Equational Axioms for Probabilistic Bisimilarity (Preliminary Report)

This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finite-state agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571-595). The axiomatization is obtained by extending the general axioms of iteration theories (or iteration algebras), which characterize the equational properties of the fixed point operator on (omega-)continuous or monotonic functions, with three axiom schemas that express laws that are specific to probabilistic bisimilarity. Hence probabilistic bisimilarity (over finite-state agents) has an equational axiomatization relative to iteration algebras

Process Algebras

Process Algebras are mathematically rigorous languages with well defined semantics that permit describing and verifying properties of concurrent communicating systems. They can be seen as models of processes, regarded as agents that act and interact continuously with other similar agents and with their common environment. The agents may be real-world objects (even people), or they may be artifacts, embodied perhaps in computer hardware or software systems. Many different approaches (operational, denotational, algebraic) are taken for describing the meaning of processes. However, the operational approach is the reference one. By relying on the so called Structural Operational Semantics (SOS), labelled transition systems are built and composed by using the different operators of the many different process algebras. Behavioral equivalences are used to abstract from unwanted details and identify those systems that react similarly to external experiments

A non-interleaving process calculus for multi-party synchronisation

We introduce the wire calculus. Its dynamic features are inspired by Milner's CCS: a unary prefix operation, binary choice and a standard recursion construct. Instead of an interleaving parallel composition operator there are operators for synchronisation along a common boundary and non-communicating parallel composition. The (operational) semantics is a labelled transition system obtained with SOS rules. Bisimilarity is a congruence with respect to the operators of the language. Quotienting terms by bisimilarity results in a compact closed category

Acute: high-level programming language design for distributed computation

Existing languages provide good support for typeful programming of standalone programs. In a distributed system, however, there may be interaction between multiple instances of many distinct programs, sharing some (but not necessarily all) of their module structure, and with some instances rebuilt with new versions of certain modules as time goes on. In this paper we discuss programming language support for such systems, focussing on their typing and naming issues. We describe an experimental language, Acute, which extends an ML core to support distributed development, deployment, and execution, allowing type-safe interaction between separately-built programs. The main features are: (1) type-safe marshalling of arbitrary values; (2) type names that are generated (freshly and by hashing) to ensure that type equality tests suffice to protect the invariants of abstract types, across the entire distributed system; (3) expression-level names generated to ensure that name equality tests suffice for type-safety of associated values, e.g. values carried on named channels; (4) controlled dynamic rebinding of marshalled values to local resources; and (5) thunkification of threads and mutexes to support computation mobility. These features are a large part of what is needed for typeful distributed programming. They are a relatively lightweight extension of ML, should be efficiently implementable, and are expressive enough to enable a wide variety of distributed infrastructure layers to be written as simple library code above the byte-string network and persistent store APIs. This disentangles the language runtime from communication intricacies. This paper highlights the main design choices in Acute. It is supported by a full language definition (of typing, compilation, and operational semantics), by a prototype implementation, and by example distribution libraries

Sequentiality vs. Concurrency in Games and Logic

Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc