Explanation Given information: Concept used: If the quotient transition diagram of the two automata are same then the two automata are equivalent. Calculation: For A : 0 − Equivalence classes - Two states are zero equivalent if both are accepting states or both are non-accepting states. Therefore, the 0-equivalance classes are: { s 1 , s 2 , s 4 , s 5 } , { s 0 , s 3 } . 1 − Equivalence classes — Two states are 1 − equivalent if, and only if they are 0 − equivalent and, after input of any symbol, their next state are 0 − equivalent. Therefore, the 1 − equivalence classes are: { s 1 , s 2 } , { s 4 , s 5 } , { s 0 , s 3 } 2 − Equivalence classes — two states are called 2 − equivalent if, 2 − and only ¡f they are 1 − equivalent and. after input of any symbol, their next state are 1 − equivalent. Therefore the 2 − equivalent classes are: { s 1 } , { s 2 } , { s 4 , s 5 } , { s 0 , s 3 } 3 − Equivalence classes — two states are called 3 − equivalent if, and only if they are 2 − equivalent and. after input of any symbol, their next state are 2 − equivalent

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Author: EPP

Publisher: CENGAGE L

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Chapter 12.3, Problem 8ES

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Are automata A−,A−' equivalent.

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Are automata A − , A − ' equivalent.

Solution Summary: The author explains that the quotient transition diagram of the two automata are equivalent.

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Are automata A−,A−' equivalent.

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