About: The Satisfiability Problem for Probabilistic CTL

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We study the satisfiability problem for qualitative PCTL (Probabilistic Computation Tree Logic), which is obtained from %22ordinary%22 CTL by replacing the EX, AX, EU, and AU operators with their qualitative counterparts X>0, X=1, U>0, and U=1, respectively. As opposed to CTL, qualitative PCTL does not have a small model property, and there are even qualitative PCTL formulae which have only infinite-state models. Nevertheless, we show that the satisfiability problem for qualitative PCTL is EXPTIME-complete and we give an exponential-time algorithm which for a given formula computes a finite description of a model (if it exists), or answers %22not satisfiable%22 (otherwise). We also consider the finite satisfiability problem and provide analogous results. That is, we show that the finite satisfiability problem for qualitative PCTL is EXPTIME-complete, and every finite satisfiable formula has a model of an exponential size which can effectively be constructed in exponential time. We study the satisfiability problem for qualitative PCTL (Probabilistic Computation Tree Logic), which is obtained from %22ordinary%22 CTL by replacing the EX, AX, EU, and AU operators with their qualitative counterparts X>0, X=1, U>0, and U=1, respectively. As opposed to CTL, qualitative PCTL does not have a small model property, and there are even qualitative PCTL formulae which have only infinite-state models. Nevertheless, we show that the satisfiability problem for qualitative PCTL is EXPTIME-complete and we give an exponential-time algorithm which for a given formula computes a finite description of a model (if it exists), or answers %22not satisfiable%22 (otherwise). We also consider the finite satisfiability problem and provide analogous results. That is, we show that the finite satisfiability problem for qualitative PCTL is EXPTIME-complete, and every finite satisfiable formula has a model of an exponential size which can effectively be constructed in exponential time. (en)
Title	The Satisfiability Problem for Probabilistic CTL The Satisfiability Problem for Probabilistic CTL (en)
skos:prefLabel	The Satisfiability Problem for Probabilistic CTL The Satisfiability Problem for Probabilistic CTL (en)
skos:notation	RIV/00216224:14330/08:00026224!RIV10-MSM-14330___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1M0545), Z(MSM0021622419)
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Brázdil, Tomáš Forejt, Vojtěch Kučera, Antonín Křetínský, Jan
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Fakulta informatiky
http://linked.open...dnocenehoVysledku	393788
http://linked.open...ai/riv/idVysledku	RIV/00216224:14330/08:00026224
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Stochastic systems; branching-time temporal logics (en)
http://linked.open.../riv/klicoveSlovo	Stochastic systems branching-time temporal logics
http://linked.open...ontrolniKodProRIV	[C11FB54C4747]
http://linked.open...v/mistoKonaniAkce	Pittsburgh, USA
http://linked.open...i/riv/mistoVydani	Los Alamitos, California
http://linked.open...i/riv/nazevZdroje	23rd IEEE Symposium on Logic in Computer Science (LICS 2008), 24-27 June 2008, Pittsburgh, USA, Proceedings
http://linked.open...in/vavai/riv/obor	IN
http://linked.open...ichTvurcuVysledku	4 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Institute for Theoretical Computer Science
http://linked.open...UplatneniVysledku	2008
http://linked.open...iv/tvurceVysledku	Brázdil, Tomáš Forejt, Vojtěch Kučera, Antonín Křetínský, Jan
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open...ain/vavai/riv/wos	000258728700033
http://linked.open.../riv/zahajeniAkce	2008-06-24 (xsd:date)
http://linked.open...n/vavai/riv/zamer	Highly Parallel and Distributed Computing Systems
number of pages	10 (xsd:int)
http://purl.org/ne...btex#hasPublisher	IEEE Computer Society
https://schema.org/isbn	978-0-7695-3183-0
http://localhost/t...ganizacniJednotka	14330
is http://linked.open...avai/riv/vysledek of	The Satisfiability Problem for Probabilistic CTL The Satisfiability Problem for Probabilistic CTL The Satisfiability Problem for Probabilistic CTL The Satisfiability Problem for Probabilistic CTL

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