Revisiting separation: algorithms and complexity

doi:10.1093/jigpal/jzz081

Title: Revisiting separation: algorithms and complexity

Abstract

Abstract Linear temporal logic (LTL) with Since and Until modalities is expressively equivalent, over the class of complete linear orders, to a fragment of first-order logic known as FOMLO (first-order monadic logic of order). It turns out that LTL, under some basic assumptions, is expressively complete if and only if it has the property, called separation, that every formula is equivalent to a Boolean combination of formulas that each refer only to the past, present or future. Herein we present simple algorithms and their implementations to perform separation of the LTL with Since and Until, over discrete and complete linear orders, and translation from FOMLO formulas into equivalent temporal logic formulas. We additionally show that the separation of a certain fragment of LTL results in at most a double exponential size growth.

Authors:

Oliveira, Daniel ^[1]; Rasga, João ^[2]

Departamento de Matemática, Instituto Superior Técnico, U Lisboa, Portugal
Departamento de Matemática, Instituto Superior Técnico, U Lisboa, Portugal and Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, U Lisboa, Portugal

Publication Date:: 2020-02-18

Sponsoring Org.:: USDOE Office of Nuclear Energy (NE), Fuel Cycle Technologies (NE-5)

OSTI Identifier:: 1600564

Grant/Contract Number:: UIDB/04561/2020

Resource Type:: Published Article

Journal Name:: Logic Journal of the IGPL

Additional Journal Information:: Journal Name: Logic Journal of the IGPL; Journal ID: ISSN 1367-0751

Publisher:: Oxford University Press

Country of Publication:: Country unknown/Code not available

Language:: English

Citation Formats


                    Oliveira, Daniel, and Rasga, João. Revisiting separation: algorithms and complexity.  Country unknown/Code not available: N. p., 2020. 
        Web.  doi:10.1093/jigpal/jzz081.

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                    Oliveira, Daniel, & Rasga, João. Revisiting separation: algorithms and complexity.  Country unknown/Code not available.  doi:10.1093/jigpal/jzz081.

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                    Oliveira, Daniel, and Rasga, João. Tue .  
        "Revisiting separation: algorithms and complexity".  Country unknown/Code not available.  doi:10.1093/jigpal/jzz081.

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@article{osti_1600564,

  title        = {Revisiting separation: algorithms and complexity},

  author       = {Oliveira, Daniel and Rasga, João},

  abstractNote = {Abstract Linear temporal logic (LTL) with Since and Until modalities is expressively equivalent, over the class of complete linear orders, to a fragment of first-order logic known as FOMLO (first-order monadic logic of order). It turns out that LTL, under some basic assumptions, is expressively complete if and only if it has the property, called separation, that every formula is equivalent to a Boolean combination of formulas that each refer only to the past, present or future. Herein we present simple algorithms and their implementations to perform separation of the LTL with Since and Until, over discrete and complete linear orders, and translation from FOMLO formulas into equivalent temporal logic formulas. We additionally show that the separation of a certain fragment of LTL results in at most a double exponential size growth.},

  doi          = {10.1093/jigpal/jzz081},

  journal      = {Logic Journal of the IGPL},

  number       = ,

  volume       = ,

  place        = {Country unknown/Code not available},

  year         = {2020},

  month        = {2}

}

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DOI: 10.1093/jigpal/jzz081

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Works referenced in this record:

An Until Hierarchy and Other Applications of an Ehrenfeucht–Fraı̈ssé Game for Temporal Logic
journal, July 2000

Etessami, Kousha; Wilke, Thomas
Information and Computation, Vol. 160, Issue 1-2
DOI: 10.1006/inco.1999.2846

The complexity of propositional linear temporal logics
journal, July 1985

Sistla, A. P.; Clarke, E. M.
Journal of the ACM (JACM), Vol. 32, Issue 3
DOI: 10.1145/3828.3837

A Proof of Kamp's theorem
journal, January 2014

Rabinovich, Alexander
Logical Methods in Computer Science, Vol. 10, Issue 1
DOI: 10.2168/LMCS-10(1:14)2014

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Title: Revisiting separation: algorithms and complexity

Abstract

Citation Formats

An Until Hierarchy and Other Applications of an Ehrenfeucht–Fraı̈ssé Game for Temporal Logic journal, July 2000

The complexity of propositional linear temporal logics journal, July 1985

A Proof of Kamp's theorem journal, January 2014

An Until Hierarchy and Other Applications of an Ehrenfeucht–Fraı̈ssé Game for Temporal Logic
journal, July 2000

The complexity of propositional linear temporal logics
journal, July 1985

A Proof of Kamp's theorem
journal, January 2014