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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.
State and Prove the Arden's theorem for Regular Expression
#Your company has 25 licenses for a computer program, but you discover that it has been copied onto 80 computers. You informed your supervisor, but he/she is not willing to take an
We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
construct a social network from the real-world data, perform some simple network analyses using Gephi, and interpret the results.
. On July 1, 2010, Harris Co. issued 6,000 bonds at $1,000 each. The bonds paid interest semiannually at 5%. The bonds had a term of 20 years. At the time of issuance, the market r
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
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
One might assume that non-closure under concatenation would imply non closure under both Kleene- and positive closure, since the concatenation of a language with itself is included
Let L 3 = {a i bc j | i, j ≥ 0}. Give a strictly 2-local automaton that recognizes L 3 . Use the construction of the proof to extend the automaton to one that recognizes L 3 . Gi
Sketch an algorithm for the universal recognition problem for SL 2 . This takes an automaton and a string and returns TRUE if the string is accepted by the automaton, FALSE otherwi
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