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Algorithms

9. Universality and incomputability

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Abstract

In the previous articles, we had studied various topics such as algorithms, programs, programming languages, and algorithm design techniques. We shall now take a look at notions such as algorithmic universality, computability, incomputability and also discuss algorithmic limitations.

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Suggested Reading

  1. B A Trakhtenbrot.Algorithms and Automatic Computing Machines. D C Heath and Company. Boston, 1963. One of the early books that nicely elucidates the notion of algorithms, effective computability and Turing machine models.

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  2. C A R Hoare and D C S Allison.Incomputability. ACM Computing Surveys. Vol. 4. No. 3. pp. 169–178, September 1972. The article nicely elucidates the notion of incomputability through Russell’s paradox using English adjectives.

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  3. Douglas Hofstadter.Gödel, Escher Bach. Penguin, 1979. Provides a general idea of Gödel’s incompleteness theorems.

  4. D Harel.Algorithmics: The Spirit of Computing. Addison-Wesley Publishing Co.Inc, 1987.

  5. Raymond Smullyan.Gödel’s Incompleteness Theorems. Oxford University Press, 1992. Provides detailed aspects of the incompleteness theorems.

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Authors and Affiliations

  1. Computer Science Group Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005, Mumbai, India

    R. K. Shyamasundar

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  1. R. K. Shyamasundar
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Correspondence to R. K. Shyamasundar.

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Shyamasundar, R.K. Algorithms. Reson 2, 17–28 (1997). https://doi.org/10.1007/BF02835975

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  • DOI: https://doi.org/10.1007/BF02835975

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