By Eitan Gurari
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Extra info for An Introduction to the Theory of Computation
Similarly, u, v, and w are sequences of natural numbers. The configuration (1, <0, 0>, <>, <1, 2, 3>, <>) states that the program is in the first instruction segment, the variables hold the value 0, no input value has been read so far, the rest of the input is "1, 2, 3", and the output is empty. The configuration (5, <3, 2>, <1, 2>, <3>, <3>) states that the program is in the fifth instruction segment, the variable last holds the value 3, the variable value holds the value 2, "1, 2" is the portion of the input consumed so far, the rest of the input contains just the value 3, and the output so far contains only the value 3.
With such an assignment, one of the following cases holds. a. , an assignment of 3 to last on input "1, 2, 3"). b. , an assignment of 1 or 2 to last on input "1, 2, 1"). c. , an assignment of 1 or 2 to last on input "1, 2, 3"). html terminate within the looping instruction upon trying to read beyond the end of the input. With such an assignment, one of the following cases hold. a. , an assignment to last of any natural number that differs from 1 and 2 on input "1, 2, 1"). b. , an assignment of any natural number to last on input " ").
Moreover, each accepting computation of the program should provide one of these outputs. d. The program outputs an input value v that appears as the vth value in the input. Example: On input "3, 2, 1, 2, 5, 3" the program should have an accepting computation with output "2", and an accepting computation with output "5". Moreover, each accepting computation of the program should provide either of these outputs. e. The program outputs an input value v that appears exactly v times in the input.
An Introduction to the Theory of Computation by Eitan Gurari