An Introduction to the Theory of Computation - download pdf or read online

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By Eitan Gurari

ISBN-10: 0716781824

ISBN-13: 9780716781820

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Example text

The program outputs an input value v that appears exactly v times in the input. Example: On input "3, 2, 1, 2, 5, 3" the program should have an accepting computation with output "1", and an accepting computation with output "2". Moreover, each accepting computation of the program should provide either of these outputs. f. The program accepts exactly those inputs whose values cannot be sorted into a sequence of consecutive numbers. Example: The program should accept the input "1, 2, 1", and the input "1, 4, 2".

4 Find all the derivations of length 3 at most that start at S in the grammar whose production rules are listed below. 5 For each of the following sets of production rules P find all the strings of length 4 or less in the language generated by the grammar . 6 Give two parse trees for the string aababb in the grammar G = , whose production rules are listed below. 7 Consider the grammar G = for arithmetic expressions, where N = {E, T, F}, *, (, ), a}, and P is the set consisting of the following production rules.

Xn) with variables x1, . . , xn whether or not there exist 1, . . , n such that Q( 1, . . , n) = 0. A LOOP program is a program that consists only of instructions of the form x 0, x y, x x + 1, and do x end. The variables can hold only natural numbers. can be any sequence of instructions. An execution of do x end causes the execution of for a number of times equal to the value of x upon encountering the do. Each LOOP program has a distinct set of variables that are initialized to hold the input values.

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An Introduction to the Theory of Computation by Eitan Gurari


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