Jurdzinski, Marcin and Laroussinie, Francois and Sproston, Jeremy - Model Checking Probabilistic Timed Automata with One or Two Clocks

lmcs:988 - Logical Methods in Computer Science, September 26, 2008, Volume 4, Issue 3
Model Checking Probabilistic Timed Automata with One or Two Clocks

Authors: Jurdzinski, Marcin and Laroussinie, Francois and Sproston, Jeremy

Probabilistic timed automata are an extension of timed automata with discrete probability distributions. We consider model-checking algorithms for the subclasses of probabilistic timed automata which have one or two clocks. Firstly, we show that PCTL probabilistic model-checking problems (such as determining whether a set of target states can be reached with probability at least 0.99 regardless of how nondeterminism is resolved) are PTIME-complete for one-clock probabilistic timed automata, and are EXPTIME-complete for probabilistic timed automata with two clocks. Secondly, we show that, for one-clock probabilistic timed automata, the model-checking problem for the probabilistic timed temporal logic PCTL is EXPTIME-complete. However, the model-checking problem for the subclass of PCTL which does not permit both punctual timing bounds, which require the occurrence of an event at an exact time point, and comparisons with probability bounds other than 0 or 1, is PTIME-complete for one-clock probabilistic timed automata.


Source : oai:arXiv.org:0809.0060
DOI : 10.2168/LMCS-4(3:12)2008
Volume: Volume 4, Issue 3
Published on: September 26, 2008
Submitted on: September 3, 2007
Keywords: Computer Science - Logic in Computer Science,D.2.4,F.4.1,G.3


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