Contextual Grammars

Let V be a finite non-void set ; V lary. Every finite sequence of elements in ia called a vocnbuV is said to be a s t r i n g o n V. G i v e n a s t r i n g x = a l a 2 . . . a n , t h e n u m b e r n i s c a l l e d t h e l e n g t h o f x . The s t r i n g o f l e n g t h z e r o i s c a l l e d t h e n t r i n g a n d i s d e n o t e d b y r~J . Any s e t o f s t r i n g s o n V i s c a l l e d a l a n g u a g e o n V. The s e t o f a l l s t r i n g s on V ( t h e n u l l s t r i n g i n c l u s i v e l y ) i s c a l l e d t h e u n i v e r s a l l a n g u a g e o n V. By a nwe denote the string a...a, where a is iterated n times. Any ordered pair (u,v~ of strings on V_ is said to be a contex~ on V. The string x is admitted by the context With respect to the language L if u~ G L. Let .~ be a finite set of strings on the vocabulary V~ and let@be a finite se@ of contexts on V. The triple (v,~, ~)) (1)