Revisiting separation: Algorithms and complexity

Journal Article · 18 February 2020 · Logic Journal of the IGPL

DOI: https://doi.org/10.1093/jigpal/jzz081 · OSTI ID:1600564

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

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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

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.

• Sponsoring Organization: USDOE Office of Nuclear Energy (NE), Nuclear Fuel Cycle and Supply Chain
• OSTI ID: 1600564
• Journal Information: Logic Journal of the IGPL, Journal Name: Logic Journal of the IGPL Journal Issue: 3 Vol. 29; ISSN 1367-0751
• Publisher: Oxford University PressCopyright Statement
• Country of Publication: Country unknown/Code not available
• Language: English