PPT-What’s Decidable for

Asynchronous Programs Rupak Majumdar Max Planck Institute for Software Systems Joint work with Pierre Ganty Michael Emmi Fernando Rosa Velardo Sequential Imperative Programs Program . In the case of deterministic 64257nite au tomata problems like equivalence can be solved even in polynomial time Also there are e64259cient parsing algorithms for context free grammars If necessary we may brie64258y review some material on regular a of auxiliary . storage. Gennaro. . Parlato. . (University of Southampton, UK). Joint work: . P. . Madhusudan. – UIUC, USA . . . Automata with aux storage. Turing machines = finite automata + 1 infinite tape. Sipser. 4.1 (pages 165-173). Hierarchy of languages. All languages. Turing-recognizable. Turing-decidable. Context-free languages. Regular languages. 0. n. 1. n. a. n. b. n. c. n. D. 0. *. 1. *. Describing Turing machine input. Unit 9: . Undecidability. [Slides . adapted from . Amos Israeli’s]. Limits to computation. There are problems for which there cannot be an algorithm, provably.. Undecidable problems. There are problems for which polynomial-time algorithms are unlikely to exist. (Section 5.1). H. éctor Muñoz-Avila. Summary of Previous Lectures. The Halting problem is undecidable:. HALT . = {<. M,w. > | M is a Turing machine, w .  *, M halts on input w. }. The proof involved a paradox. Theory of Computation. Alexander . Tsiatas. Spring 2012. Theory of Computation Lecture Slides by Alexander . Tsiatas. is licensed under a Creative Commons Attribution-. NonCommercial. -. ShareAlike. (Chapter . 4.2). H. éctor Muñoz-Avila. Undecidable Languages. We are going to make 2 proofs:. An . existence. proof:. We show that a . language L . must exist that cannot be . decided/recognized with . bn wwR Our main goal is to exhibit a language L that Sipser. 5.3 (pages 206-210). Computable functions. Definition 5.17: A function . f:Σ. *→. Σ. *. is a . computable function. if some Turing machine . M. , on every input . w. , halts with just . Theory of Computation. Alexander . Tsiatas. Spring 2012. Theory of Computation Lecture Slides by Alexander . Tsiatas. is licensed under a Creative Commons Attribution-. NonCommercial. -. ShareAlike. F. O. P. L. is . undecidable. . sketch. of proof by reduction . to Halting . problem. s. CS3518. Buchi. , J.R. (1962) “Turing machines and the . Entscheidungsproblem. ,. ”. Boolos. , G. & Jeffrey, R. (1989) “Chapter 10: First-Order Logic is . Decidability Concept 4.1. The Halting Problem 4.2. P vs. NP 7.2 and 7.3. NP-completeness & . Cook-Levin Theorem 7.4. Review: Turing Machines in a nutshell. Church-Turing Thesis. Turing Machine . Fall 2017. http://cseweb.ucsd.edu/. classes/fa17/cse105-a/. Today's learning goals . Sipser Ch 4.1. Explain what it means for a problem to be decidable.. Justify the use of encoding.. Give examples of decidable problems.. Umang Mathur. P. Madhusudan. Mahesh Viswanathan. Existing Decidable Classes. Program Verification. Unnatural program models. Undecidable. In general, verification over infinite domains is undecidable.