Structural operational semantics for stochastic and weighted transition systems

We introduce weighted GSOS, a general syntactic framework to specify well-behaved transition systems where transitions are equipped with weights coming from a commutative monoid. We prove that weighted bisimilarity is a congruence on systems defined by weighted GSOS specifications. We illustrate the flexibility of the framework by instantiating it to handle some special cases, most notably that of stochastic transition systems. Through examples we provide weighted-GSOS definitions for common stochastic operators in the literature

A uniform definition of stochastic process calculi

We introduce a unifying framework to provide the semantics of process algebras, including their quantitative variants useful for modeling quantitative aspects of behaviors. The unifying framework is then used to describe some of the most representative stochastic process algebras. This provides a general and clear support for an understanding of their similarities and differences. The framework is based on State to Function Labeled Transition Systems, FuTSs for short, that are state-transition structures where each transition is a triple of the form (s; α;P). The first andthe second components are the source state, s, and the label, α, of the transition, while the third component is the continuation function, P, associating a value of a suitable type to each state s0. For example, in the case of stochastic process algebras the value of the continuation function on s0 represents the rate of the negative exponential distribution characterizing the duration/delay of the action performed to reach state s0 from s. We first provide the semantics of a simple formalism used to describe Continuous-Time Markov Chains, then we model a number of process algebras that permit parallel composition of models according to the two main interaction paradigms (multiparty and one-to-one synchronization). Finally, we deal with formalisms where actions and rates are kept separate and address the issues related to the coexistence of stochastic, probabilistic, and non-deterministic behaviors. For each formalism, we establish the formal correspondence between the FuTSs semantics and its original semantics

Finite petri nets as models for recursive causal behaviour

Goltz (1988) discussed whether or not there exist finite Petri nets (with unbounded capacities) modelling the causal behaviour of certain recursive CCS terms. As a representative example, the following term is considered: \ud \ud B=(a.nilb.B)+c.nil. \ud \ud We will show that the answer depends on the chosen notion of behaviour. It was already known that the interleaving behaviour and the branching structure of terms as B can be modelled as long as causality is not taken into account. We now show that also the causal behaviour of B can be modelled as long as the branching structure is not taken into account. However, it is not possible to represent both causal dependencies and the behaviour with respect to choices between alternatives in a finite net. We prove that there exists no finite Petri net modelling B with respect to both pomset trace equivalence and failure equivalence

Dynamic Congruence vs. Progressing Bisimulation for CCS

Weak Observational Congruence (woc) defined on CCS agents is not a bisimulation since it does not require two states reached by bisimilar computations of woc agents to be still woc, e.g. \alpha.\tau.\beta.nil and \alpha.\beta.nil are woc but \tau.\beta.nil and \beta.nil are not. This fact prevent us from characterizing CCS semantics (when \tau is considered invisible) as a final algebra, since the semantic function would induce an equivalence over the agents that is both a congruence and a bisimulation. In the paper we introduce a new behavioural equivalence for CCS agents, which is the coarsest among those bisimulations which are also congruences. We call it Dynamic Observational Congruence because it expresses a natural notion of equivalence for concurrent systems required to simulate each other in the presence of dynamic, i.e. run time, (re)configurations. We provide an algebraic characterization of Dynamic Congruence in terms of a universal property of finality. Furthermore we introduce Progressing Bisimulation, which forces processes to simulate each other performing explicit steps. We provide an algebraic characterization of it in terms of finality, two logical characterizations via modal logic in the style of HML and a complete axiomatization for finite agents (consisting of the axioms for Strong Observational Congruence and of two of the three Milner's $\tau$-laws). Finally, we prove that Dynamic Congruence and Progressing Bisimulation coincide for CCS agents

Read Operators and their Expressiveness in Process Algebras

We study two different ways to enhance PAFAS, a process algebra for modelling asynchronous timed concurrent systems, with non-blocking reading actions. We first add reading in the form of a read-action prefix operator. This operator is very flexible, but its somewhat complex semantics requires two types of transition relations. We also present a read-set prefix operator with a simpler semantics, but with syntactic restrictions. We discuss the expressiveness of read prefixes; in particular, we compare them to read-arcs in Petri nets and justify the simple semantics of the second variant by showing that its processes can be translated into processes of the first with timed-bisimilar behaviour. It is still an open problem whether the first algebra is more expressive than the second; we give a number of laws that are interesting in their own right, and can help to find a backward translation.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

TAPAs: A Tool for the Analysis of Process Algebras

Process algebras are formalisms for modelling concurrent systems that permit mathematical reasoning with respect to a set of desired properties. TAPAs is a tool that can be used to support the use of process algebras to specify and analyze concurrent systems. It does not aim at guaranteeing high performances, but has been developed as a support to teaching. Systems are described as process algebras terms that are then mapped to labelled transition systems (LTSs). Properties are verified either by checking equivalence of concrete and abstract systems descriptions, or by model checking temporal formulae over the obtained LTS. A key feature of TAPAs, that makes it particularly suitable for teaching, is that it maintains a consistent double representation of each system both as a term and as a graph. Another useful didactical feature is the exhibition of counterexamples in case equivalences are not verified or the proposed formulae are not satisfied

CCS Dynamic Bisimulation is Progressing

Weak Observational Congruence (woc) defined on CCS agents is not a bisimulation since it does not require two states reached by bisimilar computations of woc agents to be still woc, e.g.\ $\alpha.\tau.\beta.nil$ and $\alpha.\beta.nil$ are woc but $\tau.\beta.nil$ and $\beta.nil$ are not. This fact prevents us from characterizing CCS semantics (when $\tau$ is considered invisible) as a final algebra, since the semantic function would induce an equivalence over the agents that is both a congruence and a bisimulation. In the paper we introduce a new behavioural equivalence for CCS agents, which is the coarsest among those bisimulations which are also congruences. We call it Dynamic Observational Congruence because it expresses a natural notion of equivalence for concurrent systems required to simulate each other in the presence of dynamic, i.e.\ run time, (re)configurations. We provide an algebraic characterization of Dynamic Congruence in terms of a universal property of finality. Furthermore we introduce Progressing Bisimulation, which forces processes to simulate each other performing explicit steps. We provide an algebraic characterization of it in terms of finality, two characterizations via modal logic in the style of HML, and a complete axiomatization for finite agents. Finally, we prove that Dynamic Congruence and Progressing Bisimulation coincide for CCS agents. Thus the title of the paper

A synchronous program algebra: a basis for reasoning about shared-memory and event-based concurrency

This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave) when composed in parallel. The algebra of rely/guarantee concurrency then becomes an instantiation of the more abstract algebra. Many of the core properties needed for rely/guarantee reasoning can be shown to hold in the abstract algebra where their proofs are simpler and hence allow a higher degree of automation. The algebra has been encoded in Isabelle/HOL to provide a basis for tool support for program verification. In rely/guarantee concurrency, programs are specified to guarantee certain behaviours until assumptions about the behaviour of their environment are violated. When assumptions are violated, program behaviour is unconstrained (aborting), and guarantees need no longer hold. To support these guarantees a second synchronous operator, weak conjunction, was introduced: both processes in a weak conjunction must agree to take each atomic step, unless one aborts in which case the whole aborts. In developing the laws for parallel and weak conjunction we found many properties were shared by the operators and that the proofs of many laws were essentially the same. This insight led to the idea of generalising synchronisation to an abstract operator with only the axioms that are shared by the parallel and weak conjunction operator, so that those two operators can be viewed as instantiations of the abstract synchronisation operator. The main differences between parallel and weak conjunction are how they combine individual atomic steps; that is left open in the axioms for the abstract operator.Comment: Extended version of a Formal Methods 2016 paper, "An algebra of synchronous atomic steps

Towards a homotopy theory of process algebra

This paper proves that labelled flows are expressive enough to contain all process algebras which are a standard model for concurrency. More precisely, we construct the space of execution paths and of higher dimensional homotopies between them for every process name of every process algebra with any synchronization algebra using a notion of labelled flow. This interpretation of process algebra satisfies the paradigm of higher dimensional automata (HDA): one non-degenerate full $n$-dimensional cube (no more no less) in the underlying space of the time flow corresponding to the concurrent execution of $n$ actions. This result will enable us in future papers to develop a homotopical approach of process algebras. Indeed, several homological constructions related to the causal structure of time flow are possible only in the framework of flows.Comment: 33 pages ; LaTeX2e ; 1 eps figure ; package semantics included ; v2 HDA paradigm clearly stated and simplification in a homotopical argument ; v3 "bug" fixed in notion of non-twisted shell + several redactional improvements ; v4 minor correction : the set of labels must not be ordered ; published at http://intlpress.com/HHA/v10/n1/a16