def cfpq_hellings(g: LabelGraph, cfg: GrammarCNF):
num_vert = g.num_vert
start_sym = cfg.start_symbol
result = LabelGraph()
result.num_vert = num_vert
m = deque()
for variable in cfg.variables:
result.graph_dict[variable] = Matrix.sparse(BOOL, num_vert, num_vert)
if cfg.generate_epsilon():
for v in range(num_vert):
result.graph_dict[start_sym][v, v] = True
for label in g.graph_dict:
term = Terminal(label)
result.graph_dict[term] = g.graph_dict[label].dup()
for v_from, v_to in g.get_edges(label):
for production in cfg.productions:
if (len(production.body) == 1 and production.body[0] == term):
head = production.head
result.graph_dict[head][v_from, v_to] = True
for label in result.graph_dict:
for i, j in result.get_edges(label):
m.append((label, i, j))
# 3rd step: cfpq on modified matrix
while m:
var, v, u = m.popleft()
for var_left in result.graph_dict:
for v_new, v_ in result.get_edges(var_left):
if (v_ == v):
for production in cfg.pair_productions:
if (production.body[1] == var
and production.body[0] == var_left):
if (v_new, u) not in result.get_edges(
production.head):
result.graph_dict[production.head][v_new,
u] = True
m.append((production.head, v_new, u))
for var_right in result.graph_dict:
for u_, u_new in result.get_edges(var_right):
if (u_ == u):
for production in cfg.pair_productions:
if (production.body[1] == var_right
and production.body[0] == var):
if (v, u_new) not in result.get_edges(
production.head):
result.graph_dict[production.head][
v, u_new] = True
m.append((production.head, v, u_new))
return result.graph_dict[start_sym]
def cfpq_matrix_mult(g: LabelGraph, cfg: GrammarCNF):
num_vert = g.num_vert
if (num_vert == 0):
return Matrix.sparse(BOOL, num_vert, num_vert)
result = LabelGraph()
start_sym = cfg.start_symbol
result.num_vert = num_vert
for variable in cfg.variables:
result.graph_dict[variable] = Matrix.sparse(BOOL, num_vert, num_vert)
for label in g.graph_dict:
term = Terminal(label)
result.graph_dict[term] = g.graph_dict[label].dup()
for v_from, v_to in g.get_edges(label):
for production in cfg.productions:
if (len(production.body) == 1 and production.body[0] == term):
head = production.head
result.graph_dict[head][v_from, v_to] = True
if cfg.generate_epsilon():
for v in g.vertices:
result.graph_dict[start_sym][v, v] = True
matrix_changing = True
with semiring.LOR_LAND_BOOL:
while matrix_changing:
matrix_changing = False
for production in cfg.pair_productions:
head = production.head
body = production.body
prev_nvals = result.graph_dict[head].nvals
tmp = result.graph_dict[body[0]] @ result.graph_dict[body[1]]
result.graph_dict[head] = result.graph_dict[head] + tmp
if (prev_nvals != result.graph_dict[head].nvals):
matrix_changing = True
return result.graph_dict[start_sym]