Generalized one-sided forbidding grammars

Abstract

In generalized one-sided forbidding grammars (GOFGs), each context-free rule has associated a finite set of forbidding strings, and the set of rules is divided into the sets of left and right forbidding rules. A left forbidding rule can rewrite a nonterminal if each of its forbidding strings is absent to the left of the rewritten symbol. A right forbidding rule is applied analogically. Apart from this, they work like any generalized forbidding grammar. This paper proves the following three results. (1) GOFGs where each forbidding string consists of at most two symbols characterize the family of recursively enumerable languages. (2) GOFGs where the rules in one of the two sets of rules contain only ordinary context-free rules without any forbidding strings characterize the family of context-free languages. (3) GOFGs with the set of left forbidding rules coinciding with the set of right forbidding rules characterize the family of context-free languages.

Keywords:

• formal languages
• regulated rewriting
• generalized one-sided forbidding grammars
• language families
• generative power

2010 AMS Subject Classifications:

• 68Q01
• 68Q05
• 68Q42
• 68Q45
• 68R01

Acknowledgements

This work was supported by the following grants: BUT FIT-S-11-2, MŠMT ED1.1.00/02.0070, and CEZ MŠMT MSM0021630528. The authors thank both anonymous referees for their useful comments regarding this paper.

Notes

For x∈V*, if there are u, v, w∈V* such that x=uvw, then v is a substring of x.