Confluence and Convergence in Probabilistically Terminating Reduction Systems

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

Convergence of an abstract reduction system (ARS) is the property that any derivation from an initial state will end in the same final state, a.k.a. normal form. We generalize this for probabilistic ARS as almost-sure convergence, meaning that the normal form is reached with probability one, even if diverging derivations may exist. We show and exemplify properties that can be used for proving almost-sure convergence of probabilistic ARS, generalizing known results from ARS.
Convergence of an abstract reduction system (ARS) is the property that any derivation from an initial state will end in the same final state, a.k.a. normal form. We generalize this for probabilistic ARS as almost-sure convergence, meaning that the normal form is reached with probability one, even if diverging derivations may exist. We show and exemplify properties that can be used for proving almost-sure convergence of probabilistic ARS, generalizing known results from ARS.
LanguageEnglish
Title of host publicationLogic-Based Program Synthesis and Transformation : 27th International Symposium, LOPSTR 2017, Namur, Belgium, October 10-12, 2017, Revised Selected Papers
EditorsFabio Fioravanti, John P. Gallagher
Number of pages15
Place of PublicationLecture Notes in Computer Science
PublisherSpringer, LNCS
Date10 Jul 2018
Pages164-179
ISBN (Print)978-3-319-94459-3
ISBN (Electronic)978-3-319-94460-9
DOIs
StatePublished - 10 Jul 2018
SeriesLecture Notes in Computer Science
Volume10855
ISSN0302-9743

Cite this

Kirkeby, M. H., & Christiansen, H. (2018). Confluence and Convergence in Probabilistically Terminating Reduction Systems. In F. Fioravanti, & J. P. Gallagher (Eds.), Logic-Based Program Synthesis and Transformation: 27th International Symposium, LOPSTR 2017, Namur, Belgium, October 10-12, 2017, Revised Selected Papers (pp. 164-179). Lecture Notes in Computer Science: Springer, LNCS. Lecture Notes in Computer Science, Vol.. 10855, DOI: 10.1007/978-3-319-94460-9_10
Kirkeby, Maja Hanne ; Christiansen, Henning. / Confluence and Convergence in Probabilistically Terminating Reduction Systems. Logic-Based Program Synthesis and Transformation: 27th International Symposium, LOPSTR 2017, Namur, Belgium, October 10-12, 2017, Revised Selected Papers. editor / Fabio Fioravanti ; John P. Gallagher. Lecture Notes in Computer Science : Springer, LNCS, 2018. pp. 164-179 (Lecture Notes in Computer Science, ???volume??? 10855).
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Kirkeby, MH & Christiansen, H 2018, Confluence and Convergence in Probabilistically Terminating Reduction Systems. in F Fioravanti & JP Gallagher (eds), Logic-Based Program Synthesis and Transformation: 27th International Symposium, LOPSTR 2017, Namur, Belgium, October 10-12, 2017, Revised Selected Papers. Springer, LNCS, Lecture Notes in Computer Science, Lecture Notes in Computer Science, vol. 10855, pp. 164-179. DOI: 10.1007/978-3-319-94460-9_10

Confluence and Convergence in Probabilistically Terminating Reduction Systems. / Kirkeby, Maja Hanne; Christiansen, Henning.

Logic-Based Program Synthesis and Transformation: 27th International Symposium, LOPSTR 2017, Namur, Belgium, October 10-12, 2017, Revised Selected Papers. ed. / Fabio Fioravanti; John P. Gallagher. Lecture Notes in Computer Science : Springer, LNCS, 2018. p. 164-179.

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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Kirkeby MH, Christiansen H. Confluence and Convergence in Probabilistically Terminating Reduction Systems. In Fioravanti F, Gallagher JP, editors, Logic-Based Program Synthesis and Transformation: 27th International Symposium, LOPSTR 2017, Namur, Belgium, October 10-12, 2017, Revised Selected Papers. Lecture Notes in Computer Science: Springer, LNCS. 2018. p. 164-179. (Lecture Notes in Computer Science, Vol. 10855). Available from, DOI: 10.1007/978-3-319-94460-9_10