Give DFA’s accepting languages over the alphabet Σ = {0, 1, 2, 3, 5}: (a) the set of all strings beginning with a 1, 3 or 5, that, when the string is interpreted as an integer in base 9, is a multiple of 5 plus 2. For example: • strings 13,30

# Define the alphabet alphabet = {'0', '1', '2', '3', '5'} # Define the states states = {'q0', 'q1', 'q2', 'q3', 'q4'} # Define the initial state initial = 'q0' # Define the final state final = 'q4' # Define the transition function def delta (state, symbol): # Check if the symbol is valid if symbol not in alphabet: return None # Check if the state is valid if state not in states: return None # Define the transition rules if state == 'q0': if symbol in {'1', '3', '5'}: return 'q1' else: return None elif state == 'q1': return 'q2' elif state == 'q2': return 'q3' elif state == 'q3': if symbol == '2': return 'q4' else: return 'q2' elif state == 'q4': return None # Define a function to check if a string is accepted by the DFA def accepts (string): # Start from the initial state current = initial # Loop through the string for symbol in string: # Get the next state current = delta (current, symbol) # If there is no next state, reject the string if current is None: return False # Check if the final state is reached return current == final # Test some examples print (accepts ('13')) # True print (accepts ('152')) # True print (accepts ('302')) # False print (accepts ('1234')) # False

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