First-order and temporal logics for nested words

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First-order and temporal logics for nested words

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by Rajeev Alur , Marcelo Arenas , Pablo Barceló , Kousha Etessami , Neil Immerman , Leonid Libkin

Venue:	In LICS 2007
Citations:	27 - 4 self

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@INPROCEEDINGS{Alur_first-orderand,
    author = {Rajeev Alur and Marcelo Arenas and Pablo Barceló and Kousha Etessami and Neil Immerman and Leonid Libkin},
    title = {First-order and temporal logics for nested words},
    booktitle = {In LICS 2007},
    year = {}
}

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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 expressivelycomplete. 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. The other logic is based on the notion of a summary path that combines the linear and nesting structures. For that logic, both model-checking and satisfiability are shown to be 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 twovariable fragment of first-order. 1

Keyphrases

nested word temporal logic return nesting structure recursive state machine new temporal logic summary path twovariable fragment three-variable property tree-structured data infinite nested word nesting structure procedural program logic caret parse tree natural extension structured model execution path first-order logic first-order expressivelycomplete

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