An Algebra of Synchronous Scheduling Interfaces

In this paper we propose an algebra of synchronous scheduling interfaces which combines the expressiveness of Boolean algebra for logical and functional behaviour with the min-max-plus arithmetic for quantifying the non-functional aspects of synchronous interfaces. The interface theory arises from a realisability interpretation of intuitionistic modal logic (also known as Curry-Howard-Isomorphism or propositions-as-types principle). The resulting algebra of interface types aims to provide a general setting for specifying type-directed and compositional analyses of worst-case scheduling bounds. It covers synchronous control flow under concurrent, multi-processing or multi-threading execution and permits precise statements about exactness and coverage of the analyses supporting a variety of abstractions. The paper illustrates the expressiveness of the algebra by way of some examples taken from network flow problems, shortest-path, task scheduling and worst-case reaction times in synchronous programming.Comment: In Proceedings FIT 2010, arXiv:1101.426

Denotational Fixed-Point Semantics for Constructive Scheduling of Synchronous Concurrency

The synchronous model of concurrent computation (SMoCC) is well established for programming languages in the domain of safety-critical reactive and embedded systems. Translated into mainstream C/Java programming, the SMoCC corresponds to a cyclic execution model in which concurrent threads are synchronised on a logical clock that cuts system computation into a sequence of macro-steps. A causality analysis verifies the existence of a schedule on memory accesses to ensure each macro-step is deadlock-free and determinate. We introduce an abstract semantic domain I(D, P) and an associated denotational fixed point semantics for reasoning about concurrent and sequential variable accesses within a synchronous cycle-based model of computation. We use this domain for a new and extended behavioural definition of Berry’s causality analysis in terms of approximation intervals. The domain I(D, P) extends the domain I(D) from our previous work and fixes a mistake in the treatment of initialisations. Based on this fixed point semantics the notion of Input Berry-constructiveness (IBC) for synchronous programs is proposed. This new IBC class lies properly between strong (SBC) and normal Berry-constructiveness (BC) defined in previous work. SBC and BC are two ways to interpret the standard constructive semantics of synchronous programming, as exemplified by imperative SMoCC languages such as Esterel or Quartz. SBC is often too restrictive as it requires all variables to be initialised by the program. BC can be too permissive because it initialises all variables to a fixed value, by default. Where the initialisation happens through the memory, e.g., when carrying values from one synchronous tick to the next, then IBC is more appropriate. IBC links two levels of execution, the macro-step level and the micro-step level. We prove that the denotational fixed point analysis for IBC, and hence Berry’s causality analysis, is sound with respect to operational micro-level scheduling. The denotational model can thus be viewed as a compositional presentation of a synchronous scheduling strategy that ensures reactiveness and determinacy for imperative concurrent programming

Dagstuhl News January - December 2001

"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic

Formal methods and digital systems validation for airborne systems

This report has been prepared to supplement a forthcoming chapter on formal methods in the FAA Digital Systems Validation Handbook. Its purpose is as follows: to outline the technical basis for formal methods in computer science; to explain the use of formal methods in the specification and verification of software and hardware requirements, designs, and implementations; to identify the benefits, weaknesses, and difficulties in applying these methods to digital systems used on board aircraft; and to suggest factors for consideration when formal methods are offered in support of certification. These latter factors assume the context for software development and assurance described in RTCA document DO-178B, 'Software Considerations in Airborne Systems and Equipment Certification,' Dec. 1992

The intuitionism behind statecharts steps

The semantics of Statecharts macro steps, as introduced by Pnueli and Shalev [1991], lacks compositionality. This article first analyzes the compositionality problem and traces it back to the invalidity of the Law of the Excluded Middle. It then characterizes the semantics via a particular class of linear intuitionistic Kripke models. This yields, for the first time in the literature, a simple fully abstract semantics that interprets Pnueli and Shalev's concept of failure naturally. The results not only give insight into the semantic subtleties of Statecharts, but also provide a basis for an implementation, for developing algebraic theories for macro steps, and for comparing different Statecharts variants