PPT-Decidable

Logics Combining Heap Structures and Data Gennaro Parlato LIAFA Paris France Joint work with P Madhusudan Xiaokang Qie . A is a decidable language q0 0111 q0 q1q2q3 01 q0q2q3 0111 Decidable Problems q0 A B is an NFA B accepts w NFA Th A is decidable NFA q1q2q3 01 q0 q0 q1 brPage 2br Decidable Problems DFA E B is a DFA LB is nonempty Th E is decidable DFA L 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. 1. . Theory of Computation Peer Instruction Lecture Slides by . Dr. Cynthia Lee, UCSD.  are licensed under a . Creative Commons Attribution-. NonCommercial. -. ShareAlike. 3.0 . Unported. License. 1. . Theory of Computation Peer Instruction Lecture Slides by . Dr. Cynthia Lee, UCSD.  are licensed under a . Creative Commons Attribution-. NonCommercial. -. ShareAlike. 3.0 . Unported. License. Class 17: . Undecidable Languages. Spring 2010. University of Virginia. David Evans. Menu. Another . Self-Rejecting . argument: . diagonalization. A language that is . Turing-recognizable. but not . bn wwR Our main goal is to exhibit a language L that Theory of Computation. Alexander . Tsiatas. Spring 2012. Theory of Computation Lecture Slides by Alexander . Tsiatas. is licensed under a Creative Commons Attribution-. NonCommercial. -. ShareAlike. Fall 2017. http://cseweb.ucsd.edu/. classes/fa17/cse105-a/. Today's learning goals . Sipser Ch 4.1, 4.2. Trace high-level descriptions of algorithms for computational problems.. Use counting arguments to prove the existence of unrecognizable (undecidable) languages.. Turing Machine: Languages. Recall that a collection of strings that a TM M accepts is called. the language of M or language recognized by M, denoted L(M).. Definition. A . language is Turing-recognizable (or recursively enumerable) if . 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.. 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.. Xiaokang Qiu. x=1;. y=1;. while (*) {. x=x 2;. y=y 1;. }. Q: is . x y. >=2 always true?.  . Q: Are . these formulae valid in arithmetic?. First-Order Theories. Q: Which statements are true in arithmetic/set-theory/groups/fields?. Umang Mathur. P. Madhusudan. Mahesh Viswanathan. Existing Decidable Classes. Program Verification. Unnatural program models. Undecidable. In general, verification over infinite domains is undecidable. Based on . M. . Sipser. , “Introduction to the Theory of Computation,” Second Edition, Thomson/Course Technology, 2006, Chapter 5.. Review. Recall the . halting problem. :. . HALT. TM. = { . .