Rob J. van Glabbeek

Branching time and abstraction in bisimulation semantics

In comparative concurrency semantics, one usually distinguishes between linear time and branching time semantic equivalences. Milners notion of observatin equivalence is often mentioned as the standard example of a branching time equivalence. In this paper we investigate whether observation equivalence really does respect the branching structure of processes, and find that in the presence of the unobservable action τ of CCS this is not the case. Therefore, the notion of branching bisimulation equivalence is introduced which strongly preserves the branching structure of processes, in the sense that it preserves computations together with the potentials in all intermediate states that are passed through, even if silent moves are involved. On closed CCS-terms branching bisimulation congruence can be completely axiomatized by the single axion scheme: a.(τ.(y+z)+y)=a.(y+z) (where a ranges over all actions) and the usual loaws for strong congruence. We also establish that for sequential processes observation equivalence is not preserved under refinement of actions, whereas branching bisimulation is. For a large class of processes, it turns out that branching bisimulation and observation equivalence are the same. As far as we know, all protocols that have been verified in the setting of observation equivalence happen to fit in this class, and hence are also valid in the stronger setting of branching bisimulation equivalence.

Petri net models for algebraic theories of concurrency

In this paper we discuss the issue of interleaving semantics versus True concurrency in an algebraic setting. We present various equivalence notions on Petri nets which can be used in the construction of algebraic models: (a) the occurrence net equivalence of Nielsen, Plotkin & Winskel; (b) bisimulation equivalence, which leads to a model which is isomorphic to the graph model of Baeten, Bergstra & Klop; (c) the concurrent bisimulation equivalence, which is also described by Nielsen & Thiagarajan, and Goltz; (d) partial order equivalences which are inspired by work of Pratt, and Boudol & Castellani.

Refinement of actions and equivalence notions for concurrent systems

Abstract. We study an operator for refinement of actions to be used in the design of concurrent systems. Actions on a given level of abstraction are replaced by more complicated processes on a lower level. This is done in such a way that the behaviour of the refined system may be inferred compositionally from the behaviour of the original system and from the behaviour of the processes substituted for actions. We recall that interleaving models of concurrent systems are not suited for defining such an operator in its general form. Instead, we define this operator on several causality based, event oriented models, taking into account the distinction between deadlock and successful termination. Then we investigate the interplay of action refinement with abstraction in terms of equivalence notions for concurrent systems, considering both linear time and branching time approaches. We show that besides the interleaving equivalences, also the equivalences based on steps are not preserved under refinement of actions. We prove that linear time partial order semantics are invariant under refinement. Finally we consider various bisimulation equivalences based on partial orders and show that the finest two of them are preserved under refinement whereas the others are not. Termination sensitive versions of these equivalences are even congruences for action refinement.

Equivalence notions for concurrent systems and refinement of actions

We investigate equivalence notions for concurrent systems. We consider ”linear time” approaches where the system behaviour is characterised as the set of possible runs as well as ”branching time” approaches where the conflict structure of systems is taken into account. We show that the usual interleaving equivalences, and also the equivalences based on steps (multisets of concurrently executed actions) are not preserved by refinement of atomic actions. We prove that ”linear time” partial order semantics, where causality in runs is explicit, is invariant under refinement. Finally, we consider various bisimulation equivalences based on partial orders and show that the strongest one of them is preserved by refinement whereas the others are not.

Bounded Nondeterminism and the Approximation Induction Principle in Process Algebra

This paper presents a new semantics of ACPτ, the Algebra of Communicating Processes with abstraction. This leads to a term model of ACPτ which is isomorphic to the model of process graphs modulo rooted τδ-bisimulation of Baeten, Bergstra & Klop

Ntyft/ntyxt Rules Reduce to Ntree Rules

Groote and Vaandrager introduced thetyft/tyxt formatfor Transition System Specifications (TSSs), and established that for each TSS in this format that iswell-founded, the bisimulation equivalence it induces is a congruence. In this paper, we construct for each TSS in tyft/tyxt format an equivalent TSS that consists oftree rulesonly. As a corollary we can give an affirmative answer to an open question, namely whether the well-foundedness condition in the congruence theorem for tyft/tyxt can be dropped. These results extend to tyft/tyxt with negative premises and predicates.

Proof nets for unit-free multiplicative-additive linear logic

A cornerstone of the theory of proof nets for unit-free multiplicative linear logic (MLL) is the abstract representation of cut-free proofs modulo inessential rule commutation. The only known extension to additives, based on monomial weights, fails to preserve this key feature: a host of cut-free monomial proof nets can correspond to the same cut-free proof. Thus, the problem of finding a satisfactory notion of proof net for unit-free multiplicative-additive linear logic (MALL) has remained open since the inception of linear logic in 1986. We present a new definition of MALL proof net which remains faithful to the cornerstone of the MLL theory.

Precongruence formats for decorated trace semantics

This paper explores the connection between semantic equivalences and preorders for concrete sequential processes, represented by means of labeled transition systems, and formats of transition system specifications using Plotkins structural approach. For several preorders in the linear time---branching time spectrum a format is given, as general as possible, such that this preorder is a precongruence for all operators specifiable in that format. The formats are derived using the modal characterizations of the corresponding preorders.

Automated analysis of AODV using UPPAAL

This paper describes an automated, formal and rigorous analysis of the Ad hoc On-Demand Distance Vector (AODV) routing protocol, a popular protocol used in wireless mesh networks. We give a brief overview of a model of AODV implemented in the UPPAAL model checker. It is derived from a process-algebraic model which reflects precisely the intention of AODV and accurately captures the protocol specification. Furthermore, we describe experiments carried out to explore AODVs behaviour in all network topologies up to 5 nodes. We were able to automatically locate problematic and undesirable behaviours. This is in particular useful to discover protocol limitations and to develop improved variants. This use of model checking as a diagnostic tool complements other formal-methods-based protocol modelling and verification techniques, such as process algebra.

A process algebra for wireless mesh networks

We propose a process algebra for wireless mesh networks that combines novel treatments of local broadcast, conditional unicast and data structures. In this framework, we model the Ad-hoc On-Demand Distance Vector (AODV) routing protocol and (dis)prove crucial properties such as loop freedom and packet delivery.