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2to1FAIntuition

# 2to1FAIntuition - Simulating 2 FSA's with 1 FSA Why the...

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Why the algorithm works! Simulating 2 FSA’s with 1 FSA

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Purpose This presentation attempts to give the reader some intuition as to why 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 works correctly . We use the example from the previous presentation to illustrate this intuition.
Why the Transformation Works a b I,A I,C II,B I,C I,B II,D II,B II,B III,B I,B I,B II,B II,D II,D III,D III,B III,B I,B III,D III,D I,D I,D I,D II,D a b b b a a I III II a,b a a b b a,b A B C D M 1 M 2 Constructed FSA

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Key Idea a b I,A I,C II,B I,C I,B II,D II,B II,B III,B I,B I,B II,B II,D II,D III,D III,B III,B I,B III,D III,D I,D I,D I,D II,D a b b b a a I III II a,b a a b b a,b A B C D M 1 M 2 Constructed FSA In all configurations, the pair of states that M 1 and M 2 are in is exactly the state that the constructed FSA is in.
Initial Configurations a b I,A I,C II,B I,C I,B II,D II,B II,B III,B I,B I,B II,B II,D

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2to1FAIntuition - Simulating 2 FSA's with 1 FSA Why the...

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