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VOLUME 4, ISSUE 4, PAPER 11


First-Order and Temporal Logics for Nested Words

©Rajeev Alur, UPenn
©Marcelo Arenas, PUC, Chile
©Pablo Barcelo, U Chile
©Kousha Etessami, U Edinburgh
©Neil Immerman, UMass
©Leonid Libkin, Edinbugh

Abstract
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.

Publication date: November 25, 2008 arxiv:0811.0537v1

Corrected Version from: March 03, 2011


Full Text: PDF | PostScript
DOI: 10.2168/LMCS-4(4:11)2008

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