Lattice structures for bisimilar Probabilistic Automata

The paper shows that there is a deep structure on certain sets of bisimilar Probabilistic Automata (PA). The key prerequisite for these structures is a notion of compactness of PA. It is shown that compact bisimilar PA form lattices. These results are then used in order to establish normal forms not only for finite automata, but also for infinite automata, as long as they are compact.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Computing Distances between Probabilistic Automata

We present relaxed notions of simulation and bisimulation on Probabilistic Automata (PA), that allow some error epsilon. When epsilon is zero we retrieve the usual notions of bisimulation and simulation on PAs. We give logical characterisations of these notions by choosing suitable logics which differ from the elementary ones, L with negation and L without negation, by the modal operator. Using flow networks, we show how to compute the relations in PTIME. This allows the definition of an efficiently computable non-discounted distance between the states of a PA. A natural modification of this distance is introduced, to obtain a discounted distance, which weakens the influence of long term transitions. We compare our notions of distance to others previously defined and illustrate our approach on various examples. We also show that our distance is not expansive with respect to process algebra operators. Although L without negation is a suitable logic to characterise epsilon-(bi)simulation on deterministic PAs, it is not for general PAs; interestingly, we prove that it does characterise weaker notions, called a priori epsilon-(bi)simulation, which we prove to be NP-difficult to decide.Comment: In Proceedings QAPL 2011, arXiv:1107.074

Probabilistic Bisimulations for PCTL Model Checking of Interval MDPs

Verification of PCTL properties of MDPs with convex uncertainties has been investigated recently by Puggelli et al. However, model checking algorithms typically suffer from state space explosion. In this paper, we address probabilistic bisimulation to reduce the size of such an MDPs while preserving PCTL properties it satisfies. We discuss different interpretations of uncertainty in the models which are studied in the literature and that result in two different definitions of bisimulations. We give algorithms to compute the quotients of these bisimulations in time polynomial in the size of the model and exponential in the uncertain branching. Finally, we show by a case study that large models in practice can have small branching and that a substantial state space reduction can be achieved by our approach.Comment: In Proceedings SynCoP 2014, arXiv:1403.784

When equivalence and bisimulation join forces in probabilistic automata

Probabilistic automata were introduced by Rabin in 1963 as language acceptors. Two automata are equivalent if and only if they accept each word with the same probability. On the other side, in the process algebra community, probabilistic automata were re-proposed by Segala in 1995 which are more general than Rabin's automata. Bisimulations have been proposed for Segala's automata to characterize the equivalence between them. So far the two notions of equivalences and their characteristics have been studied most independently. In this paper, we consider Segala's automata, and propose a novel notion of distribution-based bisimulation by joining the existing equivalence and bisimilarities. Our bisimulation bridges the two closely related concepts in the community, and provides a uniform way of studying their characteristics. We demonstrate the utility of our definition by studying distribution-based bisimulation metrics, which gives rise to a robust notion of equivalence for Rabin's automata. © 2014 Springer International Publishing Switzerland

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 proba- bilistic automata strong polynomial complexity can be ensured. We further discuss complexity bounds for generic probabilistic automata. Then we consider several practical algorithms and LP transformations that enable an efficient solution for the concrete weak transition problem. This sets the ground for effective compositional minimisation approaches for probabilistic automata and Markov decision processes

SCC-based improved reachability analysis for Markov decision processes

Markov decision processes (MDPs) are extensively used to model systems with both probabilistic and nondeterministic behavior. The problem of calculating the probability of reaching certain system states (hereafter reachability analysis) is central to the MDP-based system analysis. It is known that existing approaches on reachability analysis for MDPs are often inefficient when a given MDP contains a large number of states and loops, especially with the existence of multiple probability distributions. In this work, we propose a method to eliminate strongly connected components (SCCs) in an MDP using a divide-and-conquer algorithm, and actively remove redundant probability distributions in the MDP based on the convex property. With the removal of loops and parts of probability distributions, the probabilistic reachability analysis can be accelerated, as evidenced by our experiment results.No Full Tex

Coalgebra Encoding for Efficient Minimization

Recently, we have developed an efficient generic partition refinement algorithm, which computes behavioural equivalence on a state-based system given as an encoded coalgebra, and implemented it in the tool CoPaR. Here we extend this to a fully fledged minimization algorithm and tool by integrating two new aspects: (1) the computation of the transition structure on the minimized state set, and (2) the computation of the reachable part of the given system. In our generic coalgebraic setting these two aspects turn out to be surprisingly non-trivial requiring us to extend the previous theory. In particular, we identify a sufficient condition on encodings of coalgebras, and we show how to augment the existing interface, which encapsulates computations that are specific for the coalgebraic type functor, to make the above extensions possible. Both extensions have linear run time