On Contextual Grammars with Subregular Selection Languages

Conditional Lindenmayer systems with subregular conditions: The non-extended case

“…Thus we have almost the same situation as for external contextual grammar where most of the relations in the hierarchy of subregular families also hold in the hierarchy of external contextual languages with subregular selection languages (see [7,12]). This is a strong contrast to conditional grammars, tree controlled grammars, and networks of evolutionary processors, where the corresponding hierarchies differ (for instance, in all cases, star-free, regular suffix-closed, and regular circular languages are as powerful as arbitrary regular languages; moreover, some further different subregular families lead to identical families, if used as regular restriction).…”

“…Since on the one hand practical requirement do not ask for arbitrary regular languages and on the other hand theoretical studies -for instance proofs -show that only special regular languages are used, it is very natural to study the devices with subregular languages for the control. Investigations on the change of the generative power, if subregular restrictions defined by combinatorial and algebraic properties are done in [4] for regularly controlled grammars, in [8,10] for conditional grammars, in [16] for tree controlled grammars, in [11,25] for networks with evolutionary processors, and in [7,12] for contextual grammars. Results on the effect of subregular restrictions given by bounds on the number of states/nonterminals/productions necessary to accept/generate the regular language can be found in [6] for regularly controlled grammars, in [5] for conditional grammars, in [15] for tree controlled grammars, in [17] for networks with evolutionary processors, and in [12,26] for contextual grammars.…”

On Union-Free and Deterministic Union-Free Languages

“…They are the simplest languages in the Chomsky-hierarchy, and can be represented by regular expressions or finite automata. Nowadays, some subfamilies of the regular languages have become important in various fields [4][5][6]. One of them is the family of union-free languages: those languages described by regular expressions without the union operation.…”

On the Generative Capacity of Contextual Grammars with Strictly Locally Testable Selection Languages

“…The study of external contextual grammars with selection in special regular sets was started by Jürgen Dassow in [4]. The research was continued by Jürgen Dassow, Florin Manea, and Bianca Truthe (see [8,9,10,16]) where further subregular families of selection languages were considered and the effect of subregular selection languages on the generative power of external and internal contextual grammars was investigated. A recent survey can be found in [28].…”