# Towards a theory of recursive structures

- First Online:

DOI: 10.1007/3-540-57785-8_177

- Cite this paper as:
- Harel D. (1994) Towards a theory of recursive structures. In: Enjalbert P., Mayr E.W., Wagner K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg

## 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 or data base. In this paper we summarize our recent work on recursive structures and data bases, including (i) the high undecidability of many problems on recursive graphs, (ii) somewhat surprising ways of deducing results on the classification of NP optimization problems from results on the degree of undecidability of their infinitary analogues, and (iii) completeness results for query languages on recursive data bases.

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