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When we say "solved algorithmically" we are not asking about a speci?c programming language, in fact one of the theorems in computability is that essentially all reasonable programming languages are equivalent in their power. Rather, we want to know if there is an algorithm for solving it that can be expressed in any rigorous way at all. Similarly, we are not asking about whether the problem can be solved on any particular computer, but whether it can be solved by any computing mechanism, including a human using a pencil and paper (even a limitless supply of paper).
What we need is an abstract model of computation that we can treat in a rigorous mathematical way. We'll start with the obvious model:
Here a computer receives some input (an instance of a problem), has some computing mechanism, and produces some output (the solution of that instance). We will refer to the con?guration of the computing mechanism at a given point in it's processing as its internal state. Note that in this model the computer is not a general purpose device: it solves some speci?c problem. Rather, we consider a general purpose computer and a program to both be part of a single machine. The program, in essence, specializes the computer to solve a particular problem.
Give DFA''s accepting the following languages over the alphabet {0,1}: i. The set of all strings beginning with a 1 that, when interpreted as a binary integer, is a multiple of 5.
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 langua
For every regular language there is a constant n depending only on L such that, for all strings x ∈ L if |x| ≥ n then there are strings u, v and w such that 1. x = uvw, 2. |u
The fact that regular languages are closed under Boolean operations simpli?es the process of establishing regularity of languages; in essence we can augment the regular operations
Theorem The class of recognizable languages is closed under Boolean operations. The construction of the proof of Lemma 3 gives us a DFA that keeps track of whether or not a give
Strictly 2-local automata are based on lookup tables that are sets of 2-factors, the pairs of adjacent symbols which are permitted to occur in a word. To generalize, we extend the
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how to find whether the language is cfl or not?
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So we have that every language that can be constructed from SL languages using Boolean operations and concatenation (that is, every language in LTO) is recognizable but there are r
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