Luca Aceto

Termination, deadlock, and divergence

In this paper, a process algebra that incorporates explicit representations of successful termination, deadlock, and divergence is introduced and its semantic theory is analyzed. Both an operational and a denotational semantics for the language is given and it is shown that they agree. The operational theory is based upon a suitable adaptation of the notion of bisimulation preorder. The denotational semantics for the language is given in terms of the initial continuous algebra that satisfies a set of equations <italic>E</italic>, <italic>CI<supscrpt>E</supscrpt></italic>. It is shown that <italic>CI<supscrpt>E</supscrpt></italic> is fully abstract with respect to our choice of behavioral preorder. Several results of independent interest are obtained; namely, the finite approximability of the behavioral preorder and a partial completeness result for the set of equations <italic>E</italic> with respect to the preorder.

Timing and causality in process algebra

There has been considerable controversy in concurrency theory between the ‘interleaving’ and ‘true concurrency’ schools. The former school advocates associating a transition system with a process which captures concurrent execution via the interleaving of occurrences; the latter adopts more complex semantic structures to avoid reducing concurrency to interleaving.In this paper we show that the two approaches are not irreconcilable. We define a timed process algebra where occurrences are associated with intervals of time, and give it a transition system semantics. This semantics has many of the advantages of the interleaving approach; the algebra admits an expansion theorem, and bisimulation semantics can be used as usual. Our transition systems, however, incorporate timing information, and this enables us to express concurrency: merely adding timing appropriately generalises transition systems to asynchronous transition systems, showing that time gives a link between true concurrency and interleaving. Moreover, we can provide a complete axiomatisation of bisimulation for our algebra; a result that is often problematic in a timed setting.Another advantage of incorporating timing information into the calculus is that it allows a particularly simple definition of action refinement; this we present. The paper concludes with a comparison of the equivalence we present with those in the literature, and an example system specification in our formalism.

Towards action-refinement in process algebras

Abstract We present a simple process algebra which supports a form of refinement of an action by a process and address the question of an appropriate equivalence relation for it. The main result of the paper is that an adequate equivalence can be defined in a very intuitive manner. In fact we show that it coincides with the timed-equivalence proposed by one of the authors. We also show that it can be characterized equationally.

The power of reachability testing for timed automata

The computational engine of the verification tool UPPALL consists of a collection of efficient algorithms for the analysis of teachability properties of systems. Model-checking of properties other than plain reachability ones may currently be carried out in such a tool as follows. Given a property φ to model-check, the user must provide a test automaton Tφ for it. This test automaton must be such that the original system S has the property expressed by φ precisely when none of the distinguished reject states of Tφ can be reached in the synchronized parallel composition of S with Tφ. This raises the question of which properties may be analysed by UPPAAL in such a way. This paper gives an answer to this question by providing a complete characterization of the class of properties for which model-checking can be reduced to reachability testing in the sense outlined above. This result is obtained as a corollary of a stronger statement pertaining to the compositionality of the property language considered in this study. In particular, it is shown that our language is the least expressive compositional language that can express a simple safety property stating that no reject state can ever be reached.Finally, the property language characterizing the power of reachability testing is used to provide a definition of characteristics properties with respect to a timed version of the ready simulation preorder, for nodes of τ-free, deterministic timed automata.

A static view of localities

This paper proposes alternative, effective characterizations for nets of automata of the location equivalence and preorder presented by Boudol et al. in the companion paper [BCHK]. Contrary to the technical development in the above given reference, where locations are dynamically associated to the subparts of a process in the operational semantics, the equivalence and preorder we propose are based on a static association of locations to the parallel components of a net. Following this static approach, it is possible to give these “distributed nets” a standard operational semantics which associates with each net a finite labelled transition system. Using this operational semantics for distributed nets, we introduce effective notions of equivalence and preorder which are shown to coincide with those proposed in [BCHK].

Modelling and simulation of asynchronous real-time systems using Timed Rebeca

Abstract In this paper we propose Timed Rebeca as an extension of the Rebeca language that can be used to model distributed and asynchronous systems with timing constraints. Timed Rebeca restricts the modeller to a pure asynchronous actor-based paradigm, where the structure of the model represents the service oriented architecture, while the computational model matches the network infrastructure. The modeller can specify both computational and network delay, and assign deadlines for serving a request. We provide the formal semantics of the language using Structural Operational Semantics, and show its expressiveness by means of examples. We developed a tool for automated translation from Timed Rebeca to the Erlang language, which provides a first implementation of Timed Rebeca. We can use the tool to set the parameters of Timed Rebeca models, which represent the environment and component variables, and use McErlang to run multiple simulations for different settings. The results of the simulations can then be employed to select the most appropriate values for the parameters in the model. Simulation is shown to be an effective analysis support, specially where model checking faces almost immediate state explosion in an asynchronous setting.

Is your model checker on time? On the complexity of model checking for timed modal logics

Abstract This paper studies the structural complexity of model checking for several timed modal logics presented in the literature. More precisely, we consider (variations on) the specification formalisms used in the tools CMC and Uppaal , and fragments of a timed μ-calculus. For each of the logics, we characterize the computational complexity of model checking, as well as its specification and program complexity, using (parallel compositions of) timed automata as our system model. In particular, we show that the complexity of model checking for a timed μ-calculus interpreted over (networks of) timed automata is EXPTIME-complete, no matter whether the complexity is measured with respect to the size of the specification, of the model or of both. All the flavours of model checking for timed versions of Hennessy–Milner logic, and the restricted fragments of the timed μ-calculus studied in the literature on CMC and Uppaal , are shown to be PSPACE-complete or EXPTIME-complete. Amongst the complexity results offered in the paper is a theorem to the effect that the model checking problem for the sublanguage Ls of the timed μ-calculus, proposed by Larsen, Pettersson and Yi, is PSPACE-complete. This result is accompanied by an array of statements showing that any extension of Ls has an EXPTIME-complete model checking problem. We also argue that the model checking problem for the timed propositional μ-calculus Tμ is EXPTIME-complete, thus improving upon results by Henzinger, Nicollin, Sifakis and Yovine.

On the Ill-Timed but Well-Caused

There has been considerable controversy in concurrency theory between the ‘interleaving’ and ‘true concurrency’ schools. The former school advocates associating a transition system with a process which captures concurrent execution via the interleaving of occurrences: the latter adopts more complex semantic structures to avoid reducing concurrency to interleaving.

Axiomatizing Prefix Iteration with Silent Steps

Prefix iteration is a variation on the original binary version of the Kleene star operationP*Q, obtained by restricting the first argument to be an atomic action. The interaction of prefix iteration with silent steps is studied in the setting of Milners basic CCS. Complete equational axiomatizations are given for four notions of behavioural congruence over basic CCS with prefix iteration, viz., branching congruence,?-congruence, delay congruence, and weak congruence. The completeness proofs for?-, delay, and weak congruence are obtained by reduction to the completeness theorem for branching congruence. It is also argued that the use of the completeness result for branching congruence in obtaining the completeness result for weak congruence leads to a considerable simplification with respect to the only direct proof presented in the literature. The preliminaries and the completeness proofs focus on open terms, i.e., terms that may contain process variables. As a by-product, the?-completeness of the axiomatizations is obtained, as well as their completeness for closed terms.

Deriving Complete Inference Systems for a Class of GSOS Languages Generation Regular Behaviours

In this paper I characterize a class of infinitary GSOS specifications, obtained by relaxing some of the finiteness constraints of the original format of Bloom, Istrail and Meyer, which generate regular processes. I then show how the techniques of Aceto, Bloom and Vaandrager can be adapted to give a procedure for converting any such language definition to a complete equational axiom system for strong bisimulation of processes which does not use infinitary proof rules. Equalities between recursive, regular processes can be established in the resulting inference systems by means of standard axioms to unwind recursive definitions, and the so-called Recursive Specification Principle (RSP).