A Toolkit for First Order Extensions of Monadic Games

In 1974 R. Fagin proved that properties of structures which are in NP are exactly the same as those expressible by existential second order sentences, that is sentences of the form: there exist ¥¦ such that §, where ¥¦ is a tuple of relation symbols. and § is a first order formula. Fagin was also the first to study monadic NP: the class of properties expressible by existential second order sentences where all the quantified relations are unary. In [AFS00] Ajtai, Fagin and Stockmeyer introduce closed monadic NP: the class of properties which can be expressed by a kind of monadic second order existential formula, where the second order quantifiers can interleave with first order quantifiers. In order to prove that such alternation of quantifiers gives substantial additional expressive power they construct graph properties ¨ £ and ¨ ¤: ¨ £ is expressible by a sentence with the quantifier prefix in the class ©    ©  1 but not by a boolean combination of sen...

• Type: Conference
• Year: 2001
• Where: STACS
• Authors: David Janin, Jerzy Marcinkowski
• Keywords: Monadic Np, Order Sentences, STACS 2001, Theoretical Computer Science, first Order