Decision Algorithms for Probabilistic Bisimulation
نویسندگان
چکیده
We propose decision algorithms for bisimulation relations defined on probabilistic automata, a model for concurrent nondeterministic systems with randomization. The algorithms decide both strong and weak bisimulation relations based on deterministic as well as randomized schedulers. These algorithms extend and complete other known algorithms for simpler relations and models. The algorithm we present for strong probabilistic bisimulation has polynomial time complexity, while the algorithm for weak probabilistic bisimulation is exponential; however we argue that the latter is feasible in practice.
منابع مشابه
On the Efficiency of Deciding Probabilistic Automata Weak Bisimulation
Weak probabilistic bisimulation on probabilistic automata can be decided by an algorithm that needs to check a polynomial number of linear programming problems encoding weak transitions. It is hence polynomial, but not guaranteed to be strongly polynomial. In this paper we show that for polynomial rational probabilistic automata strong polynomial complexity can be ensured. We further discuss co...
متن کاملExploiting Robust Optimization for Interval Probabilistic Bisimulation
Verification of PCTL properties of MDPs with convex uncertainties has been investigated recently by Puggelli et al. However, model checking algorithms typically suffer from the state space explosion problem. In this paper, we discuss the use of probabilistic bisimulation to reduce the size of such an MDP while preserving the PCTL properties it satisfies. As a core part, we show that deciding bi...
متن کاملCompositional Reasoning for Interval Markov Decision Processes
Model checking probabilistic CTL properties of Markov decision processes with convex uncertainties has been recently investigated by Puggelli et al. Such model checking algorithms typically suffer from the state space explosion. In this paper, we address probabilistic bisimulation to reduce the size of such an MDP while preserving the probabilistic CTL properties it satisfies. In particular, we...
متن کاملVerifying probabilistic systems: new algorithms and complexity results
The content of the dissertation falls in the area of formal verification of probabilistic systems. It comprises four parts listed below: 1. the decision problem of (probabilistic) simulation preorder between probabilistic pushdown automata (pPDAs) and finite probabilistic automata (fPAs); 2. the decision problem of a bisimilarity metric on finite probabilistic automata (fPAs); 3. the approximat...
متن کاملCost Preserving Bisimulations for Probabilistic Automata
Probabilistic automata constitute a versatile and elegant model for concurrent probabilistic systems. They are equipped with a compositional theory supporting abstraction, enabled by weak probabilistic bisimulation serving as the reference notion for summarising the effect of abstraction. This paper considers probabilistic automata augmented with costs. It extends the notions of weak transition...
متن کامل