#Two way Finite State Automation Non-Emptiness

class TwoWayFiniteStateAutomaton:
    def __init__(self, states, alphabet, transitions, start_state, accepting_states):
        self.states = states
        self.alphabet = alphabet
        self.transitions = transitions
        self.start_state = start_state
        self.accepting_states = accepting_states

    def accepts(self, string):
        current_state = self.start_state
        head_position = 0

        while True:
            if current_state in self.accepting_states:
                return True

            if head_position < 0 or head_position >= len(string):
                return False

            symbol = string[head_position]
            direction = self.transitions[current_state].get(symbol, None)

            if direction is None:
                return False

            new_state, movement = direction
            current_state = new_state

            if movement == 'L':
                head_position -= 1
            elif movement == 'R':
                head_position += 1


# Example usage
# Define a two-way finite state automaton
fsa = TwoWayFiniteStateAutomaton(
    states={'q0', 'q1', 'q2'},
    alphabet={'0', '1'},
    transitions={
        'q0': {'0': ('q1', 'R'), '1': ('q2', 'R')},
        'q1': {'0': ('q0', 'R'), '1': ('q1', 'L')},
        'q2': {'0': ('q2', 'R'), '1': ('q1', 'L')}
    },
    start_state='q0',
    accepting_states={'q0'}
)

# Check if the automaton accepts any input string
result = fsa.accepts("1010101")
print(f"Does the automaton accept any input string? {result}")
