Bracketed context-free languages*

https://doi.org/10.1016/S0022-0000(67)80003-5Get rights and content
Under an Elsevier user license
open archive

Abstract

A bracketed grammar is a context-free grammar in which indexed brackets are inserted around the right-hand sides of the rules. The language generated by a bracketed grammar is a bracketed language. An algebraic condition is given for one bracketed language to be a subset of another. The intersection and the difference of two bracketed languages with the same brackets and terminals are context-free (although not necessarily bracketed) languages. Whether L(G1)⊆L(G2) and whether L(G1)∩L(G2) is empty are solvable problems for arbitrary bracketed grammars G1 and G2 with the same brackets and same terminals. Finally, bracketed languages are shown to be codes with strong properties.

Cited by (0)

*

The research reported in this paper was sponsored in part by the Air Force Cambridge Research Laboratories, Office of Aerospace Research, under Contract AF 19(628)-5166, CRL—Algorithmic Languages Program.

Consultant for System Development Corporation, Santa Monica, California.