Labelled domains and automata with concurrency

AbstractWe investigate an operational model of concurrent systems, called automata with concurrency relations. These are labelled transition systems A in which the event set is endowed with a collection of binary concurrency relations which indicate when two events, in a particular state of the automaton, commute. This model generalizes asynchronous transition systems, and as in trace theory we obtain, through a permutation equivalence for computation sequences of A, an induced domain (D(A), ⩽). Here, we construct a categorical equivalence between a large category of (“cancellative”) automata with concurrency relations and the associated domains. We show that each cancellative automaton can be reduced to a minimal cancellative automaton generating, up to isomorphism, the same domain. Furthermore, when fixing the event set, this minimal automaton is unique

Comparing Transition Systems with Independence and Asynchronous Transition Systems

Transition systems with independence and asynchronous transition systems are noninterleaving models for concurrency arising from the same simple idea of decorating transitions with events. They differ for the choice of a derived versus a primitive notion of event which induces considerable differences and makes the two models suitable for different purposes. This opens the problem of investigating their mutual relationships, to which this paper gives a fully comprehensive answer. In details, we characterise the category of extensional asynchronous transitions systems as the largest full subcategory of the category of (labelled) asynchronous transition systems which admits $TSI$, the category of transition systems with independence, as a coreflective subcategory. In addition, we introduce event-maximal asynchronous transitions systems and we show that their category is equivalent to $TSI$, so providing an exhaustive characterisation of transition systems with independence in terms of asynchronous transition systems

Modal logics are coalgebraic

Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility

Relating BIP and Reo

Coordination languages simplify design and development of concurrent systems. Particularly, exogenous coordination languages, like BIP and Reo, enable system designers to express the interactions among components in a system explicitly. In this paper we establish a formal relation between BI(P) (i.e., BIP without the priority layer) and Reo, by defining transformations between their semantic models. We show that these transformations preserve all properties expressible in a common semantics. This formal relation comprises the basis for a solid comparison and consolidation of the fundamental coordination concepts behind these two languages. Moreover, this basis offers translations that enable users of either language to benefit from the toolchains of the other.Comment: In Proceedings ICE 2015, arXiv:1508.0459

A Logic for True Concurrency

We propose a logic for true concurrency whose formulae predicate about events in computations and their causal dependencies. The induced logical equivalence is hereditary history preserving bisimilarity, and fragments of the logic can be identified which correspond to other true concurrent behavioural equivalences in the literature: step, pomset and history preserving bisimilarity. Standard Hennessy-Milner logic, and thus (interleaving) bisimilarity, is also recovered as a fragment. We also propose an extension of the logic with fixpoint operators, thus allowing to describe causal and concurrency properties of infinite computations. We believe that this work contributes to a rational presentation of the true concurrent spectrum and to a deeper understanding of the relations between the involved behavioural equivalences.Comment: 31 pages, a preliminary version appeared in CONCUR 201

Buffered Simulation Games for B\"uchi Automata

Simulation relations are an important tool in automata theory because they provide efficiently computable approximations to language inclusion. In recent years, extensions of ordinary simulations have been studied, for instance multi-pebble and multi-letter simulations which yield better approximations and are still polynomial-time computable. In this paper we study the limitations of approximating language inclusion in this way: we introduce a natural extension of multi-letter simulations called buffered simulations. They are based on a simulation game in which the two players share a FIFO buffer of unbounded size. We consider two variants of these buffered games called continuous and look-ahead simulation which differ in how elements can be removed from the FIFO buffer. We show that look-ahead simulation, the simpler one, is already PSPACE-hard, i.e. computationally as hard as language inclusion itself. Continuous simulation is even EXPTIME-hard. We also provide matching upper bounds for solving these games with infinite state spaces.Comment: In Proceedings AFL 2014, arXiv:1405.527

A Classification of Models for Concurrency

Models for concurrency can be classified with respect to the three relevant parameters: behaviour/system, interleaving/noninterleaving, linear/branching time. When modelling a process, a choice concerning such parameters corresponds to choosing the level of abstraction of the resulting semantics. The classifications are formalised through the medium of category theory

History-Preserving Bisimilarity for Higher-Dimensional Automata via Open Maps

We show that history-preserving bisimilarity for higher-dimensional automata has a simple characterization directly in terms of higher-dimensional transitions. This implies that it is decidable for finite higher-dimensional automata. To arrive at our characterization, we apply the open-maps framework of Joyal, Nielsen and Winskel in the category of unfoldings of precubical sets.Comment: Minor updates in accordance with reviewer comments. Submitted to MFPS 201