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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.
implementation of operator precedence grammer
The Universality Problem is the dual of the emptiness problem: is L(A) = Σ∗? It can be solved by minor variations of any one of the algorithms for Emptiness or (with a little le
Given any NFA A, we will construct a regular expression denoting L(A) by means of an expression graph, a generalization of NFA transition graphs in which the edges are labeled with
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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
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The k-local Myhill graphs provide an easy means to generalize the suffix substitution closure property for the strictly k-local languages. Lemma (k-Local Suffix Substitution Clo
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