, sx, sy))
+
+  # Een relatie op de output-elementen.
+  def var_rel(self, rid, o1, o2) -> int:
+    return self.var_rel_abs(('output', rid), o1, o2)
 
   # De relatie op outputs geeft een relaties op states. Deze relatie moet ook een
   # bisimulatie zijn.
-  def var_state_rel(self, rid, s1, s2):
+  def var_state_rel(self, rid, s1, s2) -> int:
-    if s1 == s2:
+    return self.var_rel_abs(('state', rid), s1, s2)
-      return self.var_const(True)
-
-    [ss1, ss2] = sorted([s1, s2])
-    return self.vpool.id(('state_rel', rid, ss1, ss2))
 
   # Voor elke relatie, en elke equivalentie-klasse, kiezen we precies 1 state
   # als representant. Deze variabele geeft aan welk element.
-  def var_state_rep(self, rid, s):
+  def var_state_rep(self, rid, s) -> int:
     return self.vpool.id(('state_rep', rid, s))
 
   def encode(self):
+    # lokale variabelen om het wat leesbaarder te maken
+    rids, os, states, inputs = self.rids, list(self.machine.outputs), list(self.machine.states), list(self.machine.inputs)
+
     print('===============')
     print('Start encoding')
     self.add_clause([self.var_const(True)])
@@ -216,41 +246,41 @@ class Encoder:
 
     # Contraints zodat de relatie een equivalentie relatie is. We hoeven alleen
     # maar transitiviteit te encoderen, want refl en symm zijn ingebouwd in de var.
-    self.progress.reset('transitivity (o)', guess=len(self.rids) * len(self.os) ** 3)
+    self.progress.reset('transitivity (o)', guess=len(rids) * len(os) ** 3)
-    for rid in self.rids:
+    for rid in rids:
-      for xo in self.os:
+      for xo in os:
-        for yo in self.os:
+        for yo in os:
-          for zo in self.os:
+          for zo in os:
             # als xo R yo en yo R zo dan xo R zo
             self.add_clause([-self.var_rel(rid, xo, yo), -self.var_rel(rid, yo, zo), self.var_rel(rid, xo, zo)])
             self.progress.add()
 
-    if self.args.add_state_trans:
+    if self.add_state_trans:
-      self.progress.reset('transitivity (s)', guess=len(self.rids) * len(self.machine.states) ** 3)
+      self.progress.reset('transitivity (s)', guess=len(rids) * len(states) ** 3)
-      for rid in self.rids:
+      for rid in rids:
-        for sx in self.machine.states:
+        for sx in states:
-          for sy in self.machine.states:
+          for sy in states:
-            for sz in self.machine.states:
+            for sz in states:
               # als sx R sy en sy R sz dan sx R sz
               self.add_clause([-self.var_state_rel(rid, sx, sy), -self.var_state_rel(rid, sy, sz), self.var_state_rel(rid, sx, sz)])
               self.progress.add()
 
     # Constraint zodat de relaties samen alle elementen kunnen onderscheiden.
     # (Aka: the bijbehorende quotienten zijn joint-injective.)
-    self.progress.reset('injectivity', guess=len(self.os) * (len(self.os) - 1) / 2)
+    self.progress.reset('injectivity', guess=len(os) * (len(os) - 1) / 2)
-    for xi, xo in enumerate(self.os):
+    for xi, xo in enumerate(os):
-      for yo in self.os[xi + 1 :]:
+      for yo in os[xi + 1 :]:
         # Tenminste een rid moet een verschil maken
         self.add_clause([-self.var_rel(rid, xo, yo) for rid in self.rids])
         self.progress.add()
 
     # sx ~ sy => for each input: (1) outputs equivalent AND (2) successors related
     # Momenteel hebben we niet de inverse implicatie, is misschien ook niet nodig?
-    self.progress.reset('bisimulation modulo rel', guess=len(self.rids) * len(self.machine.states) * len(self.machine.states) * len(self.machine.inputs))
+    self.progress.reset('bisimulation modulo rel', guess=len(rids) * len(states) * len(states) * len(inputs))
-    for rid in self.rids:
+    for rid in rids:
-      for sx in self.machine.states:
+      for sx in states:
-        for sy in self.machine.states:
+        for sy in states:
-          for i in self.machine.inputs:
+          for i in inputs:
             # sx ~ sy => output(sx, i) ~ output(sy, i)
             ox = self.machine.output(sx, i)
             oy = self.machine.output(sy, i)
@@ -264,9 +294,8 @@ class Encoder:
             self.progress.add()
 
     # De constraints die zorgen dat representanten ook echt representanten zijn.
-    states = list(self.machine.states)
+    self.progress.reset('representatives', guess=len(rids) * len(states))
-    self.progress.reset('representatives', guess=len(self.rids) * len(states))
+    for rid in rids:
-    for rid in self.rids:
       for ix, sx in enumerate(states):
         # Belangrijkste: een element is een representant, of equivalent met een
         # eerder element. We forceren hiermee dat de solver representanten moet
@@ -280,40 +309,84 @@ class Encoder:
 
         self.progress.add()
 
-    # Tot slot willen we weinig representanten. Dit doen we met een "atmost"
+    # Op dit punt is de encodering klaar, op de constraints voor de grootte na.
-    # formule. We gaan een binaire zoek doen met incremental sat solving.
+    # Dit hangt af van de weak of strict decompositie.
-    self.rhs = None
+
-    if self.args.weak:
+  def encode_weak_size_constraints(self):
+    self.rhs = []
     self.lower_bound = int(math.floor((self.N - 1) ** (1 / self.c)))
     self.upper_bound = int(self.N)
     print(f'weak size constraints {self.lower_bound} {self.upper_bound}')
-      self.rhs = []
+    # In de weak decompositie, minimaliseren we de grootte van elk component.
+    # Dus voor elk component voegen we een cardinality constraint toe. We
+    # gebruiken ITotalizer, omdat deze incrementeel is.
     for rid in self.rids:
       with ITotalizer([self.var_state_rep(rid, sx) for sx in self.machine.states], ubound=self.upper_bound, top_id=self.vpool.top) as cnf_optim:
         self.vpool.occupy(self.vpool.top + 1, cnf_optim.top_id)
         self.vpool.top = cnf_optim.top_id
         self.add_clauses(cnf_optim.cnf.clauses)
         self.rhs.append(cnf_optim.rhs)
-    else:
+
+  def encode_strict_size_constraints(self):
     self.lower_bound = int(math.floor(self.c * (self.N - 1) ** (1 / self.c)))
     self.upper_bound = int(self.N + self.c - 1)
-      print(f'size constraints {self.lower_bound} {self.upper_bound}')
+    print(f'strict size constraints {self.lower_bound} {self.upper_bound}')
+    # In de sterke decompositie, minimaliseren we de som van de componenten.
+    # Dit komt neer op het feit dat we k representanten kiezen in de lijst
+    # rids * states. We gebruiken ITotalizer, omdat deze incrementeel is.
     with ITotalizer([self.var_state_rep(rid, sx) for rid in self.rids for sx in self.machine.states], ubound=self.upper_bound, top_id=self.vpool.top) as cnf_optim:
       self.add_clauses(cnf_optim.cnf.clauses)
       self.rhs = cnf_optim.rhs
 
-  def solve(self):
+  def optimise_constraints(self):
-    print('===============')
+    if self.weak:
-    print('Start solving')
+      self.optimise_weak_constraints()
-    sat = None
+    else:
+      self.optimise_strict_constraints()
+
+    print(f'done searching, found bound(s) = {self.bound}')
+
+  def optimise_weak_constraints(self):
+    bounds = {}
+    smallest = None
+    todo = self.rids.copy()
+
+    while todo:
+      lower_bound = self.N
+      for rid in bounds:
+        lower_bound /= bounds[rid]
+
+      lower_bound = int(math.floor((math.ceil(lower_bound) - 1) ** (1.0 / len(todo))))
+      upper_bound = smallest if smallest else self.N
+
+      while upper_bound - lower_bound >= 2:
+        mid_size = int((lower_bound + upper_bound) / 2)
+        print(f'W Trying {lower_bound} < {mid_size} < {upper_bound}', end='', flush=True)
+        assumptions = [-self.rhs[rid][b] for (rid, b) in bounds.items() if b < self.N]
+        assumptions += [-self.rhs[rid][mid_size] for rid in todo]
+        sat = self.solver.solve(assumptions=assumptions)
+        if sat:
+          print('\tdown')
+          upper_bound = mid_size
+          continue
+        else:
+          print('\tup')
+          lower_bound = mid_size
+          continue
+
+      print(f'Found bound {upper_bound} for {todo[0]}')
+      bounds[todo.pop(0)] = upper_bound
+      smallest = upper_bound
+
+    self.bound = bounds
+    assert len(bounds) == self.c
+
+  def optimise_strict_constraints(self):
     while self.upper_bound - self.lower_bound >= 2:
       self.mid_size = int((self.lower_bound + self.upper_bound) / 2)
-      print(f'Trying {self.lower_bound} < {self.mid_size} < {self.upper_bound}', end='', flush=True)
+      print(f'S Trying {self.lower_bound} < {self.mid_size} < {self.upper_bound}', end='', flush=True)
-      if self.args.weak:
+      assumptions = [-self.rhs[self.mid_size]]
-        assumptions = [-self.rhs[rid][self.mid_size] for rid in self.rids]
       sat = self.solver.solve(assumptions=assumptions)
-      else:
-        sat = self.solver.solve(assumptions=[-self.rhs[self.mid_size]])
       if sat:
         print('\tdown')
         self.upper_bound = self.mid_size
@@ -322,30 +395,25 @@ class Encoder:
         print('\tup')
         self.lower_bound = self.mid_size
         continue
-
     self.bound = self.upper_bound
-    print(f'done searching, found bound = {self.bound}')
 
-    if self.args.weak:
+  def solve(self):
-      assumptions = [-self.rhs[rid][self.bound] for rid in self.rids]
+    print('===============')
+    print('Start solving')
+    self.optimise_constraints()
+
+    if self.weak:
+      assumptions = [-self.rhs[rid][self.bound[rid]] for rid in self.rids if self.bound[rid] < self.N]
       sat = self.solver.solve(assumptions=assumptions)
     else:
-      sat = self.solver.solve(assumptions=[-self.rhs[self.bound]])
+      assumptions = [-self.rhs[self.bound]] if self.bound < self.N * self.c else []
+      sat = self.solver.solve(assumptions=assumptions)
     assert sat
 
     # Even omzetten in een makkelijkere data structuur
     m = self.solver.get_model()
     model = {abs(l): l > 0 for l in m}
 
-    if self.args.verbose:
-      for rid in self.rids:
-        print(f'Relation {rid}:')
-        print_eqrel(lambda x, y: model[self.var_rel(rid, x, y)], self.os)
-
-      for rid in self.rids:
-        print(f'State relation {rid}:')
-        print_eqrel(lambda x, y: model[self.var_state_rel(rid, x, y)], self.machine.states)
-
     # Precieze groottes van elk component tellen
     counts = []
     for rid in self.rids:
@@ -354,15 +422,13 @@ class Encoder:
       for s in self.machine.states:
         if model[self.var_state_rep(rid, s)]:
           count += 1
-          if self.args.verbose:
-            print(f'comp {rid} -> representative state {s}')
       counts.append(count)
 
     print(f'Reduced sizes = {counts} = {sum(counts)}')
     if self.record_file:
       with open(self.record_file, 'a') as file:
-        last_two_comps = '/'.join(self.args.filename.split('/')[-2:])
+        last_two_comps = '/'.join(filename.split('/')[-2:])
-        file.write(f'{last_two_comps}\t{self.N}\t{len(self.machine.inputs)}\t{len(self.machine.outputs)}\t{self.args.weak}\t{self.c}\t{sum(counts)}\t{sorted(counts, reverse=True)}\n')
+        file.write(f'{last_two_comps}\t{self.N}\t{len(self.machine.inputs)}\t{len(self.machine.outputs)}\t{self.weak}\t{self.c}\t{sum(counts)}\t{sorted(counts, reverse=True)}\n')
 
     projections = {}
     for rid in self.rids: