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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.
draw pda for l={an,bm,an/m,n>=0} n is in superscript
We will specify a computation of one of these automata by specifying the pair of the symbols that are in the window and the remainder of the string to the right of the window at ea
De?nition Instantaneous Description of an FSA: An instantaneous description (ID) of a FSA A = (Q,Σ, T, q 0 , F) is a pair (q,w) ∈ Q×Σ* , where q the current state and w is the p
Computations are deliberate for processing information. Computability theory was discovered in the 1930s, and extended in the 1950s and 1960s. Its basic ideas have become part of
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A.(A+C)=A
Our DFAs are required to have exactly one edge incident from each state for each input symbol so there is a unique next state for every current state and input symbol. Thus, the ne
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We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
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