arXiv subjects
Publications and source records attributed to Rob van Glabbeek.
I show that in a standard process algebra extended with time-outs one can correctly model mutual exclusion in such a way that starvation-freedom holds without assuming fairness or justness, even when one makes the problem more challenging by assuming memory accesses to be atomic. This can be achieved only when dropping the requirement of speed independence.
This paper introduces the counterpart of strong bisimilarity for labelled transition systems extended with time-out transitions. It supports this concept through a modal characterisation, congruence results for a standard process algebra with recursion, and a complete axiomatisation.
The concept of must testing is naturally parametrised with a chosen completeness criterion or fairness assumption. When taking weak fairness as used in I/O automata, I show that it characterises exactly the fair preorder on I/O automata as defined by Lynch & Tuttle.
The concept of must testing is naturally parametrised with a chosen completeness criterion, defining the complete runs of a system. Here I employ justness as this completeness criterion, instead of the traditional choice of progress. The resulting must-testing preorder is incomparable with the default one, and can be characterised as the fair failure preorder of Vogler. It also is the coarsest precongruence preserving linear time properties when assuming justness. As my system model I here employ Petri nets with read arcs. Through their Petri net semantics, this work applies equally well to process algebras. I provide a Petri net semantics for a standard process algebra extended with signals; the read arcs are necessary to capture those signals.
Goltz and Reisig generalised Petri's concept of processes of one-safe Petri nets to general nets where places carry multiple tokens. BD-processes are equivalence classes of Goltz-Reisig processes connected through the swapping transformation of Best and Devillers; they can be considered as an alternative representation of runs of nets. Here we present an order respecting bijection between the BD-processes and the FS-processes of a countable net, the latter being defined -- in an analogous way -- as equivalence classes of firing sequences. Using this, we show that a countable net without binary conflicts has a (unique) largest BD-process.
This paper shows that the $π$-calculus with implicit matching is no more expressive than CCS$γ$, a variant of CCS in which the result of a synchronisation of two actions is itself an action subject to relabelling or restriction, rather than the silent action $τ$. This is done by exhibiting a compositional translation from the $π$-calculus with implicit matching to CCS$γ$ that is valid up to strong barbed bisimilarity. The full $π$-calculus can be similarly expressed in CCS$γ$ enriched with the triggering operation of Meije. I also show that these results cannot be recreated with CCS in the role of CCS$γ$, not even up to reduction equivalence, and not even for the asynchronous $π$-calculus without restriction or replication. Finally I observe that CCS cannot be encoded in the $π$-calculus.
This paper poses that transition systems constitute a good model of distributed systems only in combination with a criterion telling which paths model complete runs of the represented systems. Among such criteria, progress is too weak to capture relevant liveness properties, and fairness is often too strong; for typical applications we advocate the intermediate criterion of justness. Previously, we proposed a definition of justness in terms of an asymmetric concurrency relation between transitions. Here we define such a concurrency relation for the transition systems associated to the process algebra CCS as well as its extensions with broadcast communication and signals, thereby making these process algebras suitable for capturing liveness properties requiring justness.
Most fairness assumptions used for verifying liveness properties are criticised for being too strong or unrealistic. On the other hand, justness, arguably the minimal fairness assumption required for the verification of liveness properties, is not preserved by classical semantic equivalences, such as strong bisimilarity. To overcome this deficiency, we introduce a finer alternative to strong bisimilarity, called enabling preserving bisimilarity. We prove that this equivalence is justness-preserving and a congruence for all standard operators, including parallel composition.
We investigate how different fairness assumptions affect results concerning lock-freedom, a typical liveness property targeted by session type systems. We fix a minimal session calculus and systematically take into account all known fairness assumptions, thereby identifying precisely three interesting and semantically distinct notions of lock-freedom, all of which having a sound session type system. We then show that, by using a general merge operator in an otherwise standard approach to global session types, we obtain a session type system complete for the strongest amongst those notions of lock-freedom, which assumes only justness of execution paths, a minimal fairness assumption for concurrent systems.
This note formally defines the concept of coinductive validity of judgements, and contrasts it with inductive validity. For both notions it shows how a judgement is valid iff it has a formal proof. Finally, it defines and illustrates the notion of a proof by coinduction.
This paper extends a standard process algebra with a time-out operator, thereby increasing its absolute expressiveness, while remaining within the realm of untimed process algebra, in the sense that the progress of time is not quantified. Trace and failures equivalence fail to be congruences for this operator; their congruence closure is characterised as failure trace equivalence.
For one-safe Petri nets or condition/event-systems, a process as defined by Carl Adam Petri provides a notion of a run of a system where causal dependencies are reflected in terms of a partial order. Goltz and Reisig have generalised this concept for nets where places carry multiple tokens, by distinguishing tokens according to their causal history. However, this so-called individual token interpretation is often considered too detailed. Here we identify a subclass of Petri nets, called structural conflict nets, where no interplay between conflict and concurrency due to token multiplicity occurs. For this subclass, we define abstract processes as equivalence classes of Goltz-Reisig processes. We justify this approach by showing that there is a largest abstract process if and only if the underlying net is conflict-free with respect to a canonical notion of conflict.
We consider approaches for causal semantics of Petri nets, explicitly representing dependencies between transition occurrences. For one-safe nets or condition/event-systems, the notion of process as defined by Carl Adam Petri provides a notion of a run of a system where causal dependencies are reflected in terms of a partial order. A well-known problem is how to generalise this notion for nets where places may carry several tokens. Goltz and Reisig have defined such a generalisation by distinguishing tokens according to their causal history. However, this so-called individual token interpretation is often considered too detailed. A number of approaches have tackled the problem of defining a more abstract notion of process, thereby obtaining a so-called collective token interpretation. Here we give a short overview on these attempts and then identify a subclass of Petri nets, called structural conflict nets, where the interplay between conflict and concurrency due to token multiplicity does not occur. For this subclass, we define abstract processes as equivalence classes of Goltz-Reisig processes. We justify this approach by showing that we obtain exactly one maximal abstract process if and only if the underlying net is conflict-free with respect to a canonical notion of conflict.
Whereas standard treatments of temporal logic are adequate for closed systems, having no run-time interactions with their environment, they fall short for reactive systems, interacting with their environments through synchronisation of actions. This paper introduces reactive temporal logic, a form of temporal logic adapted for the study of reactive systems. I illustrate its use by applying it to formulate definitions of a fair scheduler, and of a correct mutual exclusion protocol. Previous definitions of these concepts were conceptually much more involved or less precise, leading to debates on whether or not a given protocol satisfies the implicit requirements.
We prove that rooted divergence-preserving branching bisimilarity is a congruence for the process specification language consisting of nil, action prefix, choice, and the recursion construct.
We consider the problem of cross-chain payment whereby customers of different escrows---implemented by a bank or a blockchain smart contract---successfully transfer digital assets without trusting each other. Prior to this work, cross-chain payment problems did not require this success, or any form of progress. We demonstrate that it is possible to solve this problem when assuming synchrony, in the sense that each message is guaranteed to arrive within a known amount of time, but impossible to solve without assuming synchrony. Yet, we solve a weaker variant of this problem, where success is conditional on the patience of the participants, without assuming synchrony, and in the presence of Byzantine failures. We also discuss the relation with the recently defined cross-chain deals.
Routing protocol specifications are traditionally written in plain English. Often this yields ambiguities, inaccuracies or even contradictions. Formal methods techniques, such as process algebras, avoid these problems, thus leading to more precise and verifiable descriptions of protocols. In this paper we use the timed process algebra T-AWN for modelling the Optimised Link State Routing protocol (OLSR) version 2.
In this paper, we consider the problem of cross-chain payment whereby customers of different escrows -- implemented by a bank or a blockchain smart contract -- successfully transfer digital assets without trusting each other. Prior to this work, cross-chain payment problems did not require this success or any form of progress. We introduce a new specification formalism called Asynchronous Networks of Timed Automata (ANTA) to formalise such protocols. We present the first cross-chain payment protocol that ensures termination in a bounded amount of time and works correctly in the presence of clock skew. We then demonstrate that it is impossible to solve this problem without assuming synchrony, in the sense that each message is guaranteed to arrive within a known amount of time. We also offer a protocol that solves an eventually terminating variant of this cross-chain payment problem without synchrony, and even in the presence of Byzantine failures.