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Unformatted text preview: Multi State Machines a.k.a.: The Powerset Construction; The Subset Construction Timo K otzing March 3, 2009 General Idea Given an NFA M = ( A , Q , , F , q ), we define the multi state machine M for M as described below. This multi state machine M will be a DFA accepting the same language as M . I M has one state for every set of states that M could be in. I M changes from a set of states { q 1 , . . . , q n } when seeing a symbol x so that the new state is exactly the set of all those states reachable in one xstep from any of the states q 1 ,. . . , q n . I M has as its initial state the set { q } . I When constructing M , we omit all unreachable states. Timo K otzing Multi State Machines General Idea Given an NFA M = ( A , Q , , F , q ), we define the multi state machine M for M as described below. This multi state machine M will be a DFA accepting the same language as M . I M has one state for every set of states that M could be in. I M changes from a set of states { q 1 , . . . , q n } when seeing a symbol x so that the new state is exactly the set of all those states reachable in one xstep from any of the states q 1 ,. . . , q n . I M has as its initial state the set { q } . I When constructing M , we omit all unreachable states. Timo K otzing Multi State Machines General Idea Given an NFA M = ( A , Q , , F , q ), we define the multi state machine M for M as described below. This multi state machine M will be a DFA accepting the same language as M . I M has one state for every set of states that M could be in. I M changes from a set of states { q 1 , . . . , q n } when seeing a symbol x so that the new state is exactly the set of all those states reachable in one xstep from any of the states q 1 ,. . . , q n . I M has as its initial state the set { q } . I When constructing M , we omit all unreachable states. Timo K otzing Multi State Machines General Idea Given an NFA M = ( A , Q , , F , q ), we define the multi state machine M for M as described below. This multi state machine M will be a DFA accepting the same language as M . I M has one state for every set of states that M could be in. I M changes from a set of states { q 1 , . . . , q n } when seeing a symbol x so that the new state is exactly the set of all those states reachable in one xstep from any of the states q 1 ,. . . , q n . I M has as its initial state the set { q } ....
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This note was uploaded on 02/01/2012 for the course CISC 303 taught by Professor Carberry,m during the Spring '08 term at University of Delaware.
 Spring '08
 Carberry,M

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