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DICHOTOMY RESULT FOR INDEPENDENCE-FRIENDLY PREFIXES OF GENERALIZED QUANTIFIERS

Published online by Cambridge University Press:  12 December 2014

MERLIJN SEVENSTER
MERLIJN SEVENSTER*
Affiliation:
PHILIPS RESEARCH NORTH AMERICA 345 SCARBOROUGH ROAD, BRIARCLIFF MANOR NY 10510, USAE-mail: [email protected]
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Abstract

We study the expressive power of independence-friendly quantifier prefixes composed of universal $\left( {\forall x/X} \right)$, existential $\left( {\exists x/X} \right)$, and majority quantifiers $\left( {Mx/X} \right)$. We provide four quantifier prefixes that can express NP hard properties and show that all quantifier prefixes capable of expressing NP-hard properties embed at least one of these four quantifier prefixes. As for the quantifier prefixes that do not embed any of these four quantifier prefixes, we show that they are equivalent to a first-order quantifier prefix composed of $\forall x$, $\exists x$, and Mx. In unison, our results imply a dichotomy result: every independence-friendly quantifier prefix is either decidable in LOGSPACE or NP hard.

Keywords

DichotomyBranching quantifiersHenkin quantifiersIndependence-friendly logicDescriptive complexityNP
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 4 , December 2014 , pp. 1224 - 1246
Copyright
Copyright © The Association for Symbolic Logic 2014 

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