Question

Draw a deterministic finite state machine for the input alphabet A where A = {1, 2, 3, 4, 5} that recognises exactly all strings that include the 2 letter string 42 exactly once. For example, the machine will accept the string 54214 but reject the strings 432 and 421421.

Answer #1

The task is to construct a DFA(deterministic finite state) machine for the the input alphabet A = {1,2,3,4,5} that recognises exactly strings that include string "42" exactly once.

Alphabet A = {1,2,3,4,5}

The above DFA has been constructed using a simulator for better understanding.

Here "start" is the starting state.

"s1", "s2" are the accepting states.

"s3" is the dead state.

TRANSITION TABLE

1 | 2 | 3 | 4 | 5 | |

start | start | start | start | s0 | start |

s0 | start | s1 | start | s0 | start |

s1 | s1 | s1 | s1 | s2 | s1 |

s2 | s2 | s3 | s2 | s2 | s2 |

s3 | s3 | s3 | s3 | s3 | s3 |

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Automata Theory and Formal Languages
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DFA for Number of a(w) mod 2 = 0 orNumber of
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