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Since the signi?cance of the states represented by the nodes of these transition graphs is arbitrary, we will allow ourselves to use any ?nite set (such as {A,B,C,D,E, F,G,H} or even pairs of the sort we used to label the LTk transition graphs) to represent them. The key characteristics of these graphs are the fact that the state set encodes everything that is signi?cant about the computation and the fact that there are ?nitely many of those states. For that reason, the corresponding automata are known as Finite State Automata (FSAs). These come in two main varieties, Deterministic Finite State Automata (DFAs) and Non-Deterministic Finite State Automata (NFAs). We will focus initially on the deterministic variety. When we are talking about ?nite state automata in general, without regard to whether they are deterministic or not, we will use the term FSA.
phases of operational reaserch
Computation of a DFA or NFA without ε-transitions An ID (q 1 ,w 1 ) computes (qn,wn) in A = (Q,Σ, T, q 0 , F) (in zero or more steps) if there is a sequence of IDs (q 1
For every regular language there is a constant n depending only on L such that, for all strings x ∈ L if |x| ≥ n then there are strings u, v and w such that 1. x = uvw, 2. |u
A finite, nonempty ordered set will be called an alphabet if its elements are symbols, or characters. A finite sequence of symbols from a given alphabet will be called a string ove
The computation of an SL 2 automaton A = ( Σ, T) on a string w is the maximal sequence of IDs in which each sequential pair of IDs is related by |- A and which starts with the in
The universe of strings is a very useful medium for the representation of information as long as there exists a function that provides the interpretation for the information carrie
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De?nition Deterministic Finite State Automaton: For any state set Q and alphabet Σ, both ?nite, a ?nite state automaton (FSA) over Q and Σ is a ?ve-tuple (Q,Σ, T, q 0 , F), w
Another way of interpreting a strictly local automaton is as a generator: a mechanism for building strings which is restricted to building all and only the automaton as an inexh
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