sat: rework to use integral variable, not individual bools
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51
sat.py
51
sat.py
@ -1,5 +1,6 @@
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import copy
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from pysmt.shortcuts import Symbol, Bool, Not, Implies, Iff, And, Or, AtMostOne, ExactlyOne, get_model, get_atoms, get_formula_size, get_unsat_core
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from pysmt.shortcuts import Symbol, Bool, Not, Implies, Iff, And, Or, AtMostOne, ExactlyOne, get_model, get_atoms, get_formula_size, get_unsat_core, Equals, GE, NotEquals, Int
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from pysmt.typing import INT
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from pysmt.rewritings import conjunctive_partition
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import json
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from typing import List, Optional, Tuple
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@ -19,28 +20,15 @@ class Literals():
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# default distribution among all suits is assumed
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def __init__(self, instance: HanabiInstance):
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# clues[m][i] == "after move m we have at least i clues"
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# clues[m][i] == "after move m we have i clues", in clue starved, this counts half clues
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self.clues = {
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-1: { i: Bool(i < 9) for i in range(0, 10) } # we have 8 clues after turn -1
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-1: Int(16 if instance.clue_starved else 8) # we have 8 clues after turn
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, **{
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m: {
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0: Bool(True), # always at least 0 clues
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**{ i: Symbol('m{}clues{}'.format(m, i)) for i in range(1, 9) },
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9: Bool(False) # never 9 or more clues. This will implicitly forbid discarding at 8 clues later
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}
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m: Symbol('m{}clues'.format(m), INT)
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for m in range(instance.max_winning_moves)
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}
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}
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# half_clue[m] == "after move we have (an additional) half a clue [relevant for ClueStarved variants]"
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self.half_clue = {
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-1: Bool(False)
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, **{
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m: Symbol('m{}halfclue'.format(m))
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for m in range(instance.max_winning_moves)
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}
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}
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# strikes[m][i] == "after move m we have at least i strikes"
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self.strikes = {
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-1: {i: Bool(i == 0) for i in range(0, instance.num_strikes + 1)} # no strikes when we start
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@ -152,8 +140,8 @@ def solve_sat(starting_state: GameState | HanabiInstance) -> Tuple[bool, Optiona
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# have to set additional variables
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# set initial clues
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for i in range(0,10):
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ls.clues[first_turn - 1][i] = Bool(i <= game_state.clues)
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for i in range(0, 10):
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ls.clues[first_turn - 1] = Int(game_state.clues)
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# set initial strikes
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for i in range(0, instance.num_strikes + 1):
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@ -162,7 +150,7 @@ def solve_sat(starting_state: GameState | HanabiInstance) -> Tuple[bool, Optiona
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# check if extraround has started (usually not)
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ls.extraround[first_turn - 1] = Bool(game_state.remaining_extra_turns < game_state.num_players)
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ls.dummyturn[first_turn -1] = Bool(False)
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# set recent draws: important to model progress
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# we just pretend that the last card drawn was in fact drawn last turn,
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# regardless of when it was actually drawn
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@ -180,7 +168,7 @@ def solve_sat(starting_state: GameState | HanabiInstance) -> Tuple[bool, Optiona
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ls.progress[first_turn - 1][s, r] = Bool(r <= game_state.stacks[s])
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### Now, model all valid moves
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valid_move = lambda m: And(
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# in dummy turns, nothing can be discarded
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Implies(ls.dummyturn[m], Not(ls.discard_any[m])),
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@ -202,18 +190,13 @@ def solve_sat(starting_state: GameState | HanabiInstance) -> Tuple[bool, Optiona
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Iff(ls.play5[m], And(ls.play[m], Or(ls.discard[m][i] for i in range(instance.deck_size) if instance.deck[i].rank == 5))),
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# definition of ls.incr_clues
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Iff(ls.incr_clues[m], And(ls.discard_any[m], Not(ls.clues[m-1][8]), Implies(ls.play[m], ls.play5[m]))),
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Iff(ls.incr_clues[m], And(ls.discard_any[m], NotEquals(ls.clues[m-1], Int(16 if instance.clue_starved else 8)), Implies(ls.play[m], ls.play5[m]))),
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# change of ls.clues
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*[
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Iff(ls.clues[m][i], Or(
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ls.clues[m-1][i+1],
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And(ls.clues[m-1][i], Or(ls.discard_any[m], ls.dummyturn[m])),
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And(ls.clues[m-1][i-1], ls.incr_clues[m], ls.half_clue[m-1] if instance.clue_starved else Bool(True))
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)
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)
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for i in range(1, 9)
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],
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Implies(And(Not(ls.discard_any[m]), Not(ls.dummyturn[m])),
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Equals(ls.clues[m], ls.clues[m-1] - (2 if instance.clue_starved else 1))),
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Implies(ls.incr_clues[m], Equals(ls.clues[m], ls.clues[m-1] + 1)),
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Implies(And(Or(ls.discard_any[m], ls.dummyturn[m]), Not(ls.incr_clues[m])), Equals(ls.clues[m], ls.clues[m-1])),
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Iff(ls.half_clue[m], Or(And(ls.half_clue[m-1], Not(ls.incr_clues[m])), And(Not(ls.half_clue[m-1])), ls.incr_clues[m]))
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if instance.clue_starved else Bool(True),
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@ -223,13 +206,13 @@ def solve_sat(starting_state: GameState | HanabiInstance) -> Tuple[bool, Optiona
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# It's easy to see that if there is any solution to the instance, then there is also one where we only strike at 8 clues
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# (or not at all) -> Just strike later if neccessary
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# So, we decrease the solution space with this formulation, but do not change whether it's empty or not
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Iff(ls.strike[m], And(ls.discard_any[m], Not(ls.play[m]), ls.clues[m-1][8])),
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Iff(ls.strike[m], And(ls.discard_any[m], Not(ls.play[m]), Equals(ls.clues[m-1], Int(16 if instance.clue_starved else 8)))),
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# change of strikes
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*[Iff(ls.strikes[m][i], Or(ls.strikes[m-1][i], And(ls.strikes[m-1][i-1], ls.strike[m]))) for i in range(1, instance.num_strikes + 1)],
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# less than 0 clues not allowed
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Implies(Not(ls.discard_any[m]), Or(ls.clues[m-1][1], ls.dummyturn[m])),
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Implies(Not(ls.discard_any[m]), Or(GE(ls.clues[m-1], Int(1)), ls.dummyturn[m])),
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# we can only draw card i if the last ls.drawn card was i-1
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*[Implies(ls.draw[m][i], Or(And(ls.draw[m0][i-1], *[Not(ls.draw_any[m1]) for m1 in range(m0+1, m)]) for m0 in range(max(first_turn - 1, m-9), m))) for i in range(game_state.progress, instance.deck_size)],
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@ -325,7 +308,7 @@ def log_model(model, cur_game_state, ls: Literals):
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logger.debug('[print_model] Note: Omitting first {} turns, since they were fixed already.'.format(first_turn))
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for m in range(first_turn, cur_game_state.instance.max_winning_moves):
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logger.debug('=== move {} ==='.format(m))
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logger.debug('clues: ' + ''.join(str(i) for i in range(1, 9) if model.get_py_value(ls.clues[m][i])))
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logger.debug('clues: {}'.format(model.get_py_value(ls.clues[m])))
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logger.debug('strikes: ' + ''.join(str(i) for i in range(1, 3) if model.get_py_value(ls.strikes[m][i])))
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logger.debug('draw: ' + ', '.join('{}: {}'.format(i, deck[i]) for i in range(cur_game_state.progress, cur_game_state.instance.deck_size) if model.get_py_value(ls.draw[m][i])))
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logger.debug('discard: ' + ', '.join('{}: {}'.format(i, deck[i]) for i in range(cur_game_state.instance.deck_size) if model.get_py_value(ls.discard[m][i])))
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