Algebraic Manipulations as a Unification and Matching Strategy for Linear Equations in Signed Binary Trees

We s tudy the u n i f i c a t i o n and match ing problems in the s igned b i n a r y t r ees t h e o r y . We show t h a t any equa t i on tl1=t2 can be t rans formed i n t o an e q u i v a l e n t one x = t . I f x does not occur in t then (x > t) i s the unique most genera l u n i f i e r i n the theory (up to an isomorph ism) . We apply t h i s technique to f i n d recur rence r e l a t i o n s between se ts o f t e rms . These r e l a t i o n s are used to syn thes ize LISP p r o grams from a set of i n p u t t r a c e s .