In this notes we consider the model of Generative Probabilistic Transition Systems, and Baier and Hermanns’ notion of weak bisimulation defined over them. We prove that, if we consider any process algebra giving rise to a Probabilistic Transition System satisfying the condition of regularity and offering prefixing, interleaving, and guarded recursion, then the coarsest congruence that is contai...

Bisimulations are a broadly used formalism to deene the semantics of process algebras. In particular, by means of weak bisimulation most of the internal activity of processes may be abstracted. Unfortunately, this is not fully accomplished: for instance, the internal choice operator becomes non-associative since bisimulation can see the branching structure of processes. In this paper we propose...

Van Glabbeek and Goltz (and later Fecher) have investigated the relationships between various equivalences on stable configuration structures, including interleaving bisimulation (IB), step bisimulation (SB), pomset bisimulation and hereditary history-preserving (H-H) bisimulation. Since H-H bisimulation may be characterised by the use of reverse as well as forward transitions, it is of interes...

Simulation preorder/equivalence and bisimulation equivalence are the most commonly used equivalences in concurrency theory. Their standard definitions are often called strong simulation/bisimulation, while weak simulation/bisimulation abstracts from internal τ -actions. We study the computational complexity of checking these strong and weak semantic preorders/equivalences between pushdown proce...

We consider the following problems: (a) Given a labelled Petri net and a finite automaton, are they equivalent? (b) Given a labelled Petri net, is it equivalent to some (unspecified) finite automaton? These questions are studied within the framework of trace and bisimulation equivalences, in both their strong and weak versions. (In the weak version a special action—likened to an "-move in autom...

Weighted labelled transition systems are LTSs whose transitions are given weights drawn from a commutative monoid. WLTSs subsume a wide range of LTSs, providing a general notion of strong (weighted) bisimulation. In this paper we extend this framework towards other behavioural equivalences, by considering semirings of weights. Taking advantage of this extra structure, we introduce a general not...

Branching bisimulation with explicit divergence, introduced by van Glabbeek and Weijland, is an important relation between processes. It is the weakest equivalence relation which is a branching bisimulation and at the same time divergence preserving. Like branching bisimulation, it has two major characterizations in the literature: a relational characterization and a coloured trace characteriza...

Language equivalence can be checked coinductively by establishing a bisimulation on suitable deterministic automata. We improve and extend this technique with bisimulation-up-to, which is an enhancement of the bisimulation proof method. First, we focus on the regular operations of union, concatenation and Kleene star, and illustrate our method with new proofs of classical results such as Arden’...

Bisimulations that abstract from internal computation have proven to be useful for veriication of compositionally deened transition system. In the literature of probabilistic extensions of such transition systems, similar bisimulations are rare. In this paper, we introduce weak bisimulation and branching bisimulation for transition systems where nondeterministic branching is replaced by probabi...

Concurrent ML is an extension of Standard ML with π-calculus-like primitives for multi-threaded programming. CML has a reduction semantics, but to date there has been no labelled transitions semantics provided for the entire language. In this paper, we present a labelled transition semantics for a fragment of CML called μνCML which includes features not covered before: dynamically generated loc...