A Fully Abstract Symbolic Semantics for Psi-Calculi

We present a symbolic transition system and bisimulation equivalence for psi-calculi, and show that it is fully abstract with respect to bisimulation congruence in the non-symbolic semantics. A psi-calculus is an extension of the pi-calculus with nominal data types for data structures and for logical assertions representing facts about data. These can be transmitted between processes and their names can be statically scoped using the standard pi-calculus mechanism to allow for scope migrations. Psi-calculi can be more general than other proposed extensions of the pi-calculus such as the applied pi-calculus, the spi-calculus, the fusion calculus, or the concurrent constraint pi-calculus. Symbolic semantics are necessary for an efficient implementation of the calculus in automated tools exploring state spaces, and the full abstraction property means the semantics of a process does not change from the original

Symbolic Bisimulation for Probabilistic Systems

International audienceThe paper introduces symbolic bisimulations for a simple probabilistic π-calculus to overcome the infinite branching problem that still exists in checking ground bisimulations between probabilistic systems. Especially the definition of weak (symbolic) bisimulation does not rely on the random capability of adversaries and sug- gests a solution to the open problem on the axiomati- zation for weak bisimulation in the case of unguarded recursion. Furthermore, we present an efficient char- acterization of symbolic bisimulations for the calculus, which allows the ”on-the-fly” instantiation of bound names and dynamic construction of equivalence rela- tions for quantitative evaluation. This directly results in a local decision algorithm that can explore just a minimal portion of the state spaces of probabilistic pro- cesses in question

A coalgebraic semantics for causality in Petri nets

In this paper we revisit some pioneering efforts to equip Petri nets with compact operational models for expressing causality. The models we propose have a bisimilarity relation and a minimal representative for each equivalence class, and they can be fully explained as coalgebras on a presheaf category on an index category of partial orders. First, we provide a set-theoretic model in the form of a a causal case graph, that is a labeled transition system where states and transitions represent markings and firings of the net, respectively, and are equipped with causal information. Most importantly, each state has a poset representing causal dependencies among past events. Our first result shows the correspondence with behavior structure semantics as proposed by Trakhtenbrot and Rabinovich. Causal case graphs may be infinitely-branching and have infinitely many states, but we show how they can be refined to get an equivalent finitely-branching model. In it, states are equipped with symmetries, which are essential for the existence of a minimal, often finite-state, model. The next step is constructing a coalgebraic model. We exploit the fact that events can be represented as names, and event generation as name generation. Thus we can apply the Fiore-Turi framework: we model causal relations as a suitable category of posets with action labels, and generation of new events with causal dependencies as an endofunctor on this category. Then we define a well-behaved category of coalgebras. Our coalgebraic model is still infinite-state, but we exploit the equivalence between coalgebras over a class of presheaves and History Dependent automata to derive a compact representation, which is equivalent to our set-theoretical compact model. Remarkably, state reduction is automatically performed along the equivalence.Comment: Accepted by Journal of Logical and Algebraic Methods in Programmin

Bisimulation for quantum processes

In this paper we introduce a novel notion of probabilistic bisimulation for quantum processes and prove that it is congruent with respect to various process algebra combinators including parallel composition even when both classical and quantum communications are present. We also establish some basic algebraic laws for this bisimulation. In particular, we prove uniqueness of the solutions to recursive equations of quantum processes, which provides a powerful proof technique for verifying complex quantum protocols.Comment: Journal versio

An Algorithm for Probabilistic Alternating Simulation

In probabilistic game structures, probabilistic alternating simulation (PA-simulation) relations preserve formulas defined in probabilistic alternating-time temporal logic with respect to the behaviour of a subset of players. We propose a partition based algorithm for computing the largest PA-simulation, which is to our knowledge the first such algorithm that works in polynomial time, by extending the generalised coarsest partition problem (GCPP) in a game-based setting with mixed strategies. The algorithm has higher complexities than those in the literature for non-probabilistic simulation and probabilistic simulation without mixed actions, but slightly improves the existing result for computing probabilistic simulation with respect to mixed actions.Comment: We've fixed a problem in the SOFSEM'12 conference versio