Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau Approach

Temporal logic has become essential for various areas in computer science, most notably for the specification and verification of hardware and software systems. For specification purposes rich temporal languages are required that, in particular, can express fairness constraints. For linear-time logi...

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Autores: Bolotov, Alexander, Hermo Huguet, Montserrat, Lucio Carrasco, Francisca
Formato: capítulo de livro
Fecha de publicación:2018
País:España
Recursos:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/64610
Acesso em linha:http://hdl.handle.net/10810/64610
Access Level:acceso abierto
Palavra-chave:temporal logic
fairness
branching-time
one-pass tableau
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spelling Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau ApproachBolotov, AlexanderHermo Huguet, MontserratLucio Carrasco, Franciscatemporal logicfairnessbranching-timeone-pass tableauTemporal logic has become essential for various areas in computer science, most notably for the specification and verification of hardware and software systems. For specification purposes rich temporal languages are required that, in particular, can express fairness constraints. For linear-time logics which deal with fairness in the linear-time setting, one-pass and two-pass tableau methods have been developed. In the repository of the CTL-type branching-time setting, the well-known logics ECTL and ECTL+ were developed to explicitly deal with fairness. However, due to the syntactical restrictions, these logics can only express restricted versions of fairness. The logic CTL*, often considered as "the full branching-time logic" overcomes these restrictions on expressing fairness. However, this logic itself is extremely challenging for the application of verification techniques, and the tableau technique, in particular. For example, there is no one-pass tableau construction for this logic, while it is known that one-pass tableau has an additional benefit enabling the formulation of dual sequent calculi that are often treated as more "natural", being more friendly for human understanding. Based on these two considerations, the following problem arises - are there logics that have richer expressiveness than ECTL+ yet "simpler" than CTL* for which a one-pass tableau can be developed? In this paper, we give a solution to this problem. We present a tree-style one-pass tableau for a sub-logic of CTL* that we call ECTL#, which is more expressive than ECTL+ allowing the formulation of a new range of fairness constraints with "until" operator. The presentation of the tableau construction is accompanied by an algorithm for constructing a systematic tableau, for any given input of admissible branching-time formulae. We prove the termination, soundness, and completeness of the method. As tree-shaped one-pass tableaux are well suited for the automation and are amenable to the implementation and the formulation of sequent calculi, our results also open a prospect of relevant developments of the automation and implementation of the tableau method for ECTL#, and of a dual sequent calculi.The authors have been partially supported by Spanish Projects TIN2013-46181-C2-2-R and TIN2017-86727-C2-2-R, and by the University of the Basque Country under Project LoRea GIU15/30Schloss Dagstuhl – Leibniz-Zentrum für Informatik202420242018info:eu-repo/semantics/bookPartapplication/pdfhttp://hdl.handle.net/10810/64610reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoIngléshttps://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2018.5info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/deed.en© Alexander Bolotov, Montserrat Hermo, and Paqui Lucio; licensed under Creative Commons License CC-BYoai:addi.ehu.eus:10810/646102026-06-18T09:23:17Z
dc.title.none.fl_str_mv Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau Approach
title Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau Approach
spellingShingle Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau Approach
Bolotov, Alexander
temporal logic
fairness
branching-time
one-pass tableau
title_short Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau Approach
title_full Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau Approach
title_fullStr Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau Approach
title_full_unstemmed Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau Approach
title_sort Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau Approach
dc.creator.none.fl_str_mv Bolotov, Alexander
Hermo Huguet, Montserrat
Lucio Carrasco, Francisca
author Bolotov, Alexander
author_facet Bolotov, Alexander
Hermo Huguet, Montserrat
Lucio Carrasco, Francisca
author_role author
author2 Hermo Huguet, Montserrat
Lucio Carrasco, Francisca
author2_role author
author
dc.subject.none.fl_str_mv temporal logic
fairness
branching-time
one-pass tableau
topic temporal logic
fairness
branching-time
one-pass tableau
description Temporal logic has become essential for various areas in computer science, most notably for the specification and verification of hardware and software systems. For specification purposes rich temporal languages are required that, in particular, can express fairness constraints. For linear-time logics which deal with fairness in the linear-time setting, one-pass and two-pass tableau methods have been developed. In the repository of the CTL-type branching-time setting, the well-known logics ECTL and ECTL+ were developed to explicitly deal with fairness. However, due to the syntactical restrictions, these logics can only express restricted versions of fairness. The logic CTL*, often considered as "the full branching-time logic" overcomes these restrictions on expressing fairness. However, this logic itself is extremely challenging for the application of verification techniques, and the tableau technique, in particular. For example, there is no one-pass tableau construction for this logic, while it is known that one-pass tableau has an additional benefit enabling the formulation of dual sequent calculi that are often treated as more "natural", being more friendly for human understanding. Based on these two considerations, the following problem arises - are there logics that have richer expressiveness than ECTL+ yet "simpler" than CTL* for which a one-pass tableau can be developed? In this paper, we give a solution to this problem. We present a tree-style one-pass tableau for a sub-logic of CTL* that we call ECTL#, which is more expressive than ECTL+ allowing the formulation of a new range of fairness constraints with "until" operator. The presentation of the tableau construction is accompanied by an algorithm for constructing a systematic tableau, for any given input of admissible branching-time formulae. We prove the termination, soundness, and completeness of the method. As tree-shaped one-pass tableaux are well suited for the automation and are amenable to the implementation and the formulation of sequent calculi, our results also open a prospect of relevant developments of the automation and implementation of the tableau method for ECTL#, and of a dual sequent calculi.
publishDate 2018
dc.date.none.fl_str_mv 2018
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv http://hdl.handle.net/10810/64610
url http://hdl.handle.net/10810/64610
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2018.5
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/deed.en
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/deed.en
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Schloss Dagstuhl – Leibniz-Zentrum für Informatik
publisher.none.fl_str_mv Schloss Dagstuhl – Leibniz-Zentrum für Informatik
dc.source.none.fl_str_mv reponame:Addi. Archivo Digital para la Docencia y la Investigación
instname:Universidad del País Vasco
instname_str Universidad del País Vasco
reponame_str Addi. Archivo Digital para la Docencia y la Investigación
collection Addi. Archivo Digital para la Docencia y la Investigación
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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