A Transducer Approach to Coxeter Groups

This paper represents an efficient way of implementing a (finite) CoxetergroupWon a computer, through the use of a tower of special subgroups ofWand the corresponding left cosets. We show how some results of Deodharʹs may be interpreted in the language of finite state machines to produce a cascade of small transducers which handle the main “word processing” problems in the group. An algorithm is described for an efficient explicit construction of the relevant transducer tables starting from the Coxeter matrix ofW. We also show (again interpreting a result of Deodharʹs) that the Bruhat ordering onWpresents a nice recursive structure in this implementation, leading to an effective enumeration of arbitrary Bruhat intervals