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Robot Turtle Programs That Return Home Are Not Context-Free

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This document describes a robot turtle that can be given instructions to move up, down, left, or right by a certain distance. A program is a string of these instructions. C is defined as the set of programs that cause the turtle to return to its starting point. The document asks to (a) prove that C is not context-free and (b) provide a formal description of a Turing machine that can determine if a given program is in set C.

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2. There and back again. Imagine a robot turtle that you can give instructions u (go up 1cm),d (go down 1cm),1 (go left 1cm ), r (go right 1cm). A program is a string of instructions. Let C be the set of programs that make the turtle return to its starting point. For example, uurdrdll is in C, as shown in this picture: (a) Prove that C is not context-free. (b) Write a formal description of a Turing machine that decides C.

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  • 1. 2. There and back again. Imagine a robot turtle that you can give instructions u (go up 1cm),d (go down 1cm),1 (go left 1cm ), r (go right 1cm). A program is a string of instructions. Let C be the set of programs that make the turtle return to its starting point. For example, uurdrdll is in C, as shown in this picture: (a) Prove that C is not context-free. (b) Write a formal description of a Turing machine that decides C.