Alternative Vidhi to Conversion of Cyclic CNF->GNF

In automata theory Greibach Normal Form shows that A->aV n*, where ‘a’ is terminal symbol and Vn is nonterminal symbol where * shows zero or more rates of Vn [1]. Most popular questions, conversion of following cyclic CNF into GNF are: Question 1 S->AA | a, A->SS | b Question 2 S->AB, A->BS | b, B->SA | a Question 3 S->AB, A->BS | b, B->AS | a [1] To solve these questions, we need two technical lemmas and required one or more another variable like Z1. In these questions, we have cyclic nature of production called cyclic CNF. We have modified the same rule by which we get the more reliable answer with less number of productions in right hand side without using lemmas and any another variable. This above method can be applied on all problems by which we produce the GNF.

A Symmetric Functions Approach to Stockhausen's Problem

We consider problems in sequence enumeration suggested by Stockhausen's problem, and derive a generating series for the number of sequences of length $k$ on $n$ available symbols such that adjacent symbols are distinct, the terminal symbol occurs exactly $r$ times, and all other symbols occur at most $r-1$ times. The analysis makes extensive use of techniques from the theory of symmetric functions. Each algebraic step is examined to obtain information for formulating a direct combinatorial construction for such sequences.

Recognition of Ricker wavelets by syntactic analysis

Syntactic pattern recognition techniques are applied to the analysis of 1-D seismic traces to classify Ricker wavelets. Seismic Ricker wavelets have structural information, and each wavelet can be represented by a string of symbols. To recognize the strings, we use a finite‐state automaton to identify each string. The automaton can accept strings having substitution, insertion, and deletion errors of the symbols. There are two attributes, terminal symbol and weight, in each transition of the automaton. A minimum‐cost, error‐correcting, finite‐state automaton is proposed to parse the input string.

On a property of probabilistic context-free grammars

It is proved that for a probabilistic context-free languageL(G), the population density of a character (terminal symbol) is equal to its relative density in the words of a sampleSfromL(G)whenever the production probabilities of the grammarGare estimated by the relative frequencies of the corresponding productions in the sample.