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.
A preliminary version 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. The main difference is the addition of Section 5.
Incumbent of the William Sussman Chair of Mathematics.
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Harel, D. (1995). Towards a theory of recursive structures. In: van Leeuwen, J. (eds) Computer Science Today. Lecture Notes in Computer Science, vol 1000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015255
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DOI: https://doi.org/10.1007/BFb0015255
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