Mikolaj Bojanczyk ; Luc Segoufin - Tree Languages Defined in First-Order Logic with One Quantifier Alternation

lmcs:699 - Logical Methods in Computer Science, October 20, 2010, Volume 6, Issue 4 - https://doi.org/10.2168/LMCS-6(4:1)2010
Tree Languages Defined in First-Order Logic with One Quantifier AlternationArticle

Authors: Mikolaj Bojanczyk ; Luc Segoufin

    We study tree languages that can be defined in \Delta_2 . These are tree languages definable by a first-order formula whose quantifier prefix is forall exists, and simultaneously by a first-order formula whose quantifier prefix is . For the quantifier free part we consider two signatures, either the descendant relation alone or together with the lexicographical order relation on nodes. We provide an effective characterization of tree and forest languages definable in \Delta_2 . This characterization is in terms of algebraic equations. Over words, the class of word languages definable in \Delta_2 forms a robust class, which was given an effective algebraic characterization by Pin and Weil.

    https://doi.org/10.2168/LMCS-6(4:1)2010
    Source: arXiv.org:1009.2854
    Volume: Volume 6, Issue 4
    Published on: October 20, 2010
    Imported on: September 17, 2010
    Keywords: Computer Science - Formal Languages and Automata Theory,Computer Science - Logic in Computer Science,cs.LO
    Licence: arXiv.org - Non-exclusive license to distribute

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