Kufleitner, Manfred and Weil, Pascal - On logical hierarchies within FO^2-definable languages

lmcs:1212 - Logical Methods in Computer Science, August 14, 2012, Volume 8, Issue 3
On logical hierarchies within FO^2-definable languages

Authors: Kufleitner, Manfred and Weil, Pascal

We consider the class of languages defined in the 2-variable fragment of the first-order logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier alternations yields an infinite hierarchy whose levels are varieties of languages (and hence admit an algebraic characterization). Using this algebraic approach, we show that the quantifier alternation hierarchy inside FO^{2}[<] is decidable within one unit. For this purpose, we relate each level of the hierarchy with decidable varieties of languages, which can be defined in terms of iterated deterministic and co-deterministic products. A crucial notion in this process is that of condensed rankers, a refinement of the rankers of Weis and Immerman and the turtle languages of Schwentick, Th\'erien and Vollmer.

Source : oai:arXiv.org:1208.0713
DOI : 10.2168/LMCS-8(3:11)2012
Volume: Volume 8, Issue 3
Published on: August 14, 2012
Submitted on: February 12, 2011
Keywords: Computer Science - Logic in Computer Science,Computer Science - Formal Languages and Automata Theory,F.4.3,F.4.1


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