**Wintersemester 2006/2007****Prof. Franz Winkler****Rewriting in Computer Science and Logic (326.007)**

This lecture is intended to give an introduction to term rewriting systems and their application in computer science and logic. In particular we will discuss general reduction relations, properties of reduction systems such as confluence and termination, completion procedures (Knuth-Bendix procedure) for word rewriting systems and term rewriting systems.

Term rewriting systems developed out o mathematical logic and are an important part of theoretical computer science. They consist of sequences of discrete transformation steps where one term is replaced with another and have applications in many areas, from functional programming to automatic theorem proving and computer algebra. The theory of rewriting is fundamental to concepts in constructive algebra, such as Gröbner bases, and also to concepts in logic, such as decision of equational theories (e.g. the theory of groups).

J. Avenhaus, *Reduktionssysteme*, Springer-Verlag, 1995

F. Baader, T. Nipkow, *Term Rewriting and All That*, Cambridge Univ.
Press, 1998

R.V. Book, F. Otto, *String-Rewriting Systems*, Springer-Verlag, 1993

N. Dershowitz, D.A. Plaisted, "Rewriting", in
A. Robinson, A. Voronkov (eds.), *Handbook of Automated Reasoning*,
pp. 535-610,
Elsevier Science Publ., 2001