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.

Revisiting Trace and Testing Equivalences for Nondeterministic and Probabilistic Processes

Two of the most studied extensions of trace and testing equivalences to nondeterministic and probabilistic processes induce distinctions that have been questioned and lack properties that are desirable. Probabilistic trace-distribution equivalence differentiates systems that can perform the same set of traces with the same probabilities, and is not a congruence for parallel composition. Probabilistic testing equivalence, which relies only on extremal success probabilities, is backward compatible with testing equivalences for restricted classes of processes, such as fully nondeterministic processes or generative/reactive probabilistic processes, only if specific sets of tests are admitted. In this paper, n

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.

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.

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.

On the Expressiveness of Markovian Process Calculi with Durational and Durationless Actions

Several Markovian process calculi have been proposed in the literature, which differ from each other for various aspects. With regard to the action representation, we distinguish between integrated-time Markovian process calculi, in which every action has an exponentially distributed duration associated with it, and orthogonal-time Markovian process calculi, in which action execution is separated from time passing. Similar to deterministically timed process calculi, we show that these two options are not irreconcilable by exhibiting three mappings from an integrated-time Markovian process calculus to an orthogonal-time Markovian process calculus that preserve the behavioral equivalence of process terms under different interpretations of action execution: eagerness, laziness, and maximal progress. The mappings are limited to classes of process terms of the integrated-time Markovian process calculus with restrictions on parallel composition and do not involve the full capability of the orthogonal-time Markovian process calculus of expressing nondeterministic choices, thus elucidating the only two important differences between the two calculi: their synchronization disciplines and their ways of solving choices.