Theoretical Computer Science
Symbolic model checking for real-time systems
Information and Computation
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Expressing interesting properties of programs in propositional temporal logic
POPL '86 Proceedings of the 13th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Performance of Computer Communication Systems: A Model-Based Approach
Performance of Computer Communication Systems: A Model-Based Approach
Automatic verification of real-time systems with discrete probability distributions
Theoretical Computer Science
A Classification of Symbolic Transition Systems
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Probabilistic Lossy Channel Systems
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Verifying Quantitative Properties of Continuous Probabilistic Timed Automata
CONCUR '00 Proceedings of the 11th International Conference on Concurrency Theory
Model Checking of Probabalistic and Nondeterministic Systems
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
Model Checking Continuous-Time Markov Chains by Transient Analysis
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
General decidability theorems for infinite-state systems
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Approximating Labeled Markov Processes
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Computing simulations on finite and infinite graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Model checking for a probabilistic branching time logic with fairness
Distributed Computing
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Verifying Randomized Byzantine Agreement
FORTE '02 Proceedings of the 22nd IFIP WG 6.1 International Conference Houston on Formal Techniques for Networked and Distributed Systems
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We study the maximal reachability probability problem for infinite-state systems featuring both nondeterministic and probabilistic choice. The problem involves the computation of the maximal probability of reaching a given set of states, and underlies decision procedures for the automatic verification of probabilistic systems. We extend the framework of symbolic transition systems, which equips an infinite-state system with an algebra of symbolic operators on its state space, with a symbolic encoding of probabilistic transitions to obtain a model for an infinite-state probabilistic system called a symbolic probabilistic system. An exact answer to the maximal reachability probability problem for symbolic probabilistic systems is obtained algorithmically via iteration of a refined version of the classical predecessor operation, combined with intersection operations. As in the non-probabilistic case, our state space exploration algorithm is semi-decidable for infinite-state systems. We illustrate our approach with examples of probabilistic timed automata, for which previous approaches to this reachability problem were either based on unnecessarily fine subdivisions of the state space, or which obtained only an upper bound on the exact reachability probability.