Network algebra for synchronous dataflow

We develop an algebraic theory of synchronous dataflow networks. First, a basic algebraic theory of networks, called BNA (Basic Network Algebra), is introduced. This theory captures the basic algebraic properties of networks. For synchronous dataflow networks, it is subsequently extended with additional constants for the branching connections that occur between the cells of synchronous dataflow networks and axioms for these additional constants. We also give two models of the resulting theory, the one based on stream transformers and the other based on processes as considered in process algebra.Comment: 24 page

Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin

On flowchart theories Part I. The deterministic case

AbstractWe give a calculus for the classes of deterministic flowchart schemes with respect to the strong equivalence relation, similar to the calculus of the classes of polynomials with respect to the reduction of similar terms. The algebraic structure involved is a strong iteration theory, i.e., an iteration theory (defined by Bloom, Elgot, and Wright, SIAM J. Comput. 9 (1980), 525–540) satisfying a “functorial dagger implication.

Polynomial Path Orders

This paper is concerned with the complexity analysis of constructor term rewrite systems and its ramification in implicit computational complexity. We introduce a path order with multiset status, the polynomial path order POP*, that is applicable in two related, but distinct contexts. On the one hand POP* induces polynomial innermost runtime complexity and hence may serve as a syntactic, and fully automatable, method to analyse the innermost runtime complexity of term rewrite systems. On the other hand POP* provides an order-theoretic characterisation of the polytime computable functions: the polytime computable functions are exactly the functions computable by an orthogonal constructor TRS compatible with POP*.Comment: LMCS version. This article supersedes arXiv:1209.379

Matrix Code

Matrix Code gives imperative programming a mathematical semantics and heuristic power comparable in quality to functional and logic programming. A program in Matrix Code is developed incrementally from a specification in pre/post-condition form. The computations of a code matrix are characterized by powers of the matrix when it is interpreted as a transformation in a space of vectors of logical conditions. Correctness of a code matrix is expressed in terms of a fixpoint of the transformation. The abstract machine for Matrix Code is the dual-state machine, which we present as a variant of the classical finite-state machine.Comment: 39 pages, 19 figures; extensions and minor correction

Synthesis, structure and power of systolic computations

AbstractA variety of problems related to systolic architectures, systems, models and computations are discussed. The emphases are on theoretical problems of a broader interest. Main motivations and interesting/important applications are also presented. The first part is devoted to problems related to synthesis, transformations and simulations of systolic systems and architectures. In the second part, the power and structure of tree and linear array computations are studied in detail. The goal is to survey main research directions, problems, methods and techniques in not too formal a way