The Generic Model of Computation

Over the past two decades, Yuri Gurevich and his colleagues have formulated axiomatic foundations for the notion of algorithm, be it classical, interactive, or parallel, and formalized them in the new generic framework of abstract state machines. This approach has recently been extended to suggest a formalization of the notion of effective computation over arbitrary countable domains. The central notions are summarized herein.Comment: In Proceedings DCM 2011, arXiv:1207.682

From analytical mechanical problems to rewriting theory through M. Janet's work

Lecture note of the Kobe-Lyon summer school 2015International audienceThis note surveys the historical background of the Gröbner basis theory for D-modules and linear rewriting theory. The objective is to present a deep interaction of these two fields largely developed in algebra throughout the twentieth century. We recall the work of M. Janet on the algebraic analysis on linear partial differential systems that leads to the notion of involutive division. We present some generalizations of the division introduced by M. Janet and their relations with Gröbner basis theory