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International Conference on Foundations of Software Technology and Theoretical Computer Science

FSTTCS 1990: Foundations of Software Technology and Theoretical Computer Science pp 33–47Cite as

Complexity of algebraic specifications

  • Logic
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 472))

Abstract

In the field of algebraic specification, the semantics of an equationally specified datatype is given by the initial algebra of the specifications. We show in this paper that in general the theory of the initial algebra of a given set of equations is II 02 -complete. The impossibility of complete finite axiomatization of equations as well as inequations true in the initial algebra is therefore established. We, further, establish that the decision problem is, in general, II 01 -complete if the equational theory is decidable. We extend the investigation to a certain semantics of parameterized specifications (the so-called free extension functor semantics) that has been proposed in the literature. We present some results characterizing the recursion-theoretic properties of (a) the theory of the free extension algebras of parameter algebras relative to the the theory of the parameter algebras, and (b) the theory of the models of a parameterized specification relative to the theory axiomatized by the specification itself.

This research was supported by U.S. Army Research Office grant DAAL03-89-C-0031PRI.

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Authors and Affiliations

  1. Department of Computer and Information Science, University of Pennsylvania, 19104, Philadelphia, PA, U.S.A.

    Ramesh Subrahmanyam

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  1. Ramesh Subrahmanyam
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Kesav V. Nori C. E. Veni Madhavan

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© 1990 Springer-Verlag Berlin Heidelberg

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Subrahmanyam, R. (1990). Complexity of algebraic specifications. In: Nori, K.V., Veni Madhavan, C.E. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1990. Lecture Notes in Computer Science, vol 472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53487-3_33

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  • DOI: https://doi.org/10.1007/3-540-53487-3_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53487-7

  • Online ISBN: 978-3-540-46313-9

  • eBook Packages: Springer Book Archive

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