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How to show something is not: Proofs in formal language and computability theory

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Published:01 August 1978Publication History
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Abstract

Most introductory courses in theoretical computer science (formal language theory or computability theory) start with a seemingly endless series of definitions, including what it means for a grammar or language to be regular, context-free, etc., or what it means for a function to be recursive, primitive recursive, or partial recursive. Bright students immediately ask two questions. First, what are examples of languages or functions that belong to one class but not the other? Second, is some particular language context-free, or is a particular function recursive?

We must develop new techniques which allow us to give a negative answer to question two (and thus to answer question one as well). In this note we will discuss some of the methods that are often used in elementary proofs in formal language theory and computability theory.

References

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  1. How to show something is not: Proofs in formal language and computability theory

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            cover image ACM SIGCSE Bulletin
            ACM SIGCSE Bulletin  Volume 10, Issue 3
            Proceedings of the 9th SIGCSE symposium on Computer science education
            August 1978
            178 pages
            ISSN:0097-8418
            DOI:10.1145/953028
            Issue’s Table of Contents
            • cover image ACM Conferences
              SIGCSE '78: Proceedings of the ninth SIGCSE technical symposium on Computer science education
              August 1978
              178 pages
              ISBN:9781450374347
              DOI:10.1145/800130

            Copyright © 1978 ACM

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            Association for Computing Machinery

            New York, NY, United States

            Publication History

            • Published: 1 August 1978

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