Universit at M Unchen Centrum F Ur Informations-und Sprachverarbeitung Word Uniication and Transformation of Generalized Equations Word Uniication and Transformation of Generalized Equations

Makanin's algorithm Ma77] shows that it is decidable whether a word equation has a solution. The original description was hard to understand and not designed for implementation. Since words represent a fundamental data type, various authors have given improved descriptions P e81, Ab87, Sc90, Ja90]. In this paper we present a version of the algorithm which probably cannot be further simpliied without fundamentally new insights which exceed Makanin's original ideas. We give a transformation which is eecient, conceptually simple and applies to arbitrary generalized equations. No further subprocedure is needed for the generation of the search tree. Particular attention is then given to the proof that proper generalized equations are transformed into proper generalized equations. This point, which is important for the termination argument, was treated erroneously in other papers. We also show that a combination of the basic algorithm for string-uniication (see Pl72, Le72, Si75, Si78] and Makanin's algorithm ooers a simple solution to the problem of terminating minimal and complete word uniication.