Adrian Atanasiu | Universitatea Bucuresti (original) (raw)

Papers by Adrian Atanasiu

World Scientific Publishing Co., Inc. eBooks, May 1, 1994

Acta Informatica, Aug 1, 1992

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

arXiv (Cornell University), Feb 16, 2020

Reaction systems, introduced by Ehrenfeucht and Rozenberg, are elementary computational models ba... more Reaction systems, introduced by Ehrenfeucht and Rozenberg, are elementary computational models based on biochemical reactions transpiring within the living cells. Numerous studies focus on mathematical aspects of minimal reaction systems due to their simplicity and rich generative power. In 2014 Manzoni, Pocas, and Porreca showed that every reaction system can be simulated by some minimal reaction system over an extended background set. Motivated by their work, we introduce the concepts of strictly minimal and hybrid reaction systems. Using our new concepts, the result of Manzoni et al. is revisited and strengthened. We also show that extension of the background set by polynomially bounded many elements is not sufficient to guarantee the aforementioned simulation. Finally, an analogous result for strong simulation is obtained.

This paper proposes an algebraic way of sentence valuation in a semiring. Actually, throughout th... more This paper proposes an algebraic way of sentence valuation 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 sentences. Two synonymy relations, with respect to a given valuation, are introduced. All sentences that are synonynous form a synonymy class. Some basic problems regarding the synonymy classes, which are actually formal languages, are formulated and studied. Some of them are completely solved whereas partial answers are provided for others.

arXiv (Cornell University), Aug 13, 2018

Certain upper triangular matrices, termed as Parikh matrices, are often used in the combinatorial... more 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

Abstract: We introduce a couple of families of codiable languages and investigate properties of t... more Abstract: We introduce a couple of families of codiable languages and investigate properties of these families as well as interrelationships between dierent families. We also develop an algorithm based on the Earley algorithm to compute the values of the inverse of the Parikh matrix mapping over a codiable context-free language. Finally, an attributed grammar that computes the values of the Parikh matrix mapping is dened.

Centro de Informacion y Documentacion Cientifica (CINDOC). C/Joaquin Costa, 22. 28002 Madrid. SPA... more Centro de Informacion y Documentacion Cientifica (CINDOC). C/Joaquin Costa, 22. 28002 Madrid. SPAIN / CINDOC - Centro de Informaciòn y Documentaciòn CientìficaSIGLEESSpai

Using the fact that the Parikh matrix mapping is not an injective mapping, the paper investigates... more Using the fact that the Parikh matrix mapping is not an injective mapping, the paper investigates some properties of the set of words having the same Parikh matrix; these words are called "amiable" or "M -equivalent". The aim is to reduce the number of amiable words using a morphism which provides additional information about them.

International Journal of Foundations of Computer Science, 2017

Some mathematical aspects of reaction systems introduced by Ehrenfeucht and Rozenberg are conside... more Some mathematical aspects of reaction systems introduced by Ehrenfeucht and Rozenberg are considered. Ehrenfeucht et al. have previously obtained a complete classification of functions specified by minimal reaction systems in terms of certain closure properties of the specified functions. In this work, a refined proof of this classification with slight extension is obtained. Furthemore, the recently introduced notion of reaction system rank is studied for functions belonging to this class, as well as for focus functions, the latter which play a significant role in the proof of the classification theorem.

J. Univers. Comput. Sci., 2001

We introduce a couple of families of codifiable languages and investigate properties of these fam... more We introduce a couple of families of codifiable languages and investigate properties of these families as well as interrelationships between different families. Also we develop an algorithm based on the Earley algorithm to compute the values of the inverse of the Parikh matrix mapping over a codifiable context-free language. Finally, an attributed grammar that computes the values of the Parikh matrix mapping is defined.

J. Univers. Comput. Sci., 2001

We introduce a couple of families of codifiable languages and investigate properties of these fam... more We introduce a couple of families of codifiable languages and investigate properties of these families as well as interrelationships between different families. Also we develop an algorithm based on the Earley algorithm to compute the values of the inverse of the Parikh matrix mapping over a codifiable context-free language. Finally, an attributed grammar that computes the values of the Parikh matrix mapping is defined.

We introduce a couple of families of codifiable languages and investigate properties of these fam... more We introduce a couple of families of codifiable languages and investigate properties of these families as well as interrelationships between different families. Also we develop an algorithm based on the Earley algorithm to compute the values of the inverse of the Parikh matrix mapping over a codifiable context-free language. Finally, an attributed grammar that computes the values of the Parikh matrix mapping is defined.

ArXiv, 2018

We introduce the notion of general prints of a word, which is substantialized by certain canonica... more We introduce the notion of general prints of a word, which is substantialized by certain canonical decompositions, to study repetition in words. These associated decompositions, when applied recursively on a word, result in what we term as core prints of the word. The length of the path to attain a core print of a general word is scrutinized. This paper also studies the class of square-free ternary words with respect to the Parikh matrix mapping, which is an extension of the classical Parikh mapping. It is shown that there are only finitely many matrix-equivalence classes of ternary words such that all words in each class are square-free. Finally, we employ square-free morphisms to generate infinitely many pairs of square-free ternary words that share the same Parikh matrix.

Journal of Information Systems and Operations Management, 2012

This article presents two new signcryption schemes. The first one is based on Schnorr digital sig... more This article presents two new signcryption schemes. The first one is based on Schnorr digital signature algorithm and the second one is using Proxy Signature scheme introduced by Mambo. Schnorr Signcryption has been implemented in a program and here are provided the steps of the algorithm, the results and some examples. The Mambo’s Proxy Signature is adapted for Shortened Digital Signature Standard, being part of a new Proxy Signcryption scheme.

Fundamenta Informaticae

Since the undecidability of the mortality problem for 3 × 3 matrices over integers was proved usi... more Since the undecidability of the mortality problem for 3 × 3 matrices over integers was proved using the Post Correspondence Problem, various studies on decision problems of matrix semigroups have emerged. The freeness problem in particular has received much attention but decidability remains open even for 2 × 2 upper triangular matrices over nonnegative integers. Parikh matrices are upper triangular matrices introduced as a generalization of Parikh vectors and have become useful tools in studying of subword occurrences. In this work, we focus on semigroups of Parikh matrices and study the freeness problem in this context.

The concept of Parikh matrix of a word was introduced by Mateescu et al. [8] to count scattered s... more The concept of Parikh matrix of a word was introduced by Mateescu et al. [8] to count scattered subwords in a given word over an ordered alphabet. Motivated by a recent study of Atanasiu [3], on this notion using morphisms, we consider, in this paper, general morphisms on words and obtain various properties related to subwords, in the context of a weak-ratio property considered in [12].

In this paper, we present a problem and propose an elegant solution for it: a protocol that allow... more In this paper, we present a problem and propose an elegant solution for it: a protocol that allows a manager to choose his team from a database of experts and then establish with them a common secret shared key. There are some restrictions on the protocol which led us to the use of proxy re-encryption: the list of experts chosen is not known outside the team and the secret key agreed on is known only by the team. The construction and security of the protocol is based on the concept of Identity-Based Proxy Re-encryption (IB-PRE). In the second part of this paper, we extend the IB-PRE scheme by combining it with an Identity-Based Time Specific Encryption (IB-TSE) scheme obtaining a time specific encryption scheme that allows not only encryption, but also re-encryption.

A new type of splicing is defined, namely the interchange of two fixed subwords, without moving t... more A new type of splicing is defined, namely the interchange of two fixed subwords, without moving the sequences situated after them. Idea of splicing grammar systems is introduced by Dassow and Mitrana, ([2]); in this paper only the derivation type is changed. The generative power is the same (are necessarily only two modules to generate all recursive enumerable languages). Two variants of derivation are considered more detailed (when at every step the rules used have the same left part, and an asincronous derivation when it is possible to apply rules only in a subset of components). The generative power remains the same but some normal forms are possible to be defined.

A new way to transform amiable words over a ternary ordered alphabet is defined and analysed: und... more A new way to transform amiable words over a ternary ordered alphabet is defined and analysed: under some conditions, several subwords of a word can be modified in the same step, obtaining another amiable word. This transformation cannot be always decomposed in sequential transformations as defined in [1], and gives almost the same final results as in [14] and [16], but without any output from the set of amiable words defined by a Parikh matrix. The class of amiable languages characterized by the number of subwords modified in the same step is defined and studied partially in the second part of the paper.

A new model of evolutionary system (ES for short) is constructed, based of definitions and notati... more A new model of evolutionary system (ES for short) is constructed, based of definitions and notation from [2]. Some results are obtained, namely any language can be generated by a darwinist ES, by a 3 − ES. Also, a very promising concept, that of halting ES is proposed; we believe that it will have many further applications.

World Scientific Publishing Co., Inc. eBooks, May 1, 1994

Acta Informatica, Aug 1, 1992

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

arXiv (Cornell University), Feb 16, 2020

Reaction systems, introduced by Ehrenfeucht and Rozenberg, are elementary computational models ba... more Reaction systems, introduced by Ehrenfeucht and Rozenberg, are elementary computational models based on biochemical reactions transpiring within the living cells. Numerous studies focus on mathematical aspects of minimal reaction systems due to their simplicity and rich generative power. In 2014 Manzoni, Pocas, and Porreca showed that every reaction system can be simulated by some minimal reaction system over an extended background set. Motivated by their work, we introduce the concepts of strictly minimal and hybrid reaction systems. Using our new concepts, the result of Manzoni et al. is revisited and strengthened. We also show that extension of the background set by polynomially bounded many elements is not sufficient to guarantee the aforementioned simulation. Finally, an analogous result for strong simulation is obtained.

This paper proposes an algebraic way of sentence valuation in a semiring. Actually, throughout th... more This paper proposes an algebraic way of sentence valuation 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 sentences. Two synonymy relations, with respect to a given valuation, are introduced. All sentences that are synonynous form a synonymy class. Some basic problems regarding the synonymy classes, which are actually formal languages, are formulated and studied. Some of them are completely solved whereas partial answers are provided for others.

arXiv (Cornell University), Aug 13, 2018

Certain upper triangular matrices, termed as Parikh matrices, are often used in the combinatorial... more 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

Abstract: We introduce a couple of families of codiable languages and investigate properties of t... more Abstract: We introduce a couple of families of codiable languages and investigate properties of these families as well as interrelationships between dierent families. We also develop an algorithm based on the Earley algorithm to compute the values of the inverse of the Parikh matrix mapping over a codiable context-free language. Finally, an attributed grammar that computes the values of the Parikh matrix mapping is dened.

Centro de Informacion y Documentacion Cientifica (CINDOC). C/Joaquin Costa, 22. 28002 Madrid. SPA... more Centro de Informacion y Documentacion Cientifica (CINDOC). C/Joaquin Costa, 22. 28002 Madrid. SPAIN / CINDOC - Centro de Informaciòn y Documentaciòn CientìficaSIGLEESSpai

Using the fact that the Parikh matrix mapping is not an injective mapping, the paper investigates... more Using the fact that the Parikh matrix mapping is not an injective mapping, the paper investigates some properties of the set of words having the same Parikh matrix; these words are called "amiable" or "M -equivalent". The aim is to reduce the number of amiable words using a morphism which provides additional information about them.

International Journal of Foundations of Computer Science, 2017

Some mathematical aspects of reaction systems introduced by Ehrenfeucht and Rozenberg are conside... more Some mathematical aspects of reaction systems introduced by Ehrenfeucht and Rozenberg are considered. Ehrenfeucht et al. have previously obtained a complete classification of functions specified by minimal reaction systems in terms of certain closure properties of the specified functions. In this work, a refined proof of this classification with slight extension is obtained. Furthemore, the recently introduced notion of reaction system rank is studied for functions belonging to this class, as well as for focus functions, the latter which play a significant role in the proof of the classification theorem.

J. Univers. Comput. Sci., 2001

We introduce a couple of families of codifiable languages and investigate properties of these fam... more We introduce a couple of families of codifiable languages and investigate properties of these families as well as interrelationships between different families. Also we develop an algorithm based on the Earley algorithm to compute the values of the inverse of the Parikh matrix mapping over a codifiable context-free language. Finally, an attributed grammar that computes the values of the Parikh matrix mapping is defined.

J. Univers. Comput. Sci., 2001

We introduce a couple of families of codifiable languages and investigate properties of these fam... more We introduce a couple of families of codifiable languages and investigate properties of these families as well as interrelationships between different families. Also we develop an algorithm based on the Earley algorithm to compute the values of the inverse of the Parikh matrix mapping over a codifiable context-free language. Finally, an attributed grammar that computes the values of the Parikh matrix mapping is defined.

We introduce a couple of families of codifiable languages and investigate properties of these fam... more We introduce a couple of families of codifiable languages and investigate properties of these families as well as interrelationships between different families. Also we develop an algorithm based on the Earley algorithm to compute the values of the inverse of the Parikh matrix mapping over a codifiable context-free language. Finally, an attributed grammar that computes the values of the Parikh matrix mapping is defined.

ArXiv, 2018

We introduce the notion of general prints of a word, which is substantialized by certain canonica... more We introduce the notion of general prints of a word, which is substantialized by certain canonical decompositions, to study repetition in words. These associated decompositions, when applied recursively on a word, result in what we term as core prints of the word. The length of the path to attain a core print of a general word is scrutinized. This paper also studies the class of square-free ternary words with respect to the Parikh matrix mapping, which is an extension of the classical Parikh mapping. It is shown that there are only finitely many matrix-equivalence classes of ternary words such that all words in each class are square-free. Finally, we employ square-free morphisms to generate infinitely many pairs of square-free ternary words that share the same Parikh matrix.

Journal of Information Systems and Operations Management, 2012

This article presents two new signcryption schemes. The first one is based on Schnorr digital sig... more This article presents two new signcryption schemes. The first one is based on Schnorr digital signature algorithm and the second one is using Proxy Signature scheme introduced by Mambo. Schnorr Signcryption has been implemented in a program and here are provided the steps of the algorithm, the results and some examples. The Mambo’s Proxy Signature is adapted for Shortened Digital Signature Standard, being part of a new Proxy Signcryption scheme.

Fundamenta Informaticae

Since the undecidability of the mortality problem for 3 × 3 matrices over integers was proved usi... more Since the undecidability of the mortality problem for 3 × 3 matrices over integers was proved using the Post Correspondence Problem, various studies on decision problems of matrix semigroups have emerged. The freeness problem in particular has received much attention but decidability remains open even for 2 × 2 upper triangular matrices over nonnegative integers. Parikh matrices are upper triangular matrices introduced as a generalization of Parikh vectors and have become useful tools in studying of subword occurrences. In this work, we focus on semigroups of Parikh matrices and study the freeness problem in this context.

The concept of Parikh matrix of a word was introduced by Mateescu et al. [8] to count scattered s... more The concept of Parikh matrix of a word was introduced by Mateescu et al. [8] to count scattered subwords in a given word over an ordered alphabet. Motivated by a recent study of Atanasiu [3], on this notion using morphisms, we consider, in this paper, general morphisms on words and obtain various properties related to subwords, in the context of a weak-ratio property considered in [12].

In this paper, we present a problem and propose an elegant solution for it: a protocol that allow... more In this paper, we present a problem and propose an elegant solution for it: a protocol that allows a manager to choose his team from a database of experts and then establish with them a common secret shared key. There are some restrictions on the protocol which led us to the use of proxy re-encryption: the list of experts chosen is not known outside the team and the secret key agreed on is known only by the team. The construction and security of the protocol is based on the concept of Identity-Based Proxy Re-encryption (IB-PRE). In the second part of this paper, we extend the IB-PRE scheme by combining it with an Identity-Based Time Specific Encryption (IB-TSE) scheme obtaining a time specific encryption scheme that allows not only encryption, but also re-encryption.

A new type of splicing is defined, namely the interchange of two fixed subwords, without moving t... more A new type of splicing is defined, namely the interchange of two fixed subwords, without moving the sequences situated after them. Idea of splicing grammar systems is introduced by Dassow and Mitrana, ([2]); in this paper only the derivation type is changed. The generative power is the same (are necessarily only two modules to generate all recursive enumerable languages). Two variants of derivation are considered more detailed (when at every step the rules used have the same left part, and an asincronous derivation when it is possible to apply rules only in a subset of components). The generative power remains the same but some normal forms are possible to be defined.

A new way to transform amiable words over a ternary ordered alphabet is defined and analysed: und... more A new way to transform amiable words over a ternary ordered alphabet is defined and analysed: under some conditions, several subwords of a word can be modified in the same step, obtaining another amiable word. This transformation cannot be always decomposed in sequential transformations as defined in [1], and gives almost the same final results as in [14] and [16], but without any output from the set of amiable words defined by a Parikh matrix. The class of amiable languages characterized by the number of subwords modified in the same step is defined and studied partially in the second part of the paper.

A new model of evolutionary system (ES for short) is constructed, based of definitions and notati... more A new model of evolutionary system (ES for short) is constructed, based of definitions and notation from [2]. Some results are obtained, namely any language can be generated by a darwinist ES, by a 3 − ES. Also, a very promising concept, that of halting ES is proposed; we believe that it will have many further applications.

In the combinatorial study of words, the Parikh matrix mapping was introduced by Mateescu et al. ... more 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 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 S ¸erbˇanut¸ˇa's 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 S ¸erbˇanut¸ˇa is conclusively addressed.