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A Journey to Computably Enumerable Structures (Tutorial Lectures)

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Sailing Routes in the World of Computation (CiE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10936))

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Abstract

The tutorial focuses on computably enumerable (c.e.) structures. These structures form a class that properly extends the class of all computable structures. A computably enumerable (c.e.) structure is one that has computably enumerable equality relation E such that the atomic operations and relations of the structure are induced by c.e. operations and relations that respect E. Finitely presented universal algebras (e.g. groups, rings) are natural examples of c.e. structures. The first lecture gives an introduction to the theory, provides many examples, and proves several simple yet important results about c.e. structures. The second lecture addresses a particular problem about finitely presented expansions of universal algebras with an emphasis to semigroups and groups. The lecture is based on the interplay between important constructions, concepts, and results in computability (Post’s construction of simple sets), universal algebra (residual finiteness), and algebra (Golod-Shafarevich theorem). The third lecture is devoted to studying dependency of various properties of c.e. structures on their domains.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Auckland, Auckland, New Zealand

    Bakh Khoussainov

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  1. Bakh Khoussainov
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Correspondence to Bakh Khoussainov .

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Editors and Affiliations

  1. Kiel University, Kiel, Germany

    Florin Manea

  2. Queens College, CUNY, Queens, New York, USA

    Russell G. Miller

  3. Kiel University, Kiel, Germany

    Dirk Nowotka

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Khoussainov, B. (2018). A Journey to Computably Enumerable Structures (Tutorial Lectures). In: Manea, F., Miller, R., Nowotka, D. (eds) Sailing Routes in the World of Computation. CiE 2018. Lecture Notes in Computer Science(), vol 10936. Springer, Cham. https://doi.org/10.1007/978-3-319-94418-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-94418-0_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94417-3

  • Online ISBN: 978-3-319-94418-0

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