state-minimize

state-minimize - 8b: State Minimization One obvious way to...

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8b: State Minimization One obvious way to reduce the number of states is to eliminate any states that are not reachable from the start state. Hereafter, we shall assume that all states in the given DFA M are reachable from the start state. Let M =( K. Σ ,δ,s,F )beaDFA . De±ne a relation A M K × Σ as follows: ( q, w ) A M if and only if w drives M from q to an accepting state. That is, ( ) A M if and only if ( ) ± M ( f, e )for some f F . Defnition Two states q, p K are equivalent, denoted q p , if the following holds: for all z Σ , ( q, z ) A M if and only if ( p, z ) A M . i.e., all strings z drive M from both p and q to some ±nal state(s) or both to some non-±nal state(s). Note that is an equivalence relation (i.e., reflexive, sym- metric, and transitive) thus it induces a partition on the 1
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set K . 2
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Constructing minimum-state automata Given a DFA M , there exists an algorithm that construct a minimum-state automaton M ± such that L ( M ± )= L ( M ).
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This note was uploaded on 09/22/2011 for the course COMP 272 taught by Professor Prof.tai during the Spring '10 term at HKUST.

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state-minimize - 8b: State Minimization One obvious way to...

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