Generating All Permutations by Context-Free Grammars in Greibach Normal Form

We consider context-free grammars $G_n$ in Greibach normal form and, particularly, in Greibach $m$-form ($m=1,2$) which generates the finite language $L_n$ of all $n!$ strings that are permutations of $n$ different symbols ($n\geq 1$). These grammars are investigated with respect to their descriptional complexity, i.e., we determine the number of nonterminal symbols and the number of production rules of $G_n$ as functions of $n$. As in the case of Chomsky normal form these descriptional complexity measures grow faster than any polynomial function

Complexity of normal form grammars

AbstractVarious types of grammars can be used to describe context-free languages. Such are context-free grammars and their normal form restrictions. Rewriting of a context-free grammar to an equivalent grammar in required (normal) form can cause a change of parameters of the grammar such as the number of rules, the number of nonterminals, etc. Greibach normal form grammars and position restricted grammars will be investigated from the point of view of descriptional complexity of context-free languages

Regular realizability problems and context-free languages

We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. In this paper we focus on the case of context-free filters. Algorithmic complexity of the RR problem is a very coarse measure of context-free languages complexity. This characteristic is compatible with rational dominance. We present examples of P-complete RR problems as well as examples of RR problems in the class NL. Also we discuss RR problems with context-free filters that might have intermediate complexity. Possible candidates are the languages with polynomially bounded rational indices.Comment: conference DCFS 201

From left-regular to Greibach normal form grammars

Each context-free grammar can be transformed to a context-free grammar in Greibach normal form, that is, a context-free grammar where each right-hand side of a prorfuction begins with a terminal symbol and the remainder of the right-hand side consists of nonterminal symbols. In this short paper we show that for a left-regular grammar G we can obtain a right-regular grammar G’ (which is by definition in Greibach normal form) which left-to-right covers G (in this case left parses of G’ can be mapped by a homomorphism on right parses of G. Moreover, it is possible to obtain a context-free grammar G” in Greibach normal form which right covers the left-regular grammar G (in this case right parses of G” are mapped on right parses of G)

A survey of normal form covers for context-free grammars

An overview is given of cover results for normal forms of context-free grammars. The emphasis in this paper is on the possibility of constructing ɛ-free grammars, non-left-recursive grammars and grammars in Greibach normal form. Among others it is proved that any ɛ-free context-free grammar can be right covered with a context-free grammar in Greibach normal form. All the cover results concerning the ɛ-free grammars, the non-left-recursive grammars and the grammars in Greibach normal form are listed, with respect to several types of covers, in a cover-table

Structure preserving transformations on non-left-recursive grammars

We will be concerned with grammar covers, The first part of this paper presents a general framework for covers. The second part introduces a transformation from nonleft-recursive grammars to grammars in Greibach normal form. An investigation of the structure preserving properties of this transformation, which serves also as an illustration of our framework for covers, is presented

Languages, machines, and classical computation

3rd ed, 2021. A circumscription of the classical theory of computation building up from the Chomsky hierarchy. With the usual topics in formal language and automata theory