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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.
Let ? ={0,1} design a Turing machine that accepts L={0^m 1^m 2^m } show using Id that a string from the language is accepted & if not rejected .
turing machine
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1. An integer is said to be a “continuous factored” if it can be expresses as a product of two or more continuous integers greater than 1. Example of continuous factored integers
Theorem (Myhill-Nerode) A language L ⊆ Σ is recognizable iff ≡L partitions Σ* into ?nitely many Nerode equivalence classes. Proof: For the "only if" direction (that every recogn
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
Construct a Moore machine to convert a binary string of radix 4.
While the SL 2 languages include some surprisingly complex languages, the strictly 2-local automata are, nevertheless, quite limited. In a strong sense, they are almost memoryless
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