L homomorphisms and reductions of OL systems

L homomorphisms, i.e. structure preserving mappings between OL systems, are introduced. Every L homomorphism is determined in a unique way by a homomorphism between thefree monoids generated by the alphabets of the related systems and by a nonnegative integer. Thereby the notion of L homomorphism is characterized in a decidable way. L homomorphisms are related to all essential notions of L systems like derivations, adult languages, local catenativity, and ranks of DOL systems. Using the notion of L homomorphism a letter merging procedure for the reduction of OL systems is developed which is similar to the state merging algorithm for the reduction of finite state machines.