Rank Order Filters and Priority Queues

A derivation of a parallel algorithm for rank order filtering is presented. Both derivation and result differ from earlier designs: the derivations are less complicated and the result allows a number of different implementations. The same derivation is used to design a collection of priority queues. Both filters and priority queues are highly efficient: they have constant response time and small latency

Using a Partial Order and a Metric to Analyze a Recursive Trace Set Equation

In Trace Theory the notion of a process is defined in terms of a set of finite-length traces over an alphabet. These processes are used as the semantics for a program notation. The program text for a recursive component naturally gives rise to an equation over trace sets. This paper takes two approaches at the analysis of that equation. The first approach is based on a partial order and it concentrates on the projection operator for processes. This yields a condition under which the greatest solution of that equation can be approximated by iteration. The second approach introduces a metric on the process domain. Application of Banach\u27s Contraction Theorem results in a condition under which there exists a unique solution that can be approximated by iteration starting anywhere

The Specification Statement Refined

In this paper, we present a rigorous treatment of so-called logical constants, which are used to relate the values of program variables between the precondition and the postcondition of a program. In order to do so, we generalize the latest proof rule for procedures and give a new definition for the specification statement. We show that the specification statement with this definition is the greatest lower bound of all its implementations under the usual refinement ordering and that it is A-distributive. We also demonstrate that a previous treatment of logical constants in specification statements does not have these properties

Quicksort in Constant Space

An in situ sorting algorithm, based on Quicksort, is presented with its proof of correctness. The proof illustrates a concise and elegant way to represent a sequence that has been partially sorted by Quicksort. A list representation turns out to be well suited to this purpose, and the discussion is entirely in terms of lists

The Mathematics of Directed Specifications

In this paper we lay a mathematical foundation for processes that communicate via directed communication channels. We start from a collection of primitive specifications. Particular correctness concerns partition this collection into equivalence classes, which can serve as abstract specifications. The theory is illustrated by taking as correctness concern absence of computation interference. In this case the abstract specification space can be identified with the space of delay-insensitive specifications

An Algebra for Delay-Insensitive Circuits

A novel process algebra is presented; algebraic expressions specify delay-insensitive circuits in terms of voltage-level transitions on wires. The approach appears to have several advantages over traditional state-graph and production-rule based methods. The wealth of algebraic laws makes it possible to specify circuits concisely and facilitates the verification of designs. Individual components can be composed into circuits in which signals along internal wires are hidden from the environment

Construction of an operational semantics for DI-algebra

Numerous formalisms exist to specify delay-insensitive computations and their implementations. It is not always straightforward to compare specifications in the different formalisms. The most commonly used is that of finite automata in which nodes are annotated with progress requirements. In this paper we present an algorithm that transforms DI-algebra recursive process expressions into finite automatons. In doing so we develop an operational semantics for DI-algebra. The algorithm is proven correct and has been implemented. It turns out to be very valuable in the process of getting a specification right. 0 Introduction Over the last decade numerous formalisms have been developed to express delayinsensitive specifications and implementations [Mar86, Ebe89, BKR + 91, YLSV92, PC93, JU93, KKTV94]. Some of them have been devised so as to allow a mechanical translation to an implementation in silicon. Other ones try to capture a designer's intuition, and yet another class aims at ease of..

Composition Theorems in DI-Algebra

The design and the automated synthesis and verification of asynchronous circuits are active areas of research. Delay-insensitive circuits are a very robust class of asynchronous circuits, viz. circuits that operate correctly independent of delays in components or interconnecting wires. DI-algebra is a CSP-like language in which a process models the behavior of a delayinsensitive circuit. DI-algebra can be used in the specification and verification of such circuits. Algebraic languages such as DI-algebra allow for high level verification. Designs of DI-circuits are typically expressed in terms of basic components: relatively small building blocks, with simple functionality, from which more complex circuits can be built. Examples of such components include Merge, Wire, Fork and Join components. The verification of a design consists of the proof that the composition of the basic components implements (refines) the specification. One way of doing this is by `cumulative composition': repeat..