Gheorghe Stefanescu

Reaction and control I. Mixing additive and multiplicative network algebras

This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding Multi-Agent Systems is to find a theory which integrates the reactive part and the control part of such systems. To this end we use the calculus of flownomials. It is a polynomial-like calculus for representing flowgraphs and their behaviours. An ‘additive’ interpretation of the calculus was intensively developed to study control flowcharts and finite automata. For instance, regular algebra and iteration theories are included in a unified presentation. On the other hand, a ‘multiplicative’ interpretation of the calculus of flownomials was developed to study dataflow networks. The claim of this series of papers is that the mixture of the additive and multiplicative network algebras will contribute to the understanding of distributed computation. The rôle of this first paper is to present a few motivating examples1.

P Transducers

We introduce in this paper four classes of P transducers: arbitrary, initial, isolated arbitrary, isolated and initial. The first two classes are universal, they can compute the same word functions as Turing machines, the latter two are incomparable with finite state sequential transducers, generalized or not. We study the effect of the composition, and show that iteration increases the power of these latter classes, also leading to a new characterization of recursively enumerable languages. The “Sevilla carpet” of a computation is defined for P transducers, giving a representation of the control part for these P transducers.

On compiling structured interactive programs with registers and voices

A model (consisting of rv-systems), a core programming language (for developing rv-programs), several specification and analysis techniques appropriate for modeling, programming and reasoning about interactive computing systems have been recently introduced by Stefanescu using register machines and space-time duality, see [13]. In [3,4,5,6] the authors have have introduced and studied structured programming techniques for rv-systems. The aim of the present paper is to define a scenario-based operational semantics for structured rv-programs and to offer a translation from structured rv-programs to rv-programs. The main technical result states that the translation is correct. This is part of an effort to get a running environment for structured rv-programs built up on top of rv-programs.

A New Representation of Two-Dimensional Patterns and Applications to Interactive Programming

Regular expressions and the associated regular algebra provide a rich formalism for specifying and analysing sequential models of computation. For parallel computation, extensions to handle two-dimensional patterns are often required. In this paper we present a new type of regular expressions for two-dimensional patterns based on contours and their composition. Targeted applications comes from the area of modelling, specification, analysis and verification of structured interactive programs via the associated scenario semantics.

Towards a Formal Representation of Interactive Systems

Powerful algebraic techniques have been developed for classical sequential computation. Many of them are based on regular expressions and the associated regular algebra. For parallel and interactive computation, extensions to handle 2-dimensional patterns are often required. Finite interactive systems, a 2-dimensional version of finite automata, may be used to recognize 2-dimensional languages. In this paper we present a blueprint for getting a formal representation of parallel, interactive programs and of their semantics. It is based on a recently introduced approach for getting regular expressions for 2-dimensional patterns, particularly using words of arbitrary shapes and powerful control mechanisms on composition. We extend the previously defined class of expressions n2RE with new control features, progressively increasing the expressive power of the formalism up to a level where a procedure for generating the words accepted by finite interactive systems may be obtained. Targeted applications come from the area of modelling, specification, analysis and verification of structured interactive programs via the associated scenario semantics.

Undecidability Results for Finite Interactive Systems

This paper is on the foundations of a recent approach to the design of massively parallel and interactive programming languages using rv-systems (interactive systems with registers and voices) and Agapia programming. It includes a few theoretical results on FISs (finite interactive systems), the underlying mechanism used for specifying control and interaction in these systems. First, we give a proof for the undecidability of the emptiness problem for FISs by reduction to the post correspondence problem. Next, we use the proof to get other undecidability results, e.g., for the accessibility of a transition in a FIS, or for the finiteness of the language recognized by a FIS. Finally, we present a simple proof of the equivalence between FISs and tile systems, making explicit that they precisely capture recognizable two-dimensional languages.

Refinement-Preserving translation from event-b to register-voice interactive systems

The state-based formal method Event-B relies on the concept of correct stepwise development, ensured by discharging corresponding proof obligations. The register-voice interactive systems (rv-IS) formalism is a recent approach for developing software systems using both structural state-based as well as interaction-based composition operators. One of the most interesting feature of the rv-IS formalism is the structuring of the components interactions. In order to study whether a more structured (rv-IS inspired) interaction approach can significantly ease the proof obligation effort needed for correct development in Event-B, we need to devise a way of integrating these formalisms. In this paper we propose a refinement-based translation from Event-B to rv-IS, exemplified with a file transfer protocol modelled in both formalisms.

A Quest for Kleene Algebra in 2 Dimensions

The term Kleene algebra refers to a certain algebraic structure, built up using sequential composition, its iterated version, and union. The key operation is composition: on strings, it connects the final point of the first string to the initial point of the second string.

Refinement of Structured Interactive Systems

The refinement concept provides a formal tool for addressing the complexity of software-intensive systems, by verified stepwise development from an abstract specification towards an implementation. In this paper we propose a novel notion of refinement for a structured formalism dedicated to interactive systems, that combines a data-flow with a control-oriented approach. Our notion is based on scenarios, extending to two dimensions the trace-based definition for the refinement of classical sequential systems. We illustrate our refinement notion with a simple example and outline several extensions to include more sophisticated distributed techniques.

Multi-Level Control Mechanisms for Non-Structured and Structured 2-Dimensional Self-Assembling

We present a multi-level approach to control the assembling of 2-dimensional patterns. The top control level uses abstract tiles, where the borders and the bodies of the tiles are labeled by abstract symbols. Tile assembling requires the match of border labels on the common borders, leading to specific 2-dimensional patterns. Further control levels may be introduced adding new data (on borders) and relations connecting these data (on bodies). This refinement process may be repeated going from an abstract and often nondeterministic self-assembling specification to a more controlled and detailed targeted specification - the former may be more related to the infrastructure, while the latter with the functionality mapped on that infrastructure. The approach is further instantiated to work with both non-structured and structured control mechanisms. The first one uses border labels to control tile assembling. It has a more pronounced self-assembling character, where tiles have little knowledge on the emerging result. The second, structured approach takes advantage on a recently introduced new class of 2-dimensional regular expressions. These expressions are based on a global knowledge of the resulted patterns and on their generation. It is a higher level control mechanism letting tiles and their composites to assemble according to the shapes described by these expressions. While the approach may be used with any kind of interpretation of the dimensions, our applications have focused on the case when one dimension represents space and the other time. In this case, the approach has produced non-structured and structured models and programming languages for open, interactive, distributed processes. We illustrate the approach with the sketch of a program for smart-car modeling.