Lecture S1: Sample Lecture. Overview. Lecture T4: What is an algorithm? Turing machine Which problems can be solved on a computer? Not the halting problem. Here’s a question for the student to fill in the answer. Here’s the secret answer. The Main Question. P = NP. NP. P. If P NP.

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Halting Problem. Background - Halting Problem. Common error: Program goes into an infinite loop. Wouldn ’ t it be nice to have a tool that would warn us that our program has this bug?. Example. Infinite loop - we get into a loop but for some reason we never get out of it. while x < 3:

The Halting Problem. Sipser 4.2 (pages 173-182). Taking stock. All languages. Turing-recognizable. ?. D. Turing-decidable. Context-free languages. a n b n c n. Regular languages. 0 n 1 n. 0 * 1 *. Are there problems a computer can’t solve?!. But they seem so powerful…

The Halting Problem. Can we design a program that, given any other program and its input, tells whether that program will halt when run on that input? Output of this program, called HALT, when applied to program P and input I, is “halts” if P(I) eventually halts

The Halting Problem. Acceptance Problem. The Problem: Given a DFA M and an input string x does M accept on input x? We can express this problem with the predicate. The Acceptance Problem is decidable.

The Halting Problem. Chuck Cusack Based on M. Sipser, “Introduction to the Theory of Computation,” Second Edition, Thomson/Course Technology, 2006, Chapter 4.2. An Important Problem. Have you even written a program that ran much longer than you expected?

Halting Problem and TSP. Wednesday, Week 8. Background - Halting Problem. Common error: Program goes into an infinite loop. Wouldn’t it be nice to have a tool that would warn us that our program has this bug? (We could make a lot of money if we could develop such a tool!). Example.

The halting problem - proof. Review. What makes a problem decidable ? 3 properties of an efficient algorithm? What is the meaning of “ complete ”, “ mechanistic ”, and “ deterministic ”? Is the Halting Problem decidable/undecidable? How would you define the Universal Turing Machine ?.

Undecidability and The Halting Problem. CS 130 Theory of Computation HMU Textbook: Chap 9. Problems and Languages. Decision problems can be captured as languages Example:

Decidability and the Halting Problem. Outline. What can be computed? Can we solve all problems? Are there problems we can’t solve? We will look at the more famous halting problem. Decidable Problems. We have now defined the class of all computable algorithms