Position-restricted grammar forms and grammars

https://doi.org/10.1016/0304-3975(82)90128-1Get rights and content
Under an Elsevier user license
open archive

Abstract

This paper deals with the question of canonical types for grammar forms and grammars. A grammar (form) is called position restricted of type (m1,…,mn+ 1) if n⩾2, each m1 is a nonnegative integer, and each production is either of the type ξ0u, u a terminal word, or ξ0w1ξ1w2wnξnwn+1, where each ξ is a variable and each wi is a terminal word of length mi. Thus a grammar (form) is position restricted if all productions in it but the terminal ones have the same relative position of terminals and variables. The main results are as follows. Each grammar form G1 is equivalent to a grammar form G2 of any desired position-restricted type (m1,…,mn,0), with the interpretation grammars of G2 of position-restricted type (m1,…,mn,0) being sufficient to define all languages in L(G1). The above result is no longer true if the position-restricted type is such that mn+1⩾1. The second main result is that each context-free language is defined by a grammar G of any desired position-restricted type.

Cited by (0)

This research was supported in part by NSF grants MCS 77-02470, MCS 73-03380, and MCS 77-22323. An early version of this paper was presented at the 1977 Fundamentals of Computation Theory Conference, Poznan-Kornik, Poland, September 19–23, 1977, under the title “Canonical forms of context-free grammars and position restricted grammar forms”.

∗∗

Current address: Department of Applied Science, University of California, Davis/Livermore, Livermore, CA94550, U.S.A.