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On problems with short certificates

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Abstract

We consider languages in NP whose certificate size is bounded by a fixed, slowly growing function (sayf (n)) of the input size. The classesf (n)-NP, which are related to classes of Kintala and Fischer, are defined in order to classify such languages. We show that several natural problems, involving Boolean satisfiability, graph colouring and Hamiltonian circuits, are complete forf (n)-NP. Each of our problems is obtained by taking a known NP-complete problem and introducing an ingredient we callforcing, whereby a partial structure is enlarged by a sequence of local improvements. As special cases of these results we obtain some new logspace completeness results for P.

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Author notes

  1. Graham Farr

    Present address: Air Operations Division, Aeronautical Research Laboratory, 506 Lorimer Street, 3207, Fishermens Bend, Victoria, Australia

Authors and Affiliations

  1. Computer Sciences Laboratory, Research School of Information Sciences and Engineering, Australian National University, G.P.O. Box 4, 2601, Canberra, A.C.T., Australia

    Graham Farr

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  1. Graham Farr
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The research reported in this paper was done while the author was a graduate student at the Mathematical Institute, Oxford, U.K. The paper was then written at the Computer Sciences Laboratory, Research School of Physical Sciences. Australian National University, Canberra, Australia.

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Farr, G. On problems with short certificates. Acta Informatica 31, 479–502 (1994). https://doi.org/10.1007/BF01178668

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