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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:
 [1];  [2]
  1. Departamento de Matemática, Instituto Superior Técnico, U Lisboa, Portugal
  2. Departamento de Matemática, Instituto Superior Técnico, U Lisboa, Portugal and Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, U Lisboa, Portugal
Publication Date:
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.
Oliveira, Daniel, & Rasga, João. Revisiting separation: algorithms and complexity. Country unknown/Code not available. doi:10.1093/jigpal/jzz081.
Oliveira, Daniel, and Rasga, João. Tue . "Revisiting separation: algorithms and complexity". Country unknown/Code not available. doi:10.1093/jigpal/jzz081.
@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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
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
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The complexity of propositional linear temporal logics
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A Proof of Kamp's theorem
journal, January 2014