PPT-Decidable

Logics Combining Heap Structures and Data Gennaro Parlato LIAFA Paris France Joint work with P Madhusudan Xiaokang Qie . 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 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 q2 q0 q1 q3 qa qr brPage 2br Problem 311 Show that a Turing machine with doublyin64257nite tape recognizes the same class of languages as an ordinary Turing machine Clearly one direction is easy The doublyin64257nite tape can simulate an ordinary TM 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. Ben Greenman, . Fabian Muehlboeck. , and Ross Tate. Cornell University. Typesafe. Equality + Generic Lists?. (. Typesafe. ) Equality. @override. public . boolean. equals(Object other) {. . if(other . will explore is reduction.To show that L1 is undecidable:Identify L2 that is undecidabl Given a Turing machine M, does M halt on the empty tape?4)Given a Turing machine M, is there any string at all o 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, 4.2. Trace high-level descriptions of algorithms for computational problems.. Use counting arguments to prove the existence of unrecognizable (undecidable) languages.. 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.