By Eitan Gurari
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Additional info for An Introduction to the Theory of Computation
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
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.
An Introduction to the Theory of Computation by Eitan Gurari