def createVariables(givenBoardCondition, k):
#creating dictionaries for each resource to hold their resources
whVariables = {}
brVariables = {}
woVariables = {}
shVariables = {}
variableDictionary = {}
#Running through each list value in the given board condition and splitting them based on the operators to just leave variable names ie. W_31
#Then creating a dictionary key value pair where the key is the variable name and the value is a Var with the variable name used as the
# constructor value
for node in givenBoardCondition:
parts = node.replace(">>",
" ").replace("&", " ").replace("|", " ").replace(
"(", " ").replace(")", " ").split()
for variable in parts:
variable.strip()
#if variables are greater than k, they are not included in the final dictionary
if (int(variable[3]) <= k + 1):
if "wh" in variable.lower():
whVariables[variable] = Var(variable)
if "wo" in variable.lower():
woVariables[variable] = Var(variable)
if "br" in variable.lower():
brVariables[variable] = Var(variable)
if "sh" in variable.lower():
shVariables[variable] = Var(variable)
#Merging variable dictionaries into 1 master dictionary containing all variables
variableDictionary = mergeDictionaries(variableDictionary, whVariables,
woVariables, shVariables,
brVariables)
return variableDictionary
def _parse_cnf(tokens: t.Iterable[str]) -> And[Or[Var]]:
clauses = set() # type: t.Set[Or[Var]]
clause = set() # type: t.Set[Var]
for token in tokens:
if token == '0':
clauses.add(Or(clause))
clause = set()
elif token == '%':
# Some example files end with:
# 0
# %
# 0
# I don't know why.
break
elif token.startswith('-'):
clause.add(Var(_parse_int(token[1:]), False))
else:
clause.add(Var(_parse_int(token)))
if clause:
# A file may or may not end with a 0
# Adding an empty clause is not desirable
clauses.add(Or(clause))
sentence = And(clauses)
NNF._is_CNF_loose.set(sentence, True)
return sentence
def load(fp: t.TextIO,
var_labels: t.Optional[t.Dict[int, Name]] = None) -> NNF:
"""Load a sentence from an open file.
An optional ``var_labels`` dictionary can map integers to other names.
"""
def decode_name(num: int) -> Name:
if var_labels is not None:
return var_labels[num]
return num
fmt, nodecount, edges, varcount = fp.readline().split()
node_specs = dict(enumerate(line.split() for line in fp))
assert fmt == 'nnf'
nodes = {} # type: t.Dict[int, NNF]
for num, spec in node_specs.items():
if spec[0] == 'L':
if spec[1].startswith('-'):
nodes[num] = Var(decode_name(int(spec[1][1:])), False)
else:
nodes[num] = Var(decode_name(int(spec[1])))
elif spec[0] == 'A':
nodes[num] = And(nodes[int(n)] for n in spec[2:])
elif spec[0] == 'O':
nodes[num] = Or(nodes[int(n)] for n in spec[3:])
else:
raise ValueError("Can't parse line {}: {}".format(num, spec))
if int(nodecount) == 0:
raise ValueError("The sentence doesn't have any nodes.")
return nodes[int(nodecount) - 1]
def create_variables(givenBoardCondition):
#creating dictionaries for each resource to hold their resources
whVariables = {}
brVariables = {}
woVariables = {}
shVariables = {}
variableDictionary = {}
#Running through each list value in the given board condition and splitting them based on the operators to just leave variable names ie. W_31
#Then creating a dictionary key value pair where the key is the variable name and the value is a Var with the variable name used as the
# constructor value
for node in givenBoardCondition:
parts = node.replace(">>",
" ").replace("&", " ").replace("|", " ").replace(
"(", " ").replace(")", " ").split()
for variable in parts:
variable.strip()
if "wh" in variable.lower():
whVariables[parts[variable]] = Var(parts[variable])
if "wo" in variable.lower():
woVariables[parts[variable]] = Var(parts[variable])
if "br" in variable.lower():
brVariables[parts[variable]] = Var(parts[variable])
if "sh" in variable.lower():
shVariables[parts[variable]] = Var(parts[variable])
#Merging variable dictionaries into 1 master dictionary containing all variables
variableDictionary = merge_dictionaries(merge_dictionaries, whVariables)
variableDictionary = merge_dictionaries(merge_dictionaries, whVariables)
variableDictionary = merge_dictionaries(merge_dictionaries, whVariables)
variableDictionary = merge_dictionaries(merge_dictionaries, whVariables)
return variableDictionary
def test_implicates_implicants_negation_rule_example():
"""These failed an old version of the previous test. See issue #3."""
sentence = Or({And({~Var(1), Var(2)}), And({~Var(3), Var(1)})})
assert (sentence.negate().implicants().negate().children >=
sentence.implicates().children)
assert (sentence.negate().implicates().negate().children <=
sentence.implicants().children)
def set_initial_state(grid_setup):
"""
Sets the inital state of a grid
@param grid_setup: a 5x5 2-dimensional list of a grid state
"""
grid_range = range(5) # A range variable used to iterate through the grid
# Instantiates Var objects for u, m and s cases for the 5x5 grid
for i in grid_range:
for j in grid_range:
# These create objects for each condition and state in the form
# mij, uij and sij. For example, m12 would be the condition that
# the square at coordinates (1, 2) is a bomb (coords start at (0, 0))
m[i].append(Var('m' + str(i) + str(j)))
u[i].append(Var('u' + str(i) + str(j)))
s[i].append(Var('s' + str(i) + str(j)))
# Each square's state is checked and constraints are added
# The if conditional is used to ignore the center square since
# we don't need constrainsts for it
if not (i == 2 and j == 2):
state = grid_setup[i][j]
# Raises an exception if a square has an illegal value
if not (-2 <= state <= 8):
raise Exception(
'error: each square of the grid must have a'
' value between -2 and 8 inclusive. Square '
'[%d][%d] has a value of %d' % (i, j, state))
if state == -2: # mine
E.add_constraint(m[i][j])
else:
E.add_constraint(~m[i][j])
if state == -1: # unknown
E.add_constraint(u[i][j])
else:
E.add_constraint(~u[i][j])
if state > -1: # revealed square
E.add_constraint(s[i][j])
else:
E.add_constraint(~s[i][j])
# Initializing x and y cases
for i in grid_range:
for j in grid_range:
# We are only initializing the x and y truth values for the inner
# 9 squares
# The outer ring of squares can sometimes be determined for x and
# y values, but that is beyond our scope
if 0 < i < 4 and 0 < j < 4:
set_X_truth(grid_setup, i, j)
set_Y_truth(grid_setup, i, j)
else:
x[i].append(Var("x" + str(i) + str(j)))
y[i].append(Var("y" + str(i) + str(j)))
def rand_var(multi, sets=[1, 1, 2], val=None):
x = 100000000
if multi == sets[0]:
return Var(str(rand(x))) | Var(str(rand(x))) # 75%
elif multi > sets[2]:
return Var(str(rand(x))) & Var(str(rand(x))) # 25%
return val # 50%
def __init__(self,size,id):
self.position = {} # Position of the final ships
self.startPosition = {} # Used to determine the independent positions of the starting ships
self.hInterPosition = {} # Board for a ship's placed position that are not the starting position
self.vInterPosition = {} # Board for a ship's placed position that are not the starting position
# Sizes of ship (only one can be true per ship object)
self.size2 = Var("%d%s" % (id, "size2")) # Destroyer
self.size3 = Var("%d%s" % (id, "size3")) # Cruiser or Submarine
self.size4 = Var("%d%s" % (id, "size4")) # Battleship
# self.size5 = Var("%d%s" % (id, "size5"))
self.horizontal = Var("%d%s" % (id, "horizontal")) # Horizontal if true, vertical if false
self.vertical = Var("%d%s" % (id,"vertical")) # Vertical if true, horizontal if false (redundant but both vars exist to help with more readable code)
for i in range(size):
for j in range(size):
# var for coordinate should be true if the starting ship coordinate is at that (x, y) position
self.startPosition[(i + 1,j + 1)] = Var("%ds(%d,%d)" % (id, i + 1, j + 1))
for i in range(size):
for j in range(size):
# var for coordinate should be true if the remainder of the ships's coordinates are at that (x, y) position and the ship is placed horizontally
self.hInterPosition[(i + 1,j + 1)] = Var("%dh(%d,%d)" % (id, i + 1, j + 1))
for i in range(size):
for j in range(size):
# var for coordinate should be true if the remainder of the ships's coordinates are at that (x, y) position and the ship is placed vertically
self.vInterPosition[(i + 1,j + 1)] = Var("%dv(%d,%d)" % (id, i + 1, j + 1))
for i in range(size):
for j in range(size):
# var for coordinate should be true if there is a ship part on the coordinate's (x, y) position
self.position[(i + 1,j + 1)] = Var("(%d,%d)" % (i + 1, j + 1))
def count_builder(name):
Count = []
for i in range(BOARD_SIZE**2):
Count.append([])
for j in range((BOARD_SIZE**2)+1):
Count[i].append(Var(f'{name}_count_by_{i}_is_{j}'))
Total_Count = []
for i in range(BOARD_SIZE**2+1):
Total_Count.append(Var(f'{name}_total_is_{i}'))
return Count, Total_Count
def check_correct(self):
var = []
ret_string = ""
chars = list(self.characters.keys())
sentence_vals = {x: False for x in chars}
chars.remove('weapon')
chars.remove('location')
for char in chars:
var.append(Var(char))
weapon = self.characters['weapon'].goals['murderweapon'].points
sus_weapon = self.characters['weapon'].goals['suspectedweapon'].points
location = self.characters['location'].goals['murderlocation'].points
sus_location = self.characters['location'].goals['suspectedlocation'].points
for char in chars:
if self.characters[char].goals['issuspect'].points == 1:
sus_killer = char
if self.characters[char].goals['iskiller'].points == 1:
killer = char
w = Var('weapon')
l = Var('location')
sentence = And({w, l, Or(tuple(var))})
if killer == sus_killer:
sentence_vals[killer] = True
ret_string += "You got the killer!\n"
else:
ret_string += "The killer got away!\n"
if weapon == sus_weapon:
sentence_vals['weapon'] = True
ret_string += "You correctly identified the weapon!\n"
else:
ret_string += "You didn't identify the murder weapon correctly.\n"
if location == sus_location:
sentence_vals['location'] = True
ret_string += "You deduced the correct location!\n\n"
else:
ret_string += "The murder took place in another location.\n\n"
if sentence.satisfied_by(sentence_vals):
ret_string += "Congratulations, you solved the mystery!\n"
else:
ret_string += "Unfortunately, you didn't solve the mystery completely.\n"
return ret_string
def process_node(node: NNF) -> Var:
if isinstance(node, Var):
return node
assert isinstance(node, Internal)
children = {process_node(c) for c in node.children}
if len(children) == 1:
[child] = children
return child
aux = Var.aux()
if any(~var in children for var in children):
if isinstance(node, And):
clauses.append(Or({~aux}))
else:
clauses.append(Or({aux}))
elif isinstance(node, And):
clauses.append(Or({~c for c in children} | {aux}))
for c in children:
clauses.append(Or({~aux, c}))
elif isinstance(node, Or):
clauses.append(Or(children | {~aux}))
for c in children:
clauses.append(Or({~c, aux}))
else:
raise TypeError(node)
return aux
def _parse_sat(tokens: 't.Deque[str]') -> NNF:
cur = tokens.popleft()
if cur == '(':
content = _parse_sat(tokens)
close = tokens.popleft()
if close != ')':
raise DecodeError(
"Expected closing paren, found {!r}".format(close))
return content
elif cur == '-':
content = _parse_sat(tokens)
if not isinstance(content, Var):
raise DecodeError(
"Only variables can be negated, not {!r}".format(content))
return ~content
elif cur == '*(':
children = []
while tokens[0] != ')':
children.append(_parse_sat(tokens))
tokens.popleft()
if children:
return And(children)
else:
return true
elif cur == '+(':
children = []
while tokens[0] != ')':
children.append(_parse_sat(tokens))
tokens.popleft()
if children:
return Or(children)
else:
return false
else:
return Var(_parse_int(cur))
def set_Y_truth(grid_setup, i, j):
"""
Sets the y truth values a given square in a grid
@param grid_setup: 5x5 2-dimensional list of a grid state
i: row number of the square
j: column number of the square
"""
# This constant list is used to quickly get the coordinates of adjacent squares
coords = [[i - 1, j - 1], [i - 1, j], [i - 1, j + 1], [i, j - 1],
[i, j + 1], [i + 1, j - 1], [i + 1, j], [i + 1, j + 1]]
counter = 0 # Used for counting the number of adjacent mines or unknown squares
for n in range(len(coords)):
adjacent_square = grid_setup[coords[n][0]][coords[n][1]]
# The following conditional checks if the nth adjacent square is a mine
# or unknown
if adjacent_square == -1 or adjacent_square == -2:
counter += 1
# Instantiates the y condition at the given coordinate and sets a constraint
# for it
y[i].append(Var("y" + str(i) + str(j)))
if grid_setup[i][j] == counter:
E.add_constraint(y[i][j])
else:
E.add_constraint(~y[i][j])
def set_X_truth(grid_setup, i, j):
"""
Sets the x truth values a given square in a grid
@param grid_setup: 5x5 2-dimensional list of a grid state
i: row number of the square
j: column number of the square
"""
# This constant list is used to quickly get the coordinates of adjacent squares
coords = [[i - 1, j - 1], [i - 1, j], [i - 1, j + 1], [i, j - 1],
[i, j + 1], [i + 1, j - 1], [i + 1, j], [i + 1, j + 1]]
counter = 0 # Used for counting the number of adjacent mines
for n in range(len(coords)):
adjacent_row = coords[n][0]
adjacent_col = coords[n][1]
# The following conditional checks if the nth adjacent square is a mine
if grid_setup[adjacent_row][adjacent_col] == -2:
counter += 1
# Instantiates a Var object for the x condition at the given coordinate and
# sets a constraint for it
x[i].append(Var("x" + str(i) + str(j)))
if grid_setup[i][j] == counter:
E.add_constraint(x[i][j])
else:
E.add_constraint(~x[i][j])
def unpack_variables(T, propositions) -> list:
""" Returns a list of all variable inputs for building a constraint
Arguments
---------
T : tuple
propositions : defaultdict(weakref.WeakValueDictionary)
Returns
-------
inputs : list
List of inputs with only unqiue variables returned.
"""
inputs = set()
for var in T:
if hasattr(var, '__qualname__'):
if var.__qualname__ in propositions:
cls = var.__qualname__
for instance_id in propositions[cls]:
inputs.add(propositions[cls][instance_id]._var)
elif classname(var) in propositions:
cls = classname(var)
for instance_id in propositions[cls]:
obj = propositions[cls][instance_id]
# apply method to object to get return values
ret = set(flatten([var(obj)]))
# check return values are valid inputs
res = unpack_variables(ret, propositions)
# add nnf.Var attribute of object
res.append(obj._var)
inputs.update(res)
# if object, add its nnf.Var attribute
elif hasattr(var, '_var'):
inputs.add(var._var)
# if nnf.Var object
elif isinstance(var, Var):
inputs.add(var)
elif isinstance(var, (list, tuple, set)):
inputs.update(unpack_variables(var, propositions))
else:
if isinstance(var, core.CustomNNF):
warnings.warn(
f"Provided input {var} is a literal, not a variable.")
try:
# convert to nnf.Var
inputs.add(Var(var))
except Exception as e:
raise ValueError(
f"Provided input {var} is not of an annotated class or method,"
" instance of such as class or method, or of type nnf.Var."
" Attempted conversion of {var} to nnf.Var also failed and"
f" yielded the following error message: {e}")
return list(inputs)
def clone_varset(models, model_vars, varset):
clones = {}
for m in models:
bitvec = model_to_bitvec(m, model_vars)
clones[bitvec] = {}
for v in varset:
clones[bitvec][v] = Var(model_to_varclone(m, model_vars, v))
return clones
def init_vars(name):
grid = []
for i in range(size):
row = []
for j in range(size):
row.append(Var(f'{name}_{i}_{j}'))
grid.append(row)
return grid
def __init__(self, size):
# Player board standardized to 6x6 for now due to computing limitations
# May be used for any encoding assessing hits
self.hit_board = {}
for i in range(size):
for j in range(size):
# var for coordinate is true if the (x, y) position is hit
self.hit_board[(i + 1,j + 1)] = Var("(%d,%d)" % (i + 1,j + 1))
def test_dsharp_compile_converting_names(sentence: And[Or[Var]]):
sentence = And(
Or(Var(str(var.name), var.true) for var in clause)
for clause in sentence)
compiled = dsharp.compile(sentence)
assert all(isinstance(name, str) for name in compiled.vars())
if sentence.satisfiable():
assert sentence.equivalent(compiled)
def example_theory():
variables = createVariables(givenBoardCondition, k)
#overall variables for overall node types and winning condition
Wh = Var("Wh")
Wo = Var("Wo")
Sh = Var("Sh")
Br = Var("Br")
W = Var("W")
#create variable arrays
wood, wheat, sheep, brick = createVariableLists(variables)
tree = buildTree(variables, createImplicationList(givenBoardCondition, k))
rowVariables = variablesToRows(variables)
E = Encoding()
#Making Constraints based on board condition
E = createBoardConstraints(givenBoardCondition, variables, E, k)
#Adding constraint for winning condition
E.add_constraint(W.negate() | (Wh & Wo & Sh & Br))
#Setting W to always true so that the solver tries to find a winning model
E.add_constraint(W)
E = setOverallVariablesTrueOrFalse(Wh, Wo, Br, Sh, variables, wood, wheat,
sheep, brick, E, S)
E = leaf_constraints(
findLeaves(
tree,
findAllParents(tree, createImplicationList(givenBoardCondition,
k))), E, variables)
E = implementRequiredNodes(S, E, Wo, Wh, Sh, Br)
E = rowVariablesToConstraints(rowVariables, E)
#print(findLeaves(tree,findAllParents(tree,createImplicationList(givenBoardCondition,k))))
print(E.constraints)
return E
def kemeny(votes):
labels = collections.Counter()
for vote in votes:
for name, truthiness in order_to_model(vote).items():
labels[Var(name, truthiness)] += 1
return {
model_to_order(model)
for model in amc.maxplus_reduce(lin(votes[0]), labels).models()
}
def __init__(self):
self.schedule = {}
for time in range(num_time_slots):
for processor in range(num_processors):
for process in range(num_processes):
self.schedule[time, processor,
process] = Var('schedule_' + str(time) +
'_' + str(processor) + '_' +
str(process))
def slater(votes):
totals = collections.Counter()
for vote in votes:
for name, truthiness in order_to_model(vote).items():
totals[Var(name, truthiness)] += 1
labels = {}
for var in totals:
labels[var] = 1 if totals[var] > totals[~var] else 0
return {
model_to_order(model)
for model in amc.maxplus_reduce(lin(votes[0]), labels).models()
}
def set_up_props():
"""Initializes the propositions to be used by the model"""
#loop through all stops
for i in range(len(stop_info)):
#set up propositions for travel
location = stop_info[i]["location"]
drive[location] = Var('drive from ' + location)
transit[location] = Var('take transit from ' + location)
plane[location] = Var('take a plane from ' + location)
#set up other delay propositions
roadwork[location] = Var('roadwork happening on the path from ' +
location)
accident[location] = Var('accident on the path from ' + location)
toll[location] = Var('tolls on the path from ' + location)
#set up weather propositions
sunny[location] = Var('sunny from ' + location)
rainy[location] = Var('rainy from ' + location)
snowstorm[location] = Var('snowstorm from ' + location)
def build_negated_solution_nnf(self):
nnf = None
# Suppose our solution is {a=True, b=False, c=True}.
# We could construct ~(a&~b&c), but the NNF library
# would then have to perform the outer negation for us.
# We can instead construct something that's already
# in NNF, which is equivalent to what the NNF library
# would give us: ~a|b|~c
for prop,assignment in self.soln.items():
var = Var(prop, true=not assignment)
if nnf is None:
nnf = var
else:
nnf |= var
return nnf
def __init__(self, pilot_id, start):
# Name the pilots starting at A, B, ...
self.pilot_id = chr(pilot_id + 65)
self.starting_airport = start
# Increase static counter
Pilot.count += 1
self.location = []
# Initialize array of Var's for each pilot representing their location
for timestep in range(N_TIMESTEPS):
airports = []
for num in range(N_AIRPORTS):
airport = Airport(num)
airports.append(Var(airport))
self.location.append(airports)
def test_dimacs_cnf_serialize():
sample_input = """c Example CNF format file
c
p cnf 4 3
1 3 -4 0
4 0 2
-3
"""
assert dimacs.loads(sample_input) == And(
{Or({Var(1), Var(3), ~Var(4)}),
Or({Var(4)}),
Or({Var(2), ~Var(3)})})
def test_forget(sentence: nnf.NNF):
# Assumption to reduce the time in testing
assume(sentence.size() <= 15)
# Test that forgetting a backbone variable doesn't change the theory
T = sentence & Var('added_var')
assert sentence.equivalent(T.forget({'added_var'}))
# Test the tseitin projection
assert sentence.equivalent(sentence.to_CNF().forget_aux())
# Test that models of a projected theory are consistent with the original
names = list(sentence.vars())[:2]
T = sentence.forget(names)
assert not any([v in T.vars() for v in names])
for m in T.models():
assert sentence.condition(m).satisfiable()
def test_dimacs_sat_serialize():
# http://www.domagoj-babic.com/uploads/ResearchProjects/Spear/dimacs-cnf.pdf
sample_input = """c Sample SAT format
c
p sat 4
(*(+(1 3 -4)
+(4)
+(2 3)))
"""
assert dimacs.loads(sample_input) == And(
{Or({Var(1), Var(3), ~Var(4)}),
Or({Var(4)}),
Or({Var(2), Var(3)})})
def test_storing_function_constraint():
# assert failures when creating,
# add_method(e) with no arguments
# add_implies_all(e) with no left or right
# add_at_most_k with incorrect k
test = Var('test')
with pytest.raises(ValueError):
constraint.add_at_least_one(b)
constraint.add_at_most_k(b, 0)
constraint.add_implies_all(b)
constraint.add_implies_all(b, left=[], right=[test])
constraint.add_none_of(b)
assert len(b.constraints) == 0
constraint.add_implies_all(b, left=test, right=test)
assert len(b.constraints) == 1
for c in b.constraints:
assert c._constraint is cbuilder.implies_all
assert c._left == c._right
assert c._left == (test, )
