Abstract
We propose a natural generalization of the concept of implicit definitions over finite structures, allowing non-determinism at an intermediate level of a (deterministic) definition. These generalized implicit definitions offer more expressive power than classical implicit definitions. Moreover, their expressive power can be characterized over unordered finite structures in terms of the complexity class NP ∩ co-NP. Finally, we investigate a subclass of these where the non-determinism is restricted to the choice of a unique relation with respect to an implicit linear order, and prove that it captures UP ∩ co-UP also over the class of all finite structures. These results shed some light on the expressive power of non-deterministic primitives.
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Work supported in part by an EC-NSF grant DEUS EX MACHINA, and an NSERC fellowship in Canada.
Work done in the Verso Project at INRIA.
Work partially supported by NSF grant CCR-9403447 and the John C. Whitehead faculty research fund at Haverford College.
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© 1996 Springer-Verlag Berlin Heidelberg
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Grumbach, S., Lacroix, Z., Lindell, S. (1996). Generalized implicit definitions on finite structures. In: Kleine Büning, H. (eds) Computer Science Logic. CSL 1995. Lecture Notes in Computer Science, vol 1092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61377-3_42
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DOI: https://doi.org/10.1007/3-540-61377-3_42
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