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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()
```