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Towards a theory of recursive structures

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Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

In computer science, one is interested mainly in finite objects. Insofar as infinite objects are of interest, they must be computable, i.e., recursive, thus admitting an effective finite representation. This leads to the notion of a recursive graph, or, more generally, a recursive structure, model or data base. This paper summarizes recent work on recursive structures and data bases, including (i) the high undecidability of many problems on recursive graphs and structures, (ii) a method for deducing results on the descriptive complexity of finitary NP optimization problems from results on the computational complexity (i.e., the degree of undecidability) of their infinitary analogues, (iii) completeness results for query languages on recursive data bases, (iv) correspondences between descriptive and computational complexity over recursive structures, and (v) zero-one laws for recursive structures.

Preliminary versions of this paper appeared in STACS '94, Proc. 11th Ann. Symp. on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, Vol. 775, Springer-Verlag, Berlin, 1994, pp. 633–645, and in Computer Science Today, Lecture Notes in Computer Science, Vol. 1000, Springer-Verlag, 1995, pp. 374–391.

Incumbent of the William Sussman Chair of Mathematics.

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Authors and Affiliations

  1. Dept. of Applied Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot, Israel

    David Harel

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  1. David Harel
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Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Harel, D. (1998). Towards a theory of recursive structures. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055756

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  • DOI: https://doi.org/10.1007/BFb0055756

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  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

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