On logical hierarchies within FO2-definable languages

Abstract : 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 FO2[<] 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, Therien and Vollmer.
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Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2012, 8 (3:11), pp.1-30. 〈10.2168/LMCS-8(3:11)2012〉
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Manfred Kufleitner, Pascal Weil. On logical hierarchies within FO2-definable languages. Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2012, 8 (3:11), pp.1-30. 〈10.2168/LMCS-8(3:11)2012〉. 〈hal-00567171v2〉

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