Grammar In Greibach Normal Form Research Articles

Generating context-free languages using spiking neural P systems with structural plasticity

Spiking neural P system (SNP system) is a model of computation inspired by networks of spiking neurons. An SNP system is a network of neurons that can send an object, known as a spike, to each other. Spiking neural P system with structural plasticity (SNPSP system) is a variant of the classical SNP system. SNPSP system that incorporates the ideas of synaptogenesis (creating new synapses) and synaptic pruning (deletion of existing synapses), collectively known as structural plasticity, as features of the model. This gives SNPSP systems the ability to change their own structure/topology. In this work, we use SNPSP systems to generate context-free languages. We create a procedure for constructing an SNPSP system given a context-free grammar in Greibach normal form (GNF). The resulting SNPSP system essentially simulates the way in which a context-free grammar in GNF is used to generate languages. We use modules known as arithmetic-memory modules, also created using SNPSP systems, to perform arithmetic operations which are needed for the simulation.

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 ≥ 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.

An elementary proof of double Greibach normal form

In [1,6,7] elementary proofs are given of Greibach Normal Form of context-free grammars [4]. Here we do the same for Double Greibach Normal Form, where it is required that each right-hand side of a production both starts and ends with a terminal symbol [5]. In [5], first a grammar in Greibach Normal Form is con- structed, which is then transformed into Double Greibach Normal Form; both transformations use matrix manipulation. Here we give a direct con- struction, with an elementary correctness proof. We first discuss the construction of Urbanek in 161. Let G = (N,

On Greibach normal form construction

We present an algorithm which, given an arbitrary ε-free and chain-free context-free grammar, produces an equivalent context-free grammar in Greibach normal form (GNF). This algorithm is a generalization of an algorithm recently presented by Ehrenfeucht and Rozenberg. Using this algorithm the well-known GNF construction of Rosenkrantz can be obtained. Furthermore it is possible to rewrite a given context-free grammar by a GNF grammar which has at most twice as much nonterminals as the original grammar. This result is shown to be optimal (with respect to the number of nonterminals).

On greibach normal form construction

In this note we present a procedure to rewrite a given Chomsky normal form grammar in Greibach normal form (GNF). This procedure yields the same grammar as the well-known procedure of Rosenkrantz, but is based on pure derivation-oriented reasoning and not on systems of equations.

On greibach normal form construction

In this note we present a procedure to rewrite a given Chomsky normal form grammar in Greibach normal form (GNF). This procedure yields the same grammar as the well-known procedure of Rosenkrantz, but is based on pure derivation-oriented reasoning and not on systems of equations.

An easy proof of Greibach normal form

We present an algorithm which given an arbitrary A -free context-free grammar produces an equivalent context-free grammar in 2 Greibach normal form. The upper bound on the size of the resulting grammar in terms of the size of the initially given grammar is given. Our algorithm consists of an elementary construction, while the upper bound on the size of the resulting grammar is not bigger than the bounds known for other algorithms for converting context-free grammars into equivalent context-free grammars in Greibach normal form.

Infinite arrays and infinite computations

A complete metric topology is introduced on the set of all finite and infinite arrays and the topological properties of the space are studied. In this complete metric topology, infinite arrays are the limits of increasing sequences of finite arrays. The notion of successful infinite derivations in Generalized Context-free Kolam Array Grammars, yielding infinite arrays, is a subclass of Generalized context-free kolam array grammars. For this class, the finite array language generated by a reduced grammar in Greibach normal form and the set of infinite arrays generated by it are related through the notion of adherence.

A Survey of Normal form Covers for Regular Grammars

An overview is given of cover results for normal forms of regular grammars. Due to the special form of regular grammars and due to the results which are obtained it is sufficient to consider covering grammars in Greibach normal form. Among other things it is proved that any left-regular grammar can be left covered with a context-free grammar in Greibach normal form. All the cover results concerning the left- and right-regular grammars are listed, with respect to several types of covers, in a cover table.

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.

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 homomorphism theorem for weighted context-free grammars

Productions of a context-free grammar can be given coefficients from semirings, inducing weights for both derivations in the grammar and strings over the terminal alphabet. For a weighted context-free grammar in Greibach normal form, the weight of any string, as well as the set of derivations of the string, may be determined from the image under a homomorphism which maps each terminal symbol to a polynomial. The definition of the homomorphism is a straightforward function of the productions. Some examples of interesting semiring structures are included.

Matrix Equations and Normal Forms for Context-Free Grammars

The relationship between the set of productions of a context-free grammar and the corresponding set of defining equations is first pointed out. The closure operation on a matrix of strings is defined and this concept is used to formalize the solution to a set of linear equations. A procedure is then given for rewriting a context-free grammar in Greibach normal form, where the replacements string of each production begins with a terminal symbol. An additional procedure is given for rewriting the grammar so that each replacement string both begins and ends with a terminal symbol. Neither procedure requires the evaluation of regular begins and ends with a terminal symbol. Neither procedure requires the evaluation of regular expressions over the total vocabulary of the grammar, as is required by Greibach's procedure.