Adrian Atanasiu

The modular grammars

In this article a new class of grammars with derivation restrictions (similar to the matrix, conditional ones, etc.) is presented. In this situation, if a rule of a subset peculiar to P is used in a derivation then it is compulsory to use only productions of that particular subset as long as it is possible. According to the Chomsky hierarchy, naturally attributed to the grammars the generative power of the modular grammars is studied (Section 2), a series of results being obtained as well as a normal form similar to Chomskys normal one. The following two paragraphs deal with the closure properties—only for ℳ 2 and (proving that ℳ 2 is AFL) and also with decision problems connected with the modular grammars, using algorithmical proofs in general.

On a conjecture about Parikh matrices

Based on Salomaas characterization of M-equivalence, Atanasiu conjectured that a certain natural generalization of ME-equivalence solves the injectivity problem of Parikh matrices for the ternary alphabet. This paper refutes his conjecture but continues to study the interesting proposed Thue system. Characterization of certain irreducible elementary transformations under this system is obtained. Furthermore, these transformations are further scrutinized in terms of their replaceability by simpler ones.

A New Operator over Parikh Languages

The characterization of M-equivalence for the Parikh matrices is a decade old open problem. This paper studies Parikh matrices and M-equivalence in relation to the s-shuffle operator for the binary alphabet. We also study the distance between images under the s-shuffle operator in a graph associated to the corresponding class of M-equivalent words.

Authentication of Messages Using P Systems

The paper is an attempt to use P systems in dealing with a cryptographic issue, that of message authentication. Two algorithms are proposed, with and without confirmation from the sender, based on P systems with active membranes. We are not concerned with the practical usefulness of these algorithms, but with proving the usefulness of the membrane computing framework in addressing the authentication question.

On strongly M-unambiguous prints and Şerbǎnuţǎ's conjecture for Parikh matrices

Abstract In the combinatorial study of words, the Parikh matrix mapping was introduced by Mateescu et al. in 2001 as a natural expansion of the classical Parikh mapping. Solving the general injectivity problem of Parikh matrices remains as one of the most sought after triumph among researchers in this area of study. In this paper, we tackle this problem by extending Şerbǎnuţǎs work regarding prints and M -unambiguity to the context of strong M -equivalence. Consequently, we obtain results on the finiteness of strongly M -unambiguous prints for any finite alphabet. Finally, a related conjecture by Şerbǎnuţǎ is conclusively addressed.

Enriching Parikh matrix mappings

In this paper, we define the Super-Parikh (S-Parikh) matrix mapping as an extension of the Parikh matrix mapping introduced by Mateescu et al. Like the Parikh matrix, the extension revolves around a certain type of square matrices, but instead of non-negative integers, its matrix-mapped elements are non-negative rationals (fractions). We study the basic properties of the newly defined formalism and later on we investigate the injectivity of the mapping. Also, we begin a search for the reverse mapping – that is a method for obtaining a word, given the S-Parikh matrix.

A class of coders based on GSM

Using the definition of gsm and finite translators, a new class of coders is proposed. In the first part it is shown that ifM is a weakly-deterministic coder, thenM−1 is also a coder. In the second part, this class of coders is used for solving a problem of secrets transmission.

Parikh matrices for powers of words

Certain upper triangular matrices, termed as Parikh matrices, are often used in the combinatorial study of words. Given a word, the Parikh matrix of that word elegantly computes the number of occurrences of certain predefined subwords in that word. In this paper, we compute the Parikh matrix of any word raised to an arbitrary power. Furthermore, we propose canonical decompositions of both Parikh matrices and words into normal forms. Finally, given a Parikh matrix, the relation between its normal form and the normal forms of words in the corresponding M-equivalence class is established.

On the sentence valuation in a semiring

This paper proposes an algebraic way of sentence valuations in a semiring. Actually, throughout the paper only valuations in the ring of integers with usual addition and multiplication are considered. These valuations take into consideration both words and their positions within the sentences. Two synonymy relations, with respect to a given valuation, are introduced. All sentences that are synonymous form a synonymy class which is actually a formal language. Some basic problems regarding the synonymy classes are formulated in the general setting but the results presented concern only very special valuations.

C-grammars and tree-codifications

The paper introduces two new concepts, namely C -grammar and tree-codification, based on the theory of formal languages, by means of which we try to exhibit a new aspect of general coding theory. Both linear algebraic coding and convolutional coding are presented here as a particular case of tree-codification. The main result of the paper gathers the two new concepts mentioned above. Thus, Theorem 10 establishes that to each tree-codification corresponds a C -grammar in which that tree-codification can be achieved, and vice versa. Some examples are given justifying both the concepts and the assertion that any algebraic coding (linear or convolutional) can be looked upon as a tree-codification.