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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.
Another way of representing a strictly 2-local automaton is with a Myhill graph. These are directed graphs in which the vertices are labeled with symbols from the input alphabet of
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Generate 100 random numbers with the exponential distribution lambda=5.0.What is the probability that the largest of them is less than 1.0?
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
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The Last Stop Boutique is having a five-day sale. Each day, starting on Monday, the price will drop 10% of the previous day’s price. For example, if the original price of a product
We represented SLk automata as Myhill graphs, directed graphs in which the nodes were labeled with (k-1)-factors of alphabet symbols (along with a node labeled ‘?' and one labeled
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
Different types of applications and numerous programming languages have been developed to make easy the task of writing programs. The assortment of programming languages shows, dif
The path function δ : Q × Σ* → P(Q) is the extension of δ to strings: This just says that the path labeled ε from any given state q goes only to q itself (or rather never l
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