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By Eitan Gurari

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What are the outputs of P on input "2, 2"? On input "3, 2"? 3 For each of the following cases write a program that corresponds to the case. Assume that the variables have the set of natural numbers as the domain of the variables, and 0 as an initial value. a. The program outputs an input value v such that v + 2 does not appear in the input. Example: On input "1, 4, 2, 3" the program should have an accepting computation with output "3", and an accepting computation with output "4". Moreover, each accepting computation of the program should provide either the output "3" or the output "4".

Problems concerning Grammars Some of the problems concerned with programs can in a similar way be defined also for grammars. The following are some examples of such problems. Membership problem for grammars Domain: { (G, x) | G is a grammar and x is a string in * }. html Is x in L(G) for the given instance (G, x)? Emptiness problem for grammars Domain: { G | G is a grammar }. Question: Does the given grammar define an empty language? Ambiguity problem for grammars Domain: { G | G is a grammar }.

On input "-1, 2, -3"). Intuitively, an accept can be viewed as a halt command that signals a successful completion of a program execution, where the accept can be executed only after the end of the input is reached. Similarly, a reject can be viewed as a halt instruction that signals an unsuccessful completion of a program execution. The requirement that the accept commands be executed only after reading all the input values should cause no problem, because each program can be modified to satisfy this condition.

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