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

Authors: Bojanczyk, Mikolaj and Segoufin, Luc

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.


Source : oai:arXiv.org:1009.2854
DOI : 10.2168/LMCS-6(4:1)2010
Volume: Volume 6, Issue 4
Published on: October 20, 2010
Submitted on: September 17, 2010
Keywords: Computer Science - Formal Languages and Automata Theory,Computer Science - Logic in Computer Science,cs.LO


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