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# Simulating 2 FSA’s with 1 FSA - PowerPoint PPT Presentation

Simulating 2 FSA’s with 1 FSA. Purpose. This presentation presents an example execution of the algorithm which takes as input two FSA’s and produces as output an FSA which “simulates” both input FSA’s on any input string Algorithm Specification Input: FSA’s M 1 and M 2 Output: FSA M 3.

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### Simulating 2 FSA’s with 1 FSA

• This presentation presents an example execution of the algorithm which takes as input two FSA’s and produces as output an FSA which “simulates” both input FSA’s on any input string

• Algorithm Specification

• Input: FSA’s M1 and M2

• Output: FSA M3

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The two input FSA’s

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M1

M2

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Initialization

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The initial state of the output FSA M3 is the ordered pair of the initial states of M1 and M2.

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Expand State I,A

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Expand State I,C

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Expand State II,B

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Expand State I,B

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Expand State II,D

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Expand State III,B

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Expand State III,D

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Expand State I,D

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No More New States

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Determining Final States

Set Intersection

Both input machines should accept in order for new machine to accept

The one accepting state of the new machine M3 is I,D

Set Union

If either input machine accepts, new machine should accept

The six accepting states of the new machine M3 are I,A; I,C; I,B; II,D; III,D; I,D

Set Difference:

M1 should accept but M2 should not

The three accepting states of the new machine M3 are I,A; I,C; I,B

Symmetric Difference:

M1 should accept but M2 should not or M2 should accept but M1 should not

The five accepting states of the new machine M3 are I,A; I,C; I,B; II,D; III,D