On the Executability of Interactive Computation

The model of interactive Turing machines (ITMs) has been proposed to characterise which stream translations are interactively computable; the model of reactive Turing machines (RTMs) has been proposed to characterise which behaviours are reactively executable. In this article we provide a comparison of the two models. We show, on the one hand, that the behaviour exhibited by ITMs is reactively executable, and, on the other hand, that the stream translations naturally associated with RTMs are interactively computable. We conclude from these results that the theory of reactive executability subsumes the theory of interactive computability. Inspired by the existing model of ITMs with advice, which provides a model of evolving computation, we also consider RTMs with advice and we establish that a facility of advice considerably upgrades the behavioural expressiveness of RTMs: every countable transition system can be simulated by some RTM with advice up to a fine notion of behavioural equivalence.Comment: 15 pages, 0 figure

Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints

The monadic shallow linear Horn fragment is well-known to be decidable and has many application, e.g., in security protocol analysis, tree automata, or abstraction refinement. It was a long standing open problem how to extend the fragment to the non-Horn case, preserving decidability, that would, e.g., enable to express non-determinism in protocols. We prove decidability of the non-Horn monadic shallow linear fragment via ordered resolution further extended with dismatching constraints and discuss some applications of the new decidable fragment.Comment: 29 pages, long version of CADE-26 pape

Conditional Bigraphs

Bigraphs are a universal graph based model, designed for analysing reactive systems that include spatial and non-spatial (e.g. communication) relationships. Bigraphs evolve over time using a rewriting framework that finds instances of a (sub)-bigraph, and substitutes a new bigraph. In standard bigraphs, the applicability of a rewrite rule is determined completely by a local match and does not allow any non-local reasoning, i.e. contextual conditions. We introduce conditional bigraphs that add conditions to rules and show how these fit into the matching framework for standard bigraphs. An implementation is provided, along with a set of examples. Finally, we discuss the limits of application conditions within the existing matching framework and present ways to extend the range of conditions that may be expressed

Applications of Fair Testing

In this paper we present the application of the fair testing pre-order, introduced in a previous paper, to the specification and analysis of distributed systems. This pre-order combines some features of the standard testing pre-orders, viz. the possibility to refine a specification by the resolution of nondeterminism, with a powerful feature of standard observation congruence, viz. the fair abstraction from divergences. Moreover, it is a pre-congruence with respect to all standard process-algebraic combinators, thus allowing for the standard algebraic proof techniques by substitution and rewriting. In this paper we will demonstrate advantages of the fair testing pre-order by the application to a number of examples, including a scheduling problem, a version of the Alternating Bit-protocol, and fair communication channels

Weak Sequential Composition in Process Algebras

n this paper we study a special operator for sequential composition, which is defined relative to a dependency relation over the actions of a given system. The idea is that actions which are not dependent (intuitively because they share no common resources) do not have to wait for one another to proceed, even if they are composed sequentially. Such a notion has been studied before in a linear-time setting, but until recently there has been no systematic investigation in the context of process algebras. We give a structural operational semantics for a process algebraic language containing such a sequential composition operator, which shows some interesting interplay with choice. We give a complete axiomatisation of strong bisimilarity and we show consistency of the operational semantics with an event-based denotational semantics developed recently by the second author. The axiom system allows to derive the communication closed layers law, which in the linear time setting has been shown to be a very useful instrument in correctness preserving transformations. We conclude with a couple of examples

A rigorous approach to investigating common assumptions about disease transmission: Process algebra as an emerging modelling methodology for epidemiology

Changing scale, for example the ability to move seamlessly from an individual-based model to a population-based model, is an important problem in many fields. In this paper we introduce process algebra as a novel solution to this problem in the context of models of infectious disease spread. Process algebra allows us to describe a system in terms of the stochastic behaviour of individuals, and is a technique from computer science. We review the use of process algebra in biological systems, and the variety of quantitative and qualitative analysis techniques available. The analysis illustrated here solves the changing scale problem: from the individual behaviour we can rigorously derive equations to describe the mean behaviour of the system at the level of the population. The biological problem investigated is the transmission of infection, and how this relates to individual interaction