In this paper we present a solution to the long-standing problem of characterising the coarsest liveness-preserving pre-congruence with respect to a full (TCSP-inspired) process algebra. In fact, we present two distinct characterisations, which give rise to the same relation: an operational one based on a De Nicola-Hennessy-like testing modality which we call should-testing, and a denotational one based on a refined notion of failures. One of the distinguishing characteristics of the should-testing pre-congruence is that it abstracts from divergences in the same way as Milner’s observation congruence, and as a consequence is strictly coarser than observation congruence. In other words, should-testing has a built-in fairness assumption. This is in itself a property long sought-after; it is in notable contrast to the well-known must-testing of De Nicola and Hennessy (denotationally characterised by a combination of failures and divergences), which treats divergence as catrastrophic and hence is incompatible with observation congruence. Due to these characteristics, should-testing supports modular reasoning and allows to use the proof techniques of observation congruence, but also supports additional laws and techniques.

The simulation preorder for labeled transition systems is defined locally as a game that relates states with their immediate successor states. Simulation enjoys many appealing properties. First, simulation has a fully abstract semantics: system S simulates system I iff every computation tree embedded in the unrolling of I can be embedded also in the unrolling of S. Second, simulation has a logical characterization: S simulates I iff every universal branching-time formula satisfied by S is satisfied also by I. It follows that simulation is a suitable notion of implementation, and it is the coarsest abstraction of a system that preserves universal branching-time properties. Third, based on its local definition, simulation between finite-state systems can be checked in polynomial time. Finally, simulation implies trace-containment, which cannot be defined locally and requires polynomial space for verification. Hence simulation is widely used both in manual and in automatic verification. ...

Bisimulations enjoy numerous applications in the analysis of labeled transition systems. Many of these applications are based on two central observations: first, bisimilar systems satisfy the same branchingtime properties; second, bisimilarity can be checked efficiently for finitestate systems. The local character of bisimulation, however, makes it difficult to address liveness concerns. Indeed, the definitions of fair bisimulation that have been proposed in the literature sacrifice locality, and with it, also efficient checkability. We put forward a new definition of fair bisimulation which does not suffer from this drawback. The bisimilarity of

Abstract. We provide a denotational trace semantics for processes with synchronous communication and a form of weakly fair parallelism. The semantics is fully abstract: processes have the same trace sets if and only if their communication behaviors are identical in all contexts. The model can easily be adapted for asynchronously communicating processes, or for shared-memory parallel programs. We also provide a partial-order semantics, using pomsets adapted for synchronization and our form of fairness. The pomset semantics can also be adjusted to model alternative paradigms. The traces of a process can be recovered from the pomset semantics by taking all fair interleavings consistent with the partial order. 1

We produce a fully abstract model for a notion of process equivalence taking into account issues of fairness, called by Milner fair bisimilarity. The model uses Aczel's anti-foundation axiom and it is constructed along the lines of the anti-founded model for SCCS given by Aczel. We revisit Aczel's semantics for SCCS where we prove a unique fixpoint theorem under the assumption of guarded recursion. Then we consider Milner's extension of SCCS to include a finite delay operator ". Working with fair bisimilarity we construct a fully abstract model, which is also fully abstract for fortification. We discuss the solution of recursive equations in the model. The paper is concluded with an investigation of the algebraic theory of fair bisimilarity. Keywords: fairness, anti-foundation, finite delay, parallelism, fair bisimilarity, fortification. This paper was composed while I was unemployed and an unofficial visitor at the Department of Mathematics, University of Ioannina, Greece. My than...

Abstract. Although liveness and fairness have been used for a long time in classical model checking, with process-algebraic methods they have seen far less use. One problem is combining fairness with the compositionality of process algebra. In this article we analyse this problem, and then present an approach for using a class of fairness constraints. The approach fulfills all the requirements of compositionality and is compatible with an existing semantics. It is based on the standard LTS model and does not require new fairness-related constructs or rules for the process algebra. Therefore, it avoids potential conflicts between the fairness requirements and the underlying transition system. Although adding fairness can create an infinite subsystem, a larger system in which the subsystem is placed can still be finite. We present an algorithm for constructing a finite LTS which is equivalent to the larger system in every case that an exact finite representation exists, and which otherwise is a conservative estimate of it. However, checking whether an exact finite representation exists is costlier than building the representation, namely, it is PSPACE-complete in the size of an intermediate parameter system. 1

We recast Milner's work on SCCSffl, a calculus for finite but unbounded delay based on SCCS, by giving a denotational semantics for admissibility of infinite computations on a bifinite domain K. Using Abramsky's SFP domain D for bisimulation we obtain a fully abstract model in D \Theta K for an operational preorder which generalizes Milner's fortification. Our preorder includes divergence and its restriction to finite behavior corresponds to Abramsky's finitary preorder. By virtue of bifiniteness of D \Theta K we obtain a Stone dual at the level of objects. Since Milner's delay operators ffl and ffi turn out to correspond to the greatest, respectively least, fixed point on K, we consequently enrich SCCS with an additional recursive binding modeled as the greatest fixed point. For the body 1x + p, the new recursive binding imposes finite delay, whereas the ordinary recursion admits infinite, as well as finite, delay of p. We define a notion of admissibility and a denotational semantics...

This paper describes compositional semantics (operational, denotational and logical) for a process algebra enhanced with input/output actions and preemption combinators, in the presence of fairness. The context of this paper is Triveni, a process-algebra-based design methodology that combines threads and events in the context of object-oriented programming [CJJ

In this paper we define a probabilistic testing semantics which can be used to alternatively characterize fair testing. The key idea is to define a probabilistic semantics in such a way that two non-probabilistic processes are fair equivalent iff any probabilistic version of both processes are equivalent in our probabilistic testing semantics. In order to get this result we define a simple probabilistic must semantics by saying that a probabilistic process must pass a test iff the probability with which the process passes the test equals 1. Finally, we present an algorithm for deciding whether the probability with which a finite-state process passes a finite-state test equals 1. Alternatively, this algorithm can be used for computing whether a finite-state process fairly passes a finite-state test. Keywords: Testing semantics, fair testing, probabilistic processes. 1. INTRODUCTION Formal models of concurrency have been proved to be very useful to properly specify concurrent and distr...

ABSTRACT We recast Milner's work on finite delay in synchronous CCS by giving a denotational semantics for admissibility of infinite computations on a bifinite domain K. Using Abramsky's SFP domain D for bisimulation we obtain a fully abstract model D \Theta K for an operational preorder which generalizes Milner's fortification and whose restriction to finite behavior corresponds to Abramsky's finitary preorder. The bifiniteness of D \Theta K renders a program logic by considering its Stone dual. 1 Introduction This paper mainly builds upon two pieces of work: Milner's synchronous CCS with finite delay [Mil82b] and Abramsky's domain equation for bisimulation [Abr91a]. The importance of synchronous CCS with finite delay stems from its ability to make fine-grained distinctions between passive resources, like an accessible register, and active ones, like agents that need to initiate some action in finite time. To clarify this point, consider an active agent ffip which behaves like p, b...