A survey of NLC grammars

Abstract

In the las t years the theory of graph grammars has developed in to a chal lenging and mathematically in te res t ing area in computer science that is wel l -mot ivated by i t s many potent ia l f i e l ds of app l ica t ions, such as data bases, data f low analys is , concurrency, pattern recogni t ion and developmental biology (one can f ind more deta i l s in , e .g . , ~ER] and ~ I ) . Although there ex is ts already a considerable amount of l i t e rature on th is top ic , the mathematical theory of graph grammars is s t i i l much less developed than ti le theory of s t r ing grammars. In pa r t i cu la r there is a need for a un i fy ing framework for graph grammars w i th in which various issues can be discussed and compared, because in the ex is t ing theory one often encounters the undesirable s i tuat ion that various issues are invest igated w i th in various models, which makes i t d i f f i cu l t to compare the resu l ts . In ~R1] and~R2] NLC grammars were introduced as a f i r s t step towards such a un i fy ing framework. We would l i ke to bui ld up a sol id theory of NLC grammars f i r s t and then consider var#ous extensions and var ia t ions of the basic model in order to obtain a qui te general theory of graph grammars based on the NLC model. We hope that th is approach w i l l also y ie ld a better ins igh t in what are the central notions of the theory and what are the main problems to be solved yet . In th is paper we present an overview of (a part of) the resul ts obtained for NLC grammars in the las t few years. A more complete overview, together with proofs of the resul ts mentioned can be found in the Ph.D. thesis by D. Janssens (to appear).