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bugfix in decompose_mealy.py and it actually works now
This commit is contained in:
Joshua Moerman
parent
f5072a9b40
commit
f7b3d27478
2 changed files with 71 additions and 33 deletions
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@ -5,11 +5,16 @@ from pysat.formula import CNF
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### Gebruik:
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# Stap 1: pip3 install python-sat
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# Stap 2: python3 decomp-sat.py
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# Stap 2: python3 decompose_mealy.py
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###################################
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# Wat dingetjes over Mealy machines
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# Voorbeeld: 2n states, input-alfabet 'a' en 'b', outputs [0...n-1]
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def rick_koenders_machine(N):
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transition_fun = {((n, False), 'a') : ((n+1) % 3, False) for n in range(N)}
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transition_fun |= {(((n+1) % 3, True), 'a') : (n % 3, True) for n in range(N)}
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transition_fun = {((n, False), 'a') : ((n+1) % N, False) for n in range(N)}
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transition_fun |= {(((n+1) % N, True), 'a') : (n % N, True) for n in range(N)}
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transition_fun |= {((n, b), 'b') : (n, not b) for b in [False, True] for n in range(N)}
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output_fun = {((n, b), 'a') : n for b in [False, True] for n in range(N)}
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output_fun |= {((n, b), 'b') : 0 for b in [False, True] for n in range(N)}
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@ -29,23 +34,45 @@ def mealy_sem_q(machine, word, state):
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def mealy_sem(machine, word):
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return mealy_sem_q(machine, word, machine['initial_state'])
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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])
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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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################
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# Voorbeeld data
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machine = rick_koenders_machine(3)
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machine = rick_koenders_machine(4) # 8 states
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# L* table
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rows = ['', 'a', 'aa', 'b', 'ab', 'aab', 'abaa', 'aabab']
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cols = ['a', 'aa', 'aaa', 'b', 'ab', 'ba']
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# L* table: Niet noodzakelijk volledig, werkt ook met minder data, maar ik
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# weet niet wat voor garanties we dan kunnen geven. Het is sowieso maar de
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# vraag of de kolommen voldoende zijn als we projecteren.
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rows = ['', 'a', 'aa', 'aaa', 'aaaa', 'b', 'ab', 'aab', 'aaab']
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cols = ['a', 'aa', 'aaa', 'aaaa', 'b', 'ab', 'ba', 'abab']
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# We zoeken 2 componenten, grootte 5 (is minder dan 6)
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print_table(lambda r, c: str(mealy_sem(machine, r+c)), rows, cols)
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# We zoeken 2 componenten met gezamelijke grootte 6 (minder dan 8)
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# als de de total_size te laag is => UNSAT => duurt lang
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c = 2
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total_size = 5 # als deze te laag is => UNSAT => duurt lang
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os = machine['outputs'] # outputs
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rids = [i for i in range(c)] # components
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total_size = 6
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########################
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# Encodering naar logica
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print('Start encoding')
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os = 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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@ -97,7 +124,7 @@ for rid in rids:
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for ry in rows:
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for rz in rows:
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# als rx R ry en ry R rz dan rx R rz
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cnf.append([-var_rel(rid, rx, ry), -var_rel(rid, ry, rz), var_rel(rid, rx, rz)])
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cnf.append([-var_row_rel(rid, rx, ry), -var_row_rel(rid, ry, rz), var_row_rel(rid, rx, rz)])
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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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@ -107,6 +134,22 @@ for xi, xo in enumerate(os):
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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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# Als outputs equivalent zijn, dan ook sommige rijen, en andersom.
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print('rel <=> row_rel')
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for rid in rids:
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for rx in rows:
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for ry in rows:
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osx = [mealy_sem(machine, rx + c) for c in cols]
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osy = [mealy_sem(machine, ry + c) for c in cols]
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oss = list(zip(osx, osy))
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# (ox1 ~ oy1 and ox2 ~ oy2 and ...) => rx ~ ry
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cnf.append([-var_rel(rid, ox, oy) for (ox, oy) in oss] + [var_row_rel(rid, rx, ry)])
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# rx ~ ry => oxi ~ oyi
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for (ox, oy) in oss:
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cnf.append([-var_row_rel(rid, rx, ry), var_rel(rid, ox, oy)])
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# De constraints die zorgen dat representanten ook echt representanten zijn.
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print('- representatives (r)')
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for rid in rids:
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@ -126,26 +169,12 @@ print('- representatives at most k')
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cnf_optim = CardEnc.atmost([var_row_rep(rid, rx) for rid in rids for rx in rows], total_size, vpool=vpool)
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cnf.extend(cnf_optim)
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# Als outputs equivalent zijn, dan ook sommige rijen, en andersom.
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print('rel <=> row_rel')
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for rid in rids:
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for rx in rows:
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for ry in rows:
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if ry <= rx:
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continue
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osx = [mealy_sem(machine, rx + c) for c in cols]
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osy = [mealy_sem(machine, ry + c) for c in cols]
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oss = zip(osx, osy)
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# (ox1 ~ oy1 and ox2 ~ oy2 and ...) => rx ~ ry
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cnf.append([-var_rel(rid, ox, oy) for (ox, oy) in oss] + [var_row_rel(rid, rx, ry)])
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# rx ~ ry => oxi ~ oyi
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for (ox, oy) in oss:
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cnf.append([-var_row_rel(rid, rx, ry), var_rel(rid, ox, oy)])
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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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# Probleem oplossen met solver :-).
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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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@ -166,6 +195,14 @@ with Solver(bootstrap_with=cnf) as solver:
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if l < 0: model[-l] = False
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else: model[l] = True
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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'Row relation {rid}:')
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print_eqrel(lambda x, y: model[var_row_rel(rid, x, y)], rows)
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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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@ -5,12 +5,13 @@ from pysat.formula import CNF
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### Gebruik:
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# Stap 1: pip3 install python-sat
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# Stap 2: python3 decomp-sat.py
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# Stap 2: python3 decompose_set.py
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# Een verzameling X ontbinden in factoren X1 ... Xc, zodat X ⊆ X1 × ... × Xc.
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# Hierbij is c een parameter (het aantal componenten), en ook het aantal
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# elementen van X1 t/m Xc moet vooraf bepaald zijn, dat is 'total_size'.
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# Voorbeeld data
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# snel voorbeeld: n = 27, c = 3 en total_size = 9
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# langzaam vb.: n = 151, c = 4 en total_size = 15
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@ -32,7 +33,6 @@ rids = [i for i in range(c)] # components
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# c = 1 1 1 1 1 2 2 2 2 3 2 3 3 3 4 3 4 4 4 5
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print('Start encoding')
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vpool = IDPool()
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cnf = CNF()
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@ -97,6 +97,7 @@ print('- representatives at most k')
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cnf_optim = CardEnc.atmost([var_rep(rid, xo) for rid in rids for xo in os], total_size, vpool=vpool)
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cnf.extend(cnf_optim)
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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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