By Eitan Gurari

ISBN-10: 0716781824

ISBN-13: 9780716781820

**Read Online or Download An Introduction to the Theory of Computation PDF**

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**Extra resources for An Introduction to the Theory of Computation **

**Example text**

Xm) then portion of a conditional if instruction do portion of a looping instruction until Q(x1, . . , xm) portion of a looping instruction Conditional accept instruction Reject instruction Consider a program P that has k instruction segments, m variables, and a domain of variables that is denoted by D. html k, x is a sequence of m values from D, and u, v, and w are sequences of values from D. Intuitively, a configuration (i, x, u, v, w) says that P is in its ith instruction segment, its jth variable contains the jth value of x, u is the portion of the input that has already been read, the leftover of the input is v, and the output so far is w.

1 Let be the set { m | m = 2i for some integer i }. The problem of exponentiation of numbers from is reducible to the problem of multiplication of integer numbers. 2 Let KØ and K be the emptiness problem and the equivalence problem for programs, respectively. Then KØ is reducible to K by functions f and g of the following form. html whose value at program P is the pair of programs (P, PØ). PØ is a program that accepts no input, for example, the program that consists only of the instruction reject.

Trying to divide by 0). 2. 2 Two deterministic programs. Assume that the programs have the set of integers for the domains of their variables, with 0 as initial value. 2(a) has one execution sequence. In each execution sequence the program provides an output that is equal to the input. All the execution sequences of the program terminate due to the execution of the conditional accept instruction. On input "1, 2" the execution sequence repeatedly executes for three times the body of the deterministic looping instruction.

### An Introduction to the Theory of Computation by Eitan Gurari

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