A trustful monad for axiomatic reasoning with probability and nondeterminism

The algebraic properties of the combination of probabilistic choice and nondeterministic choice have long been a research topic in program semantics. This paper explains a formalization in the Coq proof assistant of a monad equipped with both choices: the geometrically convex monad. This formalization has an immediate application: it provides a model for a monad that implements a nontrivial interface, which allows for proofs by equational reasoning using probabilistic and nondeterministic effects. We explain the technical choices we made to go from the literature to a complete Coq formalization, from which we identify reusable theories about mathematical structures such as convex spaces and concrete categories, and that we integrate in a framework for monadic equational reasoning.

An Operational Semantics for True Concurrency in BDI Agent Systems

Agent programming languages have proved useful for formally modelling implemented systems such as PRS and JACK, and for reasoning about their behaviour. Over the past decades, many agent programming languages and extensions have been developed. A key feature in some of them is their support for the specification of ‘concurrent’ actions and programs. However, their notion of concurrency is still limited, as it amounts to a nondeterministic choice between (sequential) action interleavings. Thus, the notion does not represent ‘true concurrency’, which can more naturally exploit multi-core computers and multi-robot manufacturing cells. This paper provides a true concurrency operational semantics for a BDI agent programming language, allowing actions to overlap in execution. We prove key properties of the semantics, relating to true concurrency and to its link with interleaving.

The Saga of the Axiomatization of Parallel Composition

This paper surveys some classic and recent results on the finite axiomatizability of bisimilarity over CCS-like languages. It focuses, in particular, on non-finite axiomatizability results stemming from the semantic interplay between parallel composition and nondeterministic choice. The paper also highlights the role that auxiliary operators, such as Bergstra and Klop's left and communication merge and Hennessy's merge operator, play in the search for a finite, equational axiomatization of parallel composition both for classic process algebras and for their real-time extensions.

Recursion vs. Replication in Simple Cryptographic Protocols

We use some recent techniques from process algebra to draw several conclusions about the well studied class of ping-pong protocols introduced by Dolev and Yao. In particular we show that all nontrivial properties, including reachability and equivalence checking wrt. the whole van Glabbeek's spectrum, become undecidable for a very simple recursive extension of the protocol. The result holds even if no nondeterministic choice operator is allowed. We also show that the extended calculus is capable of an implicit description of the active intruder, including full analysis and synthesis of messages in the sense of Amadio, Lugiez and Vanackere. We conclude by showing that reachability analysis for a replicative variant of the protocol becomes decidable.

Unified Algebras and Action Semantics

The recently-developed framework of Unified Algebras is intended for axiomatic specification of abstract data types. In contrast, the somewhat older framework of Action Semantics (earlier known as ''Abstract Semantic Algebras'') is for denotational specification of programming languages. This paper gives an introduction to the main features of Unified Algebras and Action Semantics, and discusses the relation between them. The two frameworks both exploit nondeterministic choice in unconventional ways.

Concurrent Program Schemes

We study the programming formalism FD of “flow-diagrams” to which we gradually add various features of concurrency. The weakest form of concurrency is introduced by the construct “and”, which is dual to the nondeterministic choice “or” and plays a role similar to universal states in alternating Turing machines. Stronger (and more realistic) forms of concurrency are obtained when processes are allowed to communicate. We consider communication by channels and communication by messages. We calibrate the computational power of classes of concurrent programs FD+α against that of sequential programs, where α is the addition of one of the following features: {and}, {and, or}, {and, or, channels}, or {and, or, messages}.