Picture languages with array rewriting rules

Picture Languages: From Wang Tiles to 2D Grammars

“…This class of grammars has been introduced by Siromoney et al [52] CF Kolam grammars are defined analogously to CF string grammars. Derivation is similar: a sentential form over terminal and nonterminal symbols results from the preceding one by replacing a nonterminal with some corresponding right hand side of a rule.…”

A CKY parser for picture grammars

“…This class of grammars has been introduced by Siromoney et al [11] under the name "Array grammars", later renamed "Kolam Array grammars" in order to avoid confusion with Rosenfeld's homonymous model. Much later Matz reinvented the same model [6] (considering only CF rules).…”

Shuffle on array languages generated by array grammars

“…The generation of two-dimensional arrays by theoretical models [2,4,6,[8][9][10]] describes a wide variety of interesting classes of pictures. To develop the study on parallel contextual array grammars, the shuffle operation on finite arrays with trajectories has been introduced [3].…”

“…Several such studies are available in the literature [7]. In [9] Siromoney et al have given the generalized notion of rewriting rules in string grammars to array rewriting rules for matrix grammars. These rules are either regular, context free or context sensitive in nature but the use of production rules is restricted by the condition of row and column concatenation.…”

“…Motivated by the studies done by G. Siromoney et al (1973) and Alexandru Mateescu et al (1998) we examine the language theoretic results related to shuffle on trajectories by making use of Siromoney array grammars such as (R : …”