The categorical limit of a sequence of dynamical systems

Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns out to be subject to ambiguity. Depending on the interpretation of the sequence, i.e. depending on how the behaviors of the systems in the sequence are related, it may vary what the limit should be. Topologies, and in particular metrics, define limits uniquely, if they exist. Thus they select one interpretation implicitly and leave no room for other interpretations. In this paper, we define limits using category theory, and use the mentioned relations between system behaviors explicitly. This resolves the problem of ambiguity in a more controlled way. We introduce a category of prefix orders on executions and partial history preserving maps between them to describe both discrete and continuous branching time dynamics. We prove that in this category all projective limits exist, and illustrate how ambiguity in the definition of limits is resolved using an example. Moreover, we show how various problems with known topological approaches are now resolved, and how the construction of projective limits enables us to approximate continuous time dynamics as a sequence of discrete time systems.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690

Pabble: parameterised Scribble

© 2014, The Author(s).Many parallel and distributed message-passing programs are written in a parametric way over available resources, in particular the number of nodes and their topologies, so that a single parallel program can scale over different environments. This article presents a parameterised protocol description language, Pabble, which can guarantee safety and progress in a large class of practical, complex parameterised message-passing programs through static checking. Pabble can describe an overall interaction topology, using a concise and expressive notation, designed for a variable number of participants arranged in multiple dimensions. These parameterised protocols in turn automatically generate local protocols for type checking parameterised MPI programs for communication safety and deadlock freedom. In spite of undecidability of endpoint projection and type checking in the underlying parameterised session type theory, our method guarantees the termination of end point projection and type checking

Design-time formal verification for smart environments: an exploratory perspective

Smart environments (SmE) are richly integrated with multiple heterogeneous devices; they perform the operations in intelligent manner by considering the context and actions/behaviors of the users. Their major objective is to enable the environment to provide ease and comfort to the users. The reliance on these systems demands consistent behavior. The versatility of devices, user behavior and intricacy of communication complicate the modeling and verification of SmE's reliable behavior. Of the many available modeling and verification techniques, formal methods appear to be the most promising. Due to a large variety of implementation scenarios and support for conditional behavior/processing, the concept of SmE is applicable to diverse areas which calls for focused research. As a result, a number of modeling and verification techniques have been made available for designers. This paper explores and puts into perspective the modeling and verification techniques based on an extended literature survey. These techniques mainly focus on some specific aspects, with a few overlapping scenarios (such as user interaction, devices interaction and control, context awareness, etc.), which were of the interest to the researchers based on their specialized competencies. The techniques are categorized on the basis of various factors and formalisms considered for the modeling and verification and later analyzed. The results show that no surveyed technique maintains a holistic perspective; each technique is used for the modeling and verification of specific SmE aspects. The results further help the designers select appropriate modeling and verification techniques under given requirements and stress for more R&D effort into SmE modeling and verification researc

Behavioral types in programming languages

A recent trend in programming language research is to use behav- ioral type theory to ensure various correctness properties of large- scale, communication-intensive systems. Behavioral types encompass concepts such as interfaces, communication protocols, contracts, and choreography. The successful application of behavioral types requires a solid understanding of several practical aspects, from their represen- tation in a concrete programming language, to their integration with other programming constructs such as methods and functions, to de- sign and monitoring methodologies that take behaviors into account. This survey provides an overview of the state of the art of these aspects, which we summarize as the pragmatics of behavioral types