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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 have used in de?ning DFAs we shall see that to simulate an NFA one needs only track ?nitely much information about each string. Consider, again, the example in which we modeled the computation of the NFA as a set of automata processing the input synchronously. In order to determine if a string w is accepted by the NFA all we need to do is to track, at each stage of the computation (i.e., at each pre?x of the input), the states of those automata. Since there is never any reason to include more than one automaton for each state, this will just be some subset of Q-in fact, it is easy to see that the set of states after processing w will be just ˆ δ(q0,w). Since Q is ?nite, it has ?nitely many subsets. Thus we can simulate an NFA with state set Q with a DFA that has a state for each subset of Q. The process of constructing a deterministic analog of a non-deterministic machine is known as determinization.
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Lemma 1 A string w ∈ Σ* is accepted by an LTk automaton iff w is the concatenation of the symbols labeling the edges of a path through the LTk transition graph of A from h?, ∅i to
We now add an additional degree of non-determinism and allow transitions that can be taken independent of the input-ε-transitions. Here whenever the automaton is in state 1
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The fundamental idea of strictly local languages is that they are speci?ed solely in terms of the blocks of consecutive symbols that occur in a word. We'll start by considering lan
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Proof (sketch): Suppose L 1 and L 2 are recognizable. Then there are DFAs A 1 = (Q,Σ, T 1 , q 0 , F 1 ) and A 2 = (P,Σ, T 2 , p 0 , F 2 ) such that L 1 = L(A 1 ) and L 2 = L(
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