(Ω, Ξ)-Logic: On the Algebraic Extension of Coalgebraic Specifications

We present an extension of standard coalgebraic specification techniques for statebased systems which allows us to integrate constants and n-ary operations in a smooth way and, moreover, leads to a simplification of the coalgebraic structure of the models of a specification. The framework of (Ω,Ξ)-logic can be considered as the result of a translation of concepts of observational logic (cf. [9]) into the coalgebraic world. As a particular outcome we obtain the notion of an (Ω, Ξ)- structure and a sound and complete proof system for (first-order) observational properties of specifications

Behavioural and abstractor specifications

AbstractIn the literature, one can distinguish two main approaches to the definition of observational semantics of algebraic specifications. On one hand, observational semantics is defined using a notion of observational satisfaction for the axioms of the specifications and, on the other hand, one can define observational semantics by abstraction with respect to an observational equivalence relation between algebras. In this paper, we present an analysis and a comparative study of the different approaches in a more general framework which subsumes the observational case. The distinction between the different observational concepts is reflected by our notions of behavioural specification and abstractor specification. We provide necessary and sufficient conditions for the semantical equivalence of both kinds of specifications and we show that behavioural specifications can be characterized by an abstractor construction and, vice versa, abstractor specifications can be characterized in terms of behavioural specifications. Hence, there exists a duality between both concepts which allows to express each one by the other. We also study the relationships to fully abstract algebras which can be used for a further characterization of behavioural semantics. Finally, we provide proof-theoretic results which show that behavioural theories of specifications can be reduced to standard theories of some classes of algebras

Behavioural and abstractor specifications revisited

In the area of algebraic specification there are two main approaches for defining observational abstraction: behavioural specifications use a notion of observational satisfaction for the axioms of a specification, whereas abstractor specifications define an abstraction from the standard semantics of a specification w.r.t. an observational equivalence relation between algebras. Earlier work by Bidoit, Hennicker, Wirsing has shown that in the case of first-order logic specifications both concepts coincide semantically under mild assumptions. Analogous results have been shown by Sannella and Hofmann for higher-order logic specifications and recently, by Hennicker and Madeira, for specifications of reactive systems using a dynamic logic with binders. In this paper, we bring these results into a common setting: we isolate a small set of characteristic principles to express the behaviour/abstractor equivalence and show that all three mentioned specification frameworks satisfy these principles and therefore their behaviour and abstractor specifications coincide semantically (under mild assumptions). As a new case we consider observational modal logic where observational satisfaction of Hennessy–Milner logic formulae is defined “up to” silent transitions and observational abstraction is defined by weak bisimulation. We show that in this case the behaviour/abstractor equivalence can only be obtained, if we restrict models to weakly deterministic labelled transition systems.publishe

Interface Theories for (A)synchronously Communicating Modal I/O-Transition Systems

Interface specifications play an important role in component-based software development. An interface theory is a formal framework supporting composition, refinement and compatibility of interface specifications. We present different interface theories which use modal I/O-transition systems as their underlying domain for interface specifications: synchronous interface theories, which employ a synchronous communication schema, as well as a novel interface theory for asynchronous communication where components communicate via FIFO-buffers.Comment: In Proceedings FIT 2010, arXiv:1101.426

Compatibility properties of synchronously and asynchronously communicating components

We study interacting components and their compatibility with respect to synchronous and asynchronous composition. The behavior of components is formalized by I/O-transition systems. Synchronous composition is based on simultaneous execution of shared output and input actions of two components while asynchronous composition uses unbounded FIFO-buffers for message transfer. In both contexts we study compatibility notions based on the idea that any output issued by one component should be accepted as an input by the other. We distinguish between strong and weak versions of compatibility, the latter allowing the execution of internal actions before a message is accepted. We consider open systems and study conditions under which (strong/weak) synchronous compatibility is sufficient and necessary to get (strong/weak) asynchronous compatibility. We show that these conditions characterize half-duplex systems. Then we focus on the verification of weak asynchronous compatibility for possibly non half-duplex systems and provide a decidable criterion that ensures weak asynchronous compatibility. We investigate conditions under which this criterion is complete, i.e. if it is not satisfied then the asynchronous system is not weakly asynchronously compatible. Finally, we discuss deadlock-freeness and investigate relationships between deadlock-freeness in the synchronous and in the asynchronous case

Realisability of Global Models of Interaction (Extended Version)

We consider global models of communicating agents specified as transition systems labelled by interactions in which multiple senders and receivers can participate. A realisation of such a model is a set of local transition systems—one per agent—which are executed concurrently using synchronous communication. Our core challenge is how to check whether a global model is realisable and, if it is, how to synthesise a realisation. We identify and compare two variants to realise global interaction models, both relying on bisimulation equivalence. Then we investigate, for both variants, realisability conditions to be checked on global models. We propose a synthesis method for the construction of realisations by grouping locally indistinguishable states. The paper is accompanied by a tool that implements realisability checks and synthesises realisations. This document extends a publication accepted at the International Colloquium on Theoretical Aspects of Computing 2023 (ICTAC 2023), including the proofs of all results, more examples, and a more detailed explanation of the companion prototype tool