Expected-Delay-Summing Weak Bisimilarity for Markov Automata

A new weak bisimulation semantics is defined for Markov automata that, in addition to abstracting from internal actions, sums up the expected values of consecutive exponentially distributed delays possibly intertwined with internal actions. The resulting equivalence is shown to be a congruence with respect to parallel composition for Markov automata. Moreover, it turns out to be comparable with weak bisimilarity for timed labeled transition systems, thus constituting a step towards reconciling the semantics for stochastic time and deterministic time.Comment: In Proceedings QAPL 2015, arXiv:1509.0816

Disjunctive Probabilistic Modal Logic is Enough for Bisimilarity on Reactive Probabilistic Systems

Larsen and Skou characterized probabilistic bisimilarity over reactive probabilistic systems with a logic including true, negation, conjunction, and a diamond modality decorated with a probabilistic lower bound. Later on, Desharnais, Edalat, and Panangaden showed that negation is not necessary to characterize the same equivalence. In this paper, we prove that the logical characterization holds also when conjunction is replaced by disjunction, with negation still being not necessary. To this end, we introduce reactive probabilistic trees, a fully abstract model for reactive probabilistic systems that allows us to demonstrate expressiveness of the disjunctive probabilistic modal logic, as well as of the previously mentioned logics, by means of a compactness argument.Comment: Aligned content with version accepted at ICTCS 2016: fixed minor typos, added reference, improved definitions in Section 3. Still 10 pages in sigplanconf forma

Weak Markovian Bisimulation Congruences and Exact CTMC-Level Aggregations for Concurrent Processes

We have recently defined a weak Markovian bisimulation equivalence in an integrated-time setting, which reduces sequences of exponentially timed internal actions to individual exponentially timed internal actions having the same average duration and execution probability as the corresponding sequences. This weak Markovian bisimulation equivalence is a congruence for sequential processes with abstraction and turns out to induce an exact CTMC-level aggregation at steady state for all the considered processes. However, it is not a congruence with respect to parallel composition. In this paper, we show how to generalize the equivalence in a way that a reasonable tradeoff among abstraction, compositionality, and exactness is achieved for concurrent processes. We will see that, by enhancing the abstraction capability in the presence of concurrent computations, it is possible to retrieve the congruence property with respect to parallel composition, with the resulting CTMC-level aggregation being exact at steady state only for a certain subset of the considered processes.Comment: In Proceedings QAPL 2012, arXiv:1207.055

Uniform Labeled Transition Systems for Nondeterministic, Probabilistic, and Stochastic Process Calculi

Labeled transition systems are typically used to represent the behavior of nondeterministic processes, with labeled transitions defining a one-step state to-state reachability relation. This model has been recently made more general by modifying the transition relation in such a way that it associates with any source state and transition label a reachability distribution, i.e., a function mapping each possible target state to a value of some domain that expresses the degree of one-step reachability of that target state. In this extended abstract, we show how the resulting model, called ULTraS from Uniform Labeled Transition System, can be naturally used to give semantics to a fully nondeterministic, a fully probabilistic, and a fully stochastic variant of a CSP-like process language.Comment: In Proceedings PACO 2011, arXiv:1108.145

The Spectrum of Strong Behavioral Equivalences for Nondeterministic and Probabilistic Processes

We present a spectrum of trace-based, testing, and bisimulation equivalences for nondeterministic and probabilistic processes whose activities are all observable. For every equivalence under study, we examine the discriminating power of three variants stemming from three approaches that differ for the way probabilities of events are compared when nondeterministic choices are resolved via deterministic schedulers. We show that the first approach - which compares two resolutions relatively to the probability distributions of all considered events - results in a fragment of the spectrum compatible with the spectrum of behavioral equivalences for fully probabilistic processes. In contrast, the second approach - which compares the probabilities of the events of a resolution with the probabilities of the same events in possibly different resolutions - gives rise to another fragment composed of coarser equivalences that exhibits several analogies with the spectrum of behavioral equivalences for fully nondeterministic processes. Finally, the third approach - which only compares the extremal probabilities of each event stemming from the different resolutions - yields even coarser equivalences that, however, give rise to a hierarchy similar to that stemming from the second approach.Comment: In Proceedings QAPL 2013, arXiv:1306.241

A uniform framework for modelling nondeterministic, probabilistic, stochastic, or mixed processes and their behavioral equivalences

Labeled transition systems are typically used as behavioral models of concurrent processes, and the labeled transitions define the a one-step state-to-state reachability relation. This model can be made generalized by modifying the transition relation to associate a state reachability distribution, rather than a single target state, with any pair of source state and transition label. The state reachability distribution becomes a function mapping each possible target state to a value that expresses the degree of one-step reachability of that state. Values are taken from a preordered set equipped with a minimum that denotes unreachability. By selecting suitable preordered sets, the resulting model, called ULTraS from Uniform Labeled Transition System, can be specialized to capture well-known models of fully nondeterministic processes (LTS), fully probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and of nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. These can be defined on ULTraS by relying on appropriate measure functions that expresses the degree of reachability of a set of states when performing single-step or multi-step computations. It is shown that the specializations of bisimulation, trace, and testing equivalences for the different classes of ULTraS coincide with the behavioral equivalences defined in the literature over traditional models

Observer design for piecewise smooth and switched systems via contraction theory

The aim of this paper is to present the application of an approach to study contraction theory recently developed for piecewise smooth and switched systems. The approach that can be used to analyze incremental stability properties of so-called Filippov systems (or variable structure systems) is based on the use of regularization, a procedure to make the vector field of interest differentiable before analyzing its properties. We show that by using this extension of contraction theory to nondifferentiable vector fields, it is possible to design observers for a large class of piecewise smooth systems using not only Euclidean norms, as also done in previous literature, but also non-Euclidean norms. This allows greater flexibility in the design and encompasses the case of both piecewise-linear and piecewise-smooth (nonlinear) systems. The theoretical methodology is illustrated via a set of representative examples.Comment: Preprint accepted to IFAC World Congress 201

Revisiting bisimilarity and its modal logic for nondeterministic and probabilistic processes

We consider PML, the probabilistic version of Hennessy-Milner logic introduced by Larsen and Skou to characterize bisimilarity over probabilistic processes without internal nondeterminism.We provide two different interpretations for PML by considering nondeterministic and probabilistic processes as models, and we exhibit two new bisimulation-based equivalences that are in full agreement with those interpretations. Our new equivalences include as coarsest congruences the two bisimilarities for nondeterministic and probabilistic processes proposed by Segala and Lynch. The latter equivalences are instead in agreement with two versions of Hennessy-Milner logic extended with an additional probabilistic operator interpreted over state distributions rather than over individual states. Thus, our new interpretations of PML and the corresponding new bisimilarities offer a uniform framework for reasoning on processes that are purely nondeterministic or reactive probabilistic or are mixing nondeterminism and probability in an alternating/non-alternating way