The π-calculus offers an attractive basis for concurrent programming. It is small, elegant, and well studied, and supports (via simple encodings) a wide range of high-level constructs including data structures, higher-order functional programming, concurrent control structures, and objects. Moreover, familiar type systems for the -calculus have direct counterparts in the π-calculus, yielding strong, static typing for a high-level language using the π-calculus as its core. This paper describes Pict, a strongly-typed concurrent programming language constructed in terms of an explicitly-typed-calculus core language.

This paper develops a new testing-based semantic theory of processes that aims to circumvent difficulties that traditional testing/failures theories have in dealing with divergent behavior. Our framework incorporates a notion of fairness into the determination of when a process passes a test; we contrast this definition with existing approaches and give characterizations of the induced semantic preorders. An example highlights the utility of our results. 1 Introduction Research into algebraic models of concurrency has focused on the use of semantic equivalences and preorders for establishing that systems meet their specifications. In such an approach to verification one formulates a specification as a system describing the required high-level behavior; a design/implementation then meets such a specification if its behavior is indistinguishable from the specification's (if one is using an equivalence) or if its behavior is in some sense better than the specification's (if one is using...

Interpretation. An alternative way to analyze the behavior of a concurrent program would be to use abstract interpretation [4, 5]. Actually, from a very general viewpoint, our type-based analysis of locks can be seen as a kind of abstract interpretation. We can read a type judgment # P as "# is an abstraction of a concrete process P ." (The relation "#" corresponds to a pair of abstraction /concretization functions.) Indeed, we can regard a type environment as an abstract process: we have defined reductions of type environments in Section 3.7.

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

Abstract. Liveness/Fairness plays an important role in software specification, verification and development. Existing event-based compositional models are safety-centric. In this paper, we describe a framework for systematically specifying and verifying event-based systems under fairness assumptions. We introduce different event annotations to associate fairness constraints with individual events. Fairness annotated events can be used to embed liveness/fairness assumptions in event-based models flexibly and naturally. We show that state-of-the-art verification algorithms can be extended to verify models under fairness assumptions, with little computational overhead. We further improve the algorithm by other model checking techniques like partial order reduction. A toolset named PAT has been developed to verify fairness enhanced event-based systems. Experiments show that PAT handles large systems with multiple fairness assumptions. 1

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 present a natural semantics for the untyped lazy -calculus plus McCarthy's amb, a nondeterministic choice operator. The natural semantics includes rules for both convergent behaviour (dened inductively) and divergent behaviour (dened co-inductively). This semantics is equivalent to a small step reduction semantics that corresponds closely to our operational intuitions about McCarthy's amb. We present equivalences for convergent and divergent behaviour based on the natural semantics and prove a Context Lemma for the convergence equivalence. We then give a -theory l 8 , based on the equivalences for convergent and divergent behaviour. Since it is able to distinguish between programs that dier only in their divergent behaviour, the -theory is more discriminating than equational theories based on current domain-theoretic models. It is therefore more suitable for reasoning about functional programs containing McCarthy's amb. Contents 1 Introduction 2 2 Related Work 3 3 ...

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...

Fairness is an important concept related to specification languages which are based on concurrent and non-deterministic computation models; it is related to liveness. In this paper we formally introduce fairness to the LOTOS specification language by employing the standard LOTOS semantics together with a formalism which states restrictions on fair infinite execution sequences. We extend three fairness concepts of CSP, namely process, guard and channel fairness, to LOTOS. Certain features of LOTOS, such as the dynamic creation of processes, the dynamic relation between gates and processes, and related membership in multi-way rendezvous, not present in CSP, make the definition of fairness difficult. We introduce the concept of "transition groups", which leads to a general notion of fairness, and use LOTOS action indexes to define the concepts of process, alternative and channel for LOTOS. We explain how a fair execution model for LOTOS can be obtained, and demonstrate the use of these concepts by showing how fairness assumptions can be used to prove liveness properties for a given LOTOS specification. 1.

this paper, we propose a quantitative fairness, which is called economic-oriented fairness, to each alternatives. This fairness ensures that the expected number of selection for each alternatives are same. We give a condition for probability assignment of selection of each alternative to be satisfied for economic-oriented fairness. First we show a simple probability assignment rule. In this assignment, between any two alternatives, if an alternative is selected n times and the other m times then the probability to select the former alternative is (m + 1)=(n + 1) times the probability for the latter. We prove that this assignment satisfies the condition of economic-oriented fairness. For a model of the economic-oriented fairness, we adopt a probabilistic process algebra.