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Journal of Logic and Computation 1998 8(2):189-207; doi:10.1093/logcom/8.2.189
© 1998 by Oxford University Press
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Original Articles

Subclasses of Binary NP

ARNAUD DURAND, CLEMENS LAUTEMANN and THOMAS SCHWENTICK

Dept. d'Informatique, Université de Caen 14032 Caen cedex, France E-mail: arnaud.durand{at}info.unicaen.fr
Institut für Informatik, FB 17, Johannes Gutenberg-Universität D-55099 Mainz, Germany. E-mail: cltick{at}informatik.uni-mainz.de

Binary NP consists of all sets of finite structures which are expressible in existential second-order logic with second-order quantification restricted to relations of arity 2. We look at semantical restrictions of binary NP, where the second order quantifiers range only over certain classes of relations. We consider mainly three types of classes of relations: unary functions, order relations and graphs with degree bounds. We show that many of these restrictions have the same expressive power and establish a four-level strict hierarchy, represented by sets, permutations, unary functions and arbitrary binary relations, respectively.

Keywords: Descriptive complexity; finite model theory; existential second-order logic


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