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from pysat.formula import CNF from pysat.solvers import Solver def add_transition(cnf, current, bit, next, var_map, positive_bit=True): """ Helper function to add transition clauses. """ if positive_bit: cnf.append([-var_map[current], var_map[bit], var_map[next]]) else: cnf.append([-var_map[current], -var_map[bit], var_map[next]]) def encode_dfa(t=6): """ Function to encode the DFA into CNF using PySAT. """ cnf = CNF() var_map = {} count = 1 # Create variables for each state at each time step and input bits for step in range(t + 1): # 0 to t (inclusive), where t = 6 for state in ['q0', 'q1', 'q2', 'q3']: var_map[f'{state}_{step}'] = count count += 1 if step < t: var_map[f'bit_{step}'] = count count += 1 # Initial state configuration cnf.append([var_map['q0_0']]) for state in ['q1', 'q2', 'q3']: cnf.append([-var_map[f'{state}_0']]) # Transitions based on the DFA rules for step in range(t): add_transition(cnf, 'q0_' + str(step), 'bit_' + str(step), 'q1_' + str(step + 1), var_map) add_transition(cnf, 'q0_' + str(step), 'bit_' + str(step), 'q0_' + str(step + 1), var_map, False) add_transition(cnf, 'q1_' + str(step), 'bit_' + str(step), 'q2_' + str(step + 1), var_map) add_transition(cnf, 'q1_' + str(step), 'bit_' + str(step), 'q1_' + str(step + 1), var_map, False) add_transition(cnf, 'q2_' + str(step), 'bit_' + str(step), 'q3_' + str(step + 1), var_map) add_transition(cnf, 'q2_' + str(step), 'bit_' + str(step), 'q2_' + str(step + 1), var_map, False) add_transition(cnf, 'q3_' + str(step), 'bit_' + str(step), 'q3_' + str(step + 1), var_map) add_transition(cnf, 'q3_' + str(step), 'bit_' + str(step), 'q3_' + str(step + 1), var_map, False) # Ensure the accepting state is reached cnf.append([var_map['q3_' + str(t)]]) return cnf, var_map def solve_dfa(cnf, var_map, t=6): """ Solving the SAT problem to find accepted strings of length t. """ with Solver(bootstrap_with=cnf.clauses) as solver: if solver.solve(): model = solver.get_model() result = ''.join(['1' if model[var_map[f'bit_{i}']] > 0 else '0' for i in range(t)]) print(f"Accepted string by DFA: {result}") else: print("No solution found, which is unexpected.") def main(): cnf, var_map = encode_dfa() solve_dfa(cnf, var_map) if __name__ == "__main__": main()
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