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By Eitan Gurari

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Extra resources for An Introduction to the Theory of Computation

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The program outputs an input value v such that v + 2 also appears in the input. Example: On input "1, 4, 3, 2" 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 the output "1" or the output "2". c. The program outputs a value that does not appear exactly twice in the input. , i = 0, 1, 2, 3, 5, 6, . . ). Moreover, each accepting computation of the program should provide one of these outputs.

L(G3) = (L(G1))* e. 11 Show that from each grammar G1 = a two-nonterminal- symbols grammar G2 = <{S, A}, , P2, S> can be constructed such that L(G1) = L(G2). 5. 13 For each of the following cases find all the possible grammars G that satisfy the case, where G = , S abAS, S ab, bA with N = {S}, = {a, b}, and P being a subset of {S aS}. a. G is a Type 3 grammar. b. G is a Type 2 grammar, but not of Type 3. c. G is a Type 1 grammar, but not of Type 2. 1(a). What are the outputs of P on input "2, 2"?

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. g is the identity function, that is, g(yes) = yes and g(no) = no. 2). 2 Reduction of problem K1 to problem K2. Given an input I, the algorithm B starts by running Tf on I. Then B gives the output I' of Tf to A. Finally B gives the output S' of A to Tg, and assumes the same output S as the one obtained from Tg.

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