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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 languages on abstract automata. These are "checking machines" in which the input is a string over some speci?c alphabet. We say such a machine accepts a string if the computation on that input results in a TRUE output. We say that it recognizes a language if it accepts all and only the strings in that language.
Generally, in exploring a class of languages, we will de?ne a class of automata that recognize all and only the languages in the class-a particular sort of automaton, the peculiarities of which exactly capture the characteristics of the class of languages. We say the class of automata characterizes the class of languages. We will actually go about this both ways. Sometimes we will de?ne the class of languages ?rst, as we have in the case of the Finite Languages, and then look for a class of automata that characterize it. Other times we will specify the automata ?rst (by, for instance, modifying a previously de?ned class) and will then look for the class of languages it characterizes. We will use the same general methods no matter which way we are working.
The de?nition of the class of automata will specify the resources the machine provides along with a general algorithm for employing those resources to recognize languages in the class. The details that specialize that algorithm for a particular language are left as parameters. The only restriction on the nature of these parameters is that there must be ?nitely many of them and they must range over ?nite objects.
Myhill graphs also generalize to the SLk case. The k-factors, however, cannot simply denote edges. Rather the string σ 1 σ 2 ....... σ k-1 σ k asserts, in essence, that if we hav
State & prove pumping lemma for regular set. Show that for the language L={ap |p is a prime} is not regular
The Equivalence Problem is the question of whether two languages are equal (in the sense of being the same set of strings). An instance is a pair of ?nite speci?cations of regular
constract context free g ={ a^n b^m : m,n >=0 and n
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
You are required to design a system that controls the speed of a fan's rotation. The speed at which the fan rotates is determined by the ambient temperature, i.e. as the temperatur
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Let there L1 and L2 . We show that L1 ∩ L2 is CFG . Let M1 be a decider for L1 and M2 be a decider for L2 . Consider a 2-tape TM M: "On input x: 1. copy x on the second
When an FSA is deterministic the set of triples encoding its edges represents a relation that is functional in its ?rst and third components: for every q and σ there is exactly one
Normal forms are important because they give us a 'standard' way of rewriting and allow us to compare two apparently different grammars G1 and G2. The two grammars can be shown to
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