Paul Knuth

Formalizing Knuth-Bendix Orders and Knuth-Bendix Completion

We present extensions of our Isabelle Formalization of Rewriting that cover two historically related concepts: the Knuth-Bendix order and the Knuth-Bendix completion procedure. The former, besides being the first development of its kind in a proof assistant, is based on a generalized version of the Knuth-Bendix order. We compare our version to variants from the literature and show all propertie...

پل کلودل Paul Claudel

On Transfinite Knuth-Bendix Orders

In this paper we discuss the recently introduced transfinite Knuth-Bendix orders. We prove that any such order with finite subterm coefficients and for a finite signature is equivalent to an order using ordinals below ω, that is, finite sequences of natural numbers of a fixed length. We show that this result does not hold when subterm coefficients are infinite. However, we prove that in this ge...

Albert Benveniste , Paul Caspi , Paul

In this paper, we present a theory of synchronous data-ow languages. Our theory is supported by both some heuristic analysis of applications and some theoretical investigation of the data-ow paradigm. Our model covers both behavioural and operational aspects, and allows both synchronous and asynchronous styles of implementation for synchronous programs. This model served as a basis to establish...

Schur Operators and Knuth Correspondences

The paper presents a general combinatorial approach to the Schur functions and their modiications, respective generalized Cauchy identities, and bijective Knuth-type correspondences between matrices and pairs of tableaux. All of these appear whenever one has a pair of graphs with the same vertices such that the linear operators associated with these graphs satisfy a certain type of commutation ...