def cnf_1bitadder(cnf: Formula, a: Variable, b: Variable,
c: Variable) -> Tuple[Variable, Variable]:
res = cnf.new_var()
res_carry = cnf.new_var()
# (d|a|~b|~c)&(d|~a|b|~c)&(d|~a|~b|c)&(d|~a|~b|~c)&(~d|a|b|c)&(~d|a|b|~c)&(~d|a|~b|c)&(~d|~a|b|c)
cnf.add([res_carry, a, ~b, ~c])
cnf.add([res_carry, ~a, b, ~c])
cnf.add([res_carry, ~a, ~b, c])
cnf.add([res_carry, ~a, ~b, ~c])
cnf.add([~res_carry, a, b, c])
cnf.add([~res_carry, a, b, ~c])
cnf.add([~res_carry, a, ~b, c])
cnf.add([~res_carry, ~a, b, c])
# (d|a|b|~c)&(d|a|~b|c)&(d|~a|b|c)&(d|~a|~b|~c)&(~d|a|b|c)&(~d|a|~b|~c)&(~d|~a|b|~c)&(~d|~a|~b|c)
cnf.add([res, a, b, ~c])
cnf.add([res, a, ~b, c])
cnf.add([res, ~a, b, c])
cnf.add([res, ~a, ~b, ~c])
cnf.add([~res, a, b, c])
cnf.add([~res, a, ~b, ~c])
cnf.add([~res, ~a, b, ~c])
cnf.add([~res, ~a, ~b, c])
return res, res_carry
def cnf_1bitmultiplier(cnf: Formula, a: Variable, b: Variable) -> Variable:
#according to wolfie: CNF | (¬a ∨ ¬b ∨ d) ∧ (a ∨ ¬d) ∧ (b ∨ ¬d)
d = cnf.new_var()
cnf.add([~a, ~b, d])
cnf.add([a, ~d])
cnf.add([b, ~d])
return d
def commander_variable(cnf: Formula, group: List[Variable]) -> Variable:
at_most_one(cnf, group)
var = cnf.new_var()
# var <=> (a or b or c ...)
for i in range(len(group)):
cnf.add([~group[i], var])
clause = group[:]
clause.append(~var)
cnf.add(clause)
return var
def new_bitmap(cnf: Formula, width: int, height: int) -> List[List[Variable]]:
return [[cnf.new_var() for i in range(width)] for j in range(height)]
def new_integer(cnf: Formula, bits: int) -> List[Variable]:
return [cnf.new_var() for i in range(bits)]
