Departmental Papers (CIS)

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Journal Article

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Reprinted from:

First-Order and Temporal Logics for Nested Words. Rajeev Alur, Marcelo Arenas, Pablo Barcelo, Kousha Etessami, Neil Immerman, Leonid Libkin. Logical Methods in Computer Science. Vol. 4 (4:11) 2008, pp. 1–44


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.


Nested Word, Temporal Logic, First-Order Expressive Completeness, Three-Variable Property, Nested Word Automata, Model Checking



Date Posted: 15 October 2009

This document has been peer reviewed.