The complexity of Markov decision processes
Mathematics of Operations Research
Theoretical Computer Science
The complexity of probabilistic verification
Journal of the ACM (JACM)
An automata-theoretic approach to linear temporal logic
Proceedings of the VIII Banff Higher order workshop conference on Logics for concurrency : structure versus automata: structure versus automata
POPL '83 Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
On the Complexity of Finite Memory Policies for Markov Decision Processes
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
Model Checking of Probabalistic and Nondeterministic Systems
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
Verifying Automata Specifications of Probabilistic Real-time Systems
Proceedings of the Real-Time: Theory in Practice, REX Workshop
Symbolic model checking for probabilistic timed automata
Information and Computation
Concavely-Priced Probabilistic Timed Automata
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Strict Divergence for Probabilistic Timed Automata
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Stochastic Games for Verification of Probabilistic Timed Automata
FORMATS '09 Proceedings of the 7th International Conference on Formal Modeling and Analysis of Timed Systems
A Decidable Probability Logic for Timed Probabilistic Systems
Fundamenta Informaticae
Automatic Analysis of a Non-Repudiation Protocol
Electronic Notes in Theoretical Computer Science (ENTCS)
Automatic Analysis of the NRL Pump
Electronic Notes in Theoretical Computer Science (ENTCS)
A Classification of Time and/or Probability Dependent Security Properties
Electronic Notes in Theoretical Computer Science (ENTCS)
Probabilistic timed behavior trees
IFM'07 Proceedings of the 6th international conference on Integrated formal methods
Weak bisimulation for Probabilistic Timed Automata
Theoretical Computer Science
A framework for verification of software with time and probabilities
FORMATS'10 Proceedings of the 8th international conference on Formal modeling and analysis of timed systems
Expected reachability-time games
FORMATS'10 Proceedings of the 8th international conference on Formal modeling and analysis of timed systems
Developing UPPAAL over 15 years
Software—Practice & Experience
PRTS: an approach for model checking probabilistic real-time hierarchical systems
ICFEM'11 Proceedings of the 13th international conference on Formal methods and software engineering
Model checking for probabilistic timed automata
Formal Methods in System Design
| Hi-index | 5.23 |
We propose a model of probabilistic timed automaton which substitutes for the nondeterminism of an ordinary timed automaton, a new one (directly drawn from Markov decision processes) by means of actions which provide a probabilistic distribution over transitions. Using Büchi acceptance conditions, timed automata can refer timing properties as "during every open time interval of length 1 at least one message is delivered". A policy is a mechanism which solves the non-determinism by choosing for each finite run an action and the time moment of the next transition step implied by this action. We prove that, given a probabilistic timed automaton A, there exists a Markov (memoryless) policy which maximizes the probability p of the set of accepting runs realized by this policy. This policy as well as the maximal value of p are computable in polytime in the size of the region automaton of A. This result provides an algorithm of model-checking for properties like "there is a policy which realizes a correct behavior of the system with probability at least p".