def __init__(self):

super().__init__()

self.rename_map = dict()

@classmethod

def from_lba(cls, lba: LBA):

grammar = GrammarType1()

grammar.tm = lba

grammar.terminals = {"1", "=", "*"}

grammar.variables.add("A1")

grammar.variables.add("A2")

for a in lba.alphabet:

for x in lba.tape_symbols - {"$", "#"}:

for q in lba.states:

grammar.variables.add(f"[{q}, #, {x}, {a}, $]")

grammar.variables.add(f"[#, {q}, {x}, {a}, $]")

grammar.variables.add(f"[#, {x}, {a}, {q}, $]")

grammar.variables.add(f"[{q}, {x}, {a}]")

grammar.variables.add(f"[{q}, {x}, {a}, $]")

grammar.variables.add(f"[{x}, {a}, {q}, $]")

grammar.variables.add(f"[#, {x}, {a}]")

grammar.variables.add(f"[{x}, {a}]")

grammar.variables.add(f"[{x}, {a}, $]")

grammar.start_symb = "A1"

for a in lba.alphabet:

for x in lba.tape_symbols - {"$", "#"}:

# 1

grammar.productions.append((["A1"], [f"[{lba.start_state}, #, {a}, {a}, $]"]))

# 2

for key, value in lba.transitions.items():

key1, key2 = key

value1, value2, value3 = value

if key2 == '#' and value2 == '#' and value3 == Arrow.Right and key1 not in lba.final_states:

grammar.productions.append(([f"[{key1}, #, {x}, {a}, $]"], [f"[#, {value1}, {x}, {a}, $]"]))

if key2 not in ['#', '$'] and value2 not in ['#', '$'] and value3 == Arrow.Left and key1 not in lba.final_states:

grammar.productions.append(([f"[#, {key1}, {key2}, {a}, $]"], [f"[{value1}, #, {value2}, {a}, $]"]))

if key2 not in ['#', '$'] and value2 not in ['#', '$'] and value3 == Arrow.Right and key1 not in lba.final_states:

grammar.productions.append(([f"[#, {key1}, {key2}, {a}, $]"], [f"[#, {value2}, {a}, {value1}, $]"]))

if key2 == '$' and value2 == '$' and value3 == Arrow.Left and key1 not in lba.final_states:

grammar.productions.append(([f"[#, {x}, {a}, {key1}, $]"], [f"[#, {value1}, {x}, {a}, $]"]))

# 3

for q in lba.final_states:

grammar.productions.append(([f"[{q}, #, {x}, {a}, $]"], [a]))

grammar.productions.append(([f"[#, {q}, {x}, {a}, $]"], [a]))

grammar.productions.append(([f"[#, {x}, {a}, {q}, $]"], [a]))

# 4

q_start = lba.start_state

grammar.productions.append((["A1"], [f"[{q_start}, #, {a}, {a}]", "A2"]))

grammar.productions.append((["A2"], [f"[{a}, {a}]", "A2"]))

grammar.productions.append((["A2"], [f"[{a}, {a}, $]"]))

# 5

for key, value in lba.transitions.items():

key1, key2 = key

value1, value2, value3 = value

if key2 == '#' and value2 == '#' and value3 == Arrow.Right and key1 not in lba.final_states:

grammar.productions.append(([f"[{key1}, #, {x}, {a}]"], [f"[#, {value1}, {x}, {a}]"]))

if key2 not in ['#', '$'] and value2 not in ['#', '$'] and value3 == Arrow.Left and key1 not in lba.final_states:

grammar.productions.append(([f"[#, {key1}, {key2}, {a}]"], [f"[{value1}, #, {value2}, {a}]"]))

if key2 not in ['#', '$'] and value2 not in ['#', '$'] and value3 == Arrow.Right and key1 not in lba.final_states:

for b in lba.alphabet:

grammar.productions.append(([f"[#, {key1}, {key2}, {a}]", f"[{x}, {b}]"],

[f"[#, {value2}, {a}]", f"[{value1}, {x}, {b}]"]))

# 6

for key, value in lba.transitions.items():

key1, key2 = key

value1, value2, value3 = value

if key2 not in ['#', '$'] and value2 not in ['#', '$'] and value3 == Arrow.Right and key1 not in lba.final_states:

for b in lba.alphabet:

grammar.productions.append(([f"[{key1}, {key2}, {a}]", f"[{x}, {b}]"],

[f"[{value2}, {a}]", f"[{value1}, {x}, {b}]"]))

if key2 not in ['#', '$'] and value2 not in ['#', '$'] and value3 == Arrow.Left and key1 not in lba.final_states:

for b in lba.alphabet:

grammar.productions.append(([f"[{x}, {b}]", f"[{key1}, {key2}, {a}]"],

[f"[{value1}, {x}, {b}]", f"[{value2}, {a}]"]))

if key2 not in ['#', '$'] and value2 not in ['#', '$'] and value3 == Arrow.Right and key1 not in lba.final_states:

for b in lba.alphabet:

grammar.productions.append(([f"[{key1}, {key2}, {a}]", f"[{x}, {b}, $]"],

[f"[{value2}, {a}]", f"[{value1}, {x}, {b}, $]"]))

if key2 not in ['#', '$'] and value2 not in ['#', '$'] and value3 == Arrow.Left and key1 not in lba.final_states:

for b in lba.alphabet:

grammar.productions.append(([f"[#, {x}, {b}]", f"[{key1}, {key2}, {a}]"],

[f"[#, {value1}, {x}, {b}]", f"[{value2}, {a}]"]))

# 7

for key, value in lba.transitions.items():

key1, key2 = key

value1, value2, value3 = value

if key2 not in ['#', '$'] and value2 not in ['#', '$'] and value3 == Arrow.Right and key1 not in lba.final_states:

grammar.productions.append(([f"[{key1}, {key2}, {a}, $]"], [f"[{value2}, {a}, {value1}, $]"]))

if key2 == '$' and value2 == '$' and value3 == Arrow.Left and key1 not in lba.final_states:

grammar.productions.append(([f"[{x}, {a}, {key1}, $]"], [f"[{value1}, {x}, {a}, $]"]))

if key2 not in ['#', '$'] and value2 not in ['#', '$'] and value3 == Arrow.Left and key1 not in lba.final_states:

for b in lba.alphabet:

grammar.productions.append(([f"[{x}, {b}]", f"[{key1}, {key2}, {a}, $]"],

[f"[{value1}, {x}, {b}]", f"[{value2}, {a}, $]"]))

# 8

for q in lba.final_states:

grammar.productions.append(([f"[{q}, #, {x}, {a}]"], [a]))

grammar.productions.append(([f"[#, {q}, {x}, {a}]"], [a]))

grammar.productions.append(([f"[{q}, {x}, {a}]"], [a]))

grammar.productions.append(([f"[{q}, {x}, {a}, $]"], [a]))

grammar.productions.append(([f"[{x}, {a}, {q}, $]"], [a]))

# 9

for b in lba.alphabet:

grammar.productions.append(([a, f"[{x}, {b}]"], [a, b]))

grammar.productions.append(([a, f"[{x}, {b}, $]"], [a, b]))

grammar.productions.append(([f"[{x}, {a}]", b], [a, b]))

grammar.productions.append(([f"[#, {x}, {a}]", b], [a, b]))

unique_prod = []

for x in grammar.productions:

if x not in unique_prod:

unique_prod.append(x)

i = 1

for x in grammar.productions:

part1, part2 = x

for item in part1 + part2:

if item[0] == "[":

if item not in grammar.rename_map.keys():

grammar.rename_map[item] = f"S{i}"

i += 1

for i in range(len(grammar.productions)):

for j in range(len(grammar.productions[i][0])):

if grammar.productions[i][0][j][0] == "[":

grammar.productions[i][0][j] = grammar.rename_map[grammar.productions[i][0][j]]

for j in range(len(grammar.productions[i][1])):

if grammar.productions[i][1][j][0] == "[":

grammar.productions[i][1][j] = grammar.rename_map[grammar.productions[i][1][j]]

grammar.productions = unique_prod

return grammar

def contains(self, word: str):

queue = Queue()

prods_list = [([self.start_symb], None)]

prods_list.append(([self.rename_map[f"[{self.tm.start_state}, #, {word[0]}, {word[0]}]"], "A2"],

(["A1"], [self.rename_map[f"[{self.tm.start_state}, #, {word[0]}, {word[0]}]"], "A2"])))

tmp_sentence = [self.rename_map[f"[{self.tm.start_state}, #, {word[0]}, {word[0]}]"], "A2"]

for item in word[1:-1]:

tmp_sentence = tmp_sentence[:-1] + [self.rename_map[f"[{item}, {item}]"], "A2"]

prods_list.append((tmp_sentence,

(["A2"], [self.rename_map[f"[{item}, {item}]"], "A2"])))

tmp_sentence = tmp_sentence[:-1] + [self.rename_map[f"[{word[-1]}, {word[-1]}, $]"]]

prods_list.append((tmp_sentence,

(["A2"], [self.rename_map[f"[{word[-1]}, {word[-1]}, $]"]])))

queue.put((tmp_sentence, prods_list))

visited_sentences = []

while queue.qsize() > 0:

sentence, prods_consequence = queue.get()

sent_str = ",".join(sentence)

if sent_str in visited_sentences:

continue

else:

visited_sentences.append(sent_str)

for prod in self.productions:

head, body = prod

indexes = Grammar.get_subsequence(head, sentence)

if len(indexes) == 0:

continue

for ind_start, ind_end in indexes:

res_part1 = [sentence[i] for i in range(ind_start)]

res_part2 = body

res_part3 = [sentence[i] for i in range(ind_end, len(sentence))]

new_sentence = res_part1 + res_part2 + res_part3

new_prods_consequence = prods_consequence.copy()

new_prods_consequence.append((new_sentence, prod))

queue.put((new_sentence, new_prods_consequence))

if "".join(new_sentence) == word:

return new_sentence, new_prods_consequence