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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.
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The fact that the Recognition Problem is decidable gives us another algorithm for deciding Emptiness. The pumping lemma tells us that if every string x ∈ L(A) which has length grea
Our primary concern is to obtain a clear characterization of which languages are recognizable by strictly local automata and which aren't. The view of SL2 automata as generators le
For example, the question of whether a given regular language is positive (does not include the empty string) is algorithmically decidable. "Positiveness Problem". Note that
Paths leading to regions B, C and E are paths which have not yet seen aa. Those leading to region B and E end in a, with those leading to E having seen ba and those leading to B no
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In general non-determinism, by introducing a degree of parallelism, may increase the accepting power of a model of computation. But if we subject NFAs to the same sort of analysis
As we are primarily concerned with questions of what is and what is not computable relative to some particular model of computation, we will usually base our explorations of langua
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