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Unformatted text preview: 91.304 Foundations of (Theoretical) Computer Science Chapter 4 Lecture Notes (Section 4.1: Decidable Languages) David Martin dm@cs.uml.edu With modifications by Prof. Karen Daniels, Fall 2011 This work is licensed under the Creative Commons AttributionShareAlike License. To view a copy of this license, visit http://creativecommons.org/licenses/by 1 sa/2.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. Back to 1 The fact that 1 is not closed under complement means that there exists ome language L that is not some language L that is not recognizable by any TM. y Church uring thesis this means By ChurchTuring thesis this means that no imaginable finite computer, ven with infinite memory could even with infinite memory, could recognize this language L! 2 L ALL 1 A non 1 language LL ALL CFPP 1 RPP CFL REG FIN Each point is a language in this Venn diagram 3 Strategy oal Explore limits of algorithmic Goal : Explore limits of algorithmic solvability. ell show (later in Section 4 2) that there We ll show (later in Section 4.2) that there are more (a lot more) languages in ALL than there are in 1 Namely, that 1 is countable but ALL isnt countable hich implies that LL Which implies that 1 ALL Which implies that there exists some L that is not in 1 4 Overview of Section 4.1 ecidable Languages to foster Decidable Languages ( in ): to foster later appreciation of undecidable nguages languages Regular Languages A DFA : Acceptance problem for DFAs A NFA : Acceptance problem for NFAs A REX : Acceptance problem for Regular Expressions Emptiness testing for DFAs E DFA : Emptiness testing for DFAs EQ DFA : 2 DFAs recognizing the same language ContextFree Languages (see next slide) 5 Overview of Section 4.1 (cont.) Decidable Languages ( in ): to foster later appreciation of undecidable nguages languages ContextFree Languages Does a given CFG generate a given A CFG : Does a given CFG generate a given string? E CFG : Is the language of a given CFG empty? Every CFL is decidable by a Turing machine. 6 Overview of Section 4.1 Decidable Languages ( in ): to foster later appreciation of undecidable nguages languages Regular Languages cceptance problem for DFAs A DFA : Acceptance problem for DFAs Acceptance problem for NFAs Acceptance problem for Regular Expressions Emptiness testing for DFAs 2 DFAs recognizing the same language 7 Decidable Problems for Regular Languages: DFAs cceptance problem for DFAs Acceptance problem for DFAs...
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This note was uploaded on 02/13/2012 for the course CS 91.304 taught by Professor Staff during the Fall '11 term at UMass Lowell.
 Fall '11
 Staff
 Computer Science

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