Alur, Rajeev and Arenas, Marcelo and Barcelo, Pablo and Etessami, Kousha and Immerman, Neilet al. - First-Order and Temporal Logics for Nested Words

lmcs:782 - Logical Methods in Computer Science, November 25, 2008, Volume 4, Issue 4
First-Order and Temporal Logics for Nested Words

Authors: Alur, Rajeev and Arenas, Marcelo and Barcelo, Pablo and Etessami, Kousha and Immerman, Neil and Libkin, Leonid

Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We provide new temporal logics for finite and infinite nested words, which are natural extensions of LTL, and prove that these logics are first-order expressively-complete. One of them is based on adding a "within" modality, evaluating a formula on a subword, to a logic CaRet previously studied in the context of verifying properties of recursive state machines (RSMs). The other logic, NWTL, is based on the notion of a summary path that uses both the linear and nesting structures. For NWTL we show that satisfiability is EXPTIME-complete, and that model-checking can be done in time polynomial in the size of the RSM model and exponential in the size of the NWTL formula (and is also EXPTIME-complete). Finally, we prove that first-order logic over nested words has the three-variable property, and we present a temporal logic for nested words which is complete for the two-variable fragment of first-order.


Source : oai:arXiv.org:0811.0537
DOI : 10.2168/LMCS-4(4:11)2008
Volume: Volume 4, Issue 4
Published on: November 25, 2008
Submitted on: January 17, 2008
Keywords: Computer Science - Logic in Computer Science,F.1.1, F.3.1, F.4.1


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