## Determining Whether Path Turing Machine Homework Solution.

In computational complexity theory, NL-complete is a complexity class containing the languages that are complete for NL, the class of decision problems that can be solved by a nondeterministic Turing machine using a logarithmic amount of memory space.

Alternatively, we can think of a nondeterministic Turing machine as a deterministic Turing machine with an auxiliary input of polynomial length which tells it which computation path to choose. The original machine accepts an input if there exists an auxiliary input which causes the new machine to accept.

Of the top of my head: If your machine can simulate one of the known Turing machine equivalent machines, then your machine is also Turing machine equivalent. Probably the easiest way to go about doint something like this. EDIT: I am not implying that this is a requirement for a machine to be Turing machine equivalent, alltough it might be.

The Halting Problem for Turing Machines We can use the results of the previous section to obtain a sharpened form of the unsolvability of the halting problem. By the halting problem for a fixed given Turing machine we mean the problem of finding an algorithm to determine whether will eventually halt starting with a given configuration.

Solutions to Homework 7 (Part of this solution was provided by Andrew Shilliday) Problems. Prove that the problem of determining whether for a Turing machine M there is some input string for which M halts is undecidable. Halting Problem machine. Let’s call the problem for which we want to prove it is undecidable as the “any string” problem.

Let P be any nontrivial property of the language of a Turing machine. Prove that the problem of determining whether a given Turing machine’s language has property P is undecidable. In more formal terms, let P be a language consisting of Turing machine descriptions where P fulfills two conditions.

Handout 5: Homework 3 Instructor: Susan Hohenberger TA: Rebecca Shapiro This assignment is due by the start of lecture on Thursday, October 16. 1. (25 points) (from Sipser 5.13) A useless state in a Turing machine is one that is never entered on any input string. Consider the problem of determining whether a Turing machine has any useless states.