## Web Access Research Portal

# Researcher: Kelarev, AV (Dr Andrei Kelarev)

## Fields of Research

Algebra and number theory

Coding, information theory and compression

Information retrieval and web search

Group theory and generalisations

Computational logic and formal languages

Information systems philosophy, research methods and theory

Computational complexity and computability

Mathematical physics

Data structures and algorithms

Other mathematical sciences

Theory of computation

Combinatorics and discrete mathematics (excl. physical combinatorics)

Numerical analysis

Algebraic and differential geometry

Optimisation

Applied mathematics

Other physical sciences

Data engineering and data science

Artificial life and complex adaptive systems

Information systems organisation and management

Data management and data science

Software engineering

Genetics

Health informatics and information systems

Information systems

Other information and computing sciences

## Research Objectives

Expanding knowledge in the mathematical sciences

Computer, electronic and communication equipment

Voice and data equipment

Information systems, technologies and services

Network infrastructure equipment

Mobile technologies and communications

Other education and training

Expanding knowledge in the physical sciences

Other information and communication services

Other health

Application software packages

Expanding knowledge in the environmental sciences

Integrated systems

## Career Best Publications

A Polynomial Algorithm for Codes Based on Directed Graphs; **Computing: The Australasian Theory Symposium**

A Statistical Algorithm for Computing Information Rates of Codes with Computer Algebra Systems; **Advances and Applications in Statistics**

Information Rates and Weights of Codes in Structural Matrix Rings; **Applied Algebra, Algebraic Algorithms and Error Correcting Codes**

On congruences of automata defined by directed graphs; **Theoretical Computer Science**

On fuzzy regular languages; **AISAT 2000**

On the Structure of Incidence Rings of Group Automata; **International Journal of Algebra and Computation**

Ring Constructions and Applications; **World Scientific**

## Research Publications

A class of semisimple automata; **Journal of Applied Mathematics and Computing**

A combinatorial algorithm for BCH codes extended with FSA; **Australasian Workshop on Combinatorial Algorithms 2006**

A Combinatorial Property and Cayley Graphs of Semigroups; **Semigroup Forum**

A combinatorial property and growth for semigroups of matrices; **Communications in Algebra**

A Combinatorial Property and Power Graphs of Groups; **Contributions to General Algebra 12, Proceedings of the Vienna Conference**

A combinatorial property and power graphs of semigroups; **Commentationes Mathematicae Universitatis Carolinae**

A combinatorial property defined in terms of power graphs; **Workshop on Model Theory, Profinite Topology and Semigroups**

A combinatorial property of automata, languages, and syntactic monoids; **Words, Languages, Combinatorics**

A combinatorial property of languages and monoids; **Third International Colloquium on Words, Languages and Combinatorics**

A combinatorial property of languages and syntactic monoids; **44th Annual M of the Australian Mathematical Societyeeting**

A method for the compact coding of an image (N.Sh.Dzhikiya)

A new data structure for the engine of computer games programming; **Ultra Scientist of Physical Sciences**

A New Model for Classifying DNA Code Inspired by Neural Networks and FSA; **PKAW**

A note on rewritable products in groups and semigroups; **Bollettino Unione Mathematica Italiana**

A Polynomial Algorithm for Codes Based on Directed Graphs; **Computing: The Australasian Theory Symposium**

A primitive ring which is a sum of two Wedderburn radical subrings; **Proceedings of the American Mathematical Society**

A Statistical Algorithm for Computing Information Rates of Codes with Computer Algebra Systems; **Advances and Applications in Statistics**

Abelian groups, Rings and Modules; **American Mathematical Society**

Algebra Interactive! Learning algebra in an exciting way

Algorithms for computing parameters of graph-based extensions of BCH codes; **Journal of Discrete Algorithms**

Algorithms for computing the Jacobson radical of group rings; **Group Theory and Computation**

Algorithms for shortest paths and d-cycle problems; **Journal of Discrete Algorithms**

An algebraic construction of codes for Slepian-Wolf source networks (T.Uyematsu)

An Algorithm for 3D Image Analysis; **Far East Journal of Applied Mathematics**

An algorithm for analysis of data in geographic information systems; **AWOCA 2002**

An Algorithm for Analysis of Images in Spatial Information Systems^{1}; **Journal of Automata, Languages and Combinatorics 8 (2003)**

An Algorithm for Commutative Semigroup Algebras Which are Principal Ideal Rings; **Communications in Algebra**

An Algorithm for Computing the Minimum Distances of Extensions of BCH Codes Embedded in Semigroup Rings ; **Semigroup Forum**

An Algorithm for Languages Recognised by Graph Algebras; **AWOCA 2000**

An algorithm for repeated convex regions in geographic information systems; **Far East Journal of Applied Mathematics**

An answer to a question of Kegel on sums of rings; **Canadian Mathematical Bulletin**

Application of epigroups to graded ring theory; **Semigroup Forum**

Artinian band sums of rings; **Australian Mathematical Society. Journal. Series A. Pure Mathematics and Statistics**

Artinian semigroup-graded rings; **Bulletin of the London Mathematical Society.**

Automata with languages recognised by graph algebras; **AISAT 2000**

Band-graded rings; **Mathematica Japonica**

Bergman's lemma for graded rings; **Communications in Algebra**

Boolean functions in coding theory and cryptology

Braid-based cryptography

Cayley Graph

Central internal algebras and varieties; **Communications in Algebra**

Clustering Algorithms for ITS Sequence Data with Alignment Metrics; **AJCAI**

Combinatorial and statistical algorithms for information rates of codes defined by graphs; **AWOCA 2004**

Combinatorial Properties of Sequences in Groups and Semigroups; **DMTCS '96**

Computing parameters of graph-based extensions of BCH codes; **AWOCA2005**

Computing Statistics for Polynomial Codes: An Algorithm Based on the Mann-Whitney U-Test; **Advances and Applications in Statistics**

Computing the information rates for a class of polynomial codes; **Workshop on the Internet, Telecommunications and Signal Processing: WITSP 06**

Directed Graphs and Closure Properties For Languages; **12th Australian Workshop on Combinatorial Algorithms**

Directed graphs and combinatorial properties for groups and semigroups; **Australian Mathematical Society Joint Annual Conference with American Mathematical Society, 43**

Directed graphs and combinatorial properties of groups; **AAA58**

Directed Graphs and Combinatorial Properties of Semigroups; **Journal of Algebra**

Directed graphs and Lie superalgebras of matrices; **Journal of Algebra**

Directed graphs and minimum distances of error-correcting codes in matrix rings; **New Zealand Journal of Mathematics**

Directed Graphs and Nilpotent Rings; **Journal of Australian Mathematical Society**

Directed graphs and syntactic algebras of tree languages; **Journal of Automata, Languages and Combinatorics**

Early termination in sparse interpolation algorithms

Entropy and expected acceptance counts for finite automata

Equality algebras and varieties; **Fundamental Applications in Mathematics**

Error-correcting Codes as Ideals in Group Rings; **AGRAM 2000**

Error-correcting codes as ideals in ring constructions; **Workshop "Algebra and its applications" at Kaariku**

Error-correcting codes in group rings; **ACRAM 2000**

Factorizations in the monoid of languages

Factorizations of infinite sequences in semigroups; **Annali di Matematica Pura ed Applicata**

FBN Hopf module algebras; **Communications in Algebra**

Finite state automata (B. Steinberg)

Finiteness conditions and sums of rings; **Publicationes Mathematicae**

Finiteness conditions for rewiriting systems

Finiteness conditions for semigroup-graded modules; **Revue Roumaine Math matiques Pures et Appliqu es**

Generalised radical semigroup rings; **Southeast Asian Bulletin of Mathematics**

Generator polynomials of characteristic ideal of maximal periodic arrays over Galois rings

Generators and weights of polynomial codes; **Archiv der Mathematik**

Graph Algebras and Automata; **Marcel Dekker Inc**

Grobner bases over Galois rings with an application to decoding alternant codes (E. Byrne, P. Fitzpatrick)

Improvements for evaluation codes and new characterizations of Arf semi-groups

Information Rates and Weights of Codes in Structural Matrix Rings; **Applied Algebra, Algebraic Algorithms and Error Correcting Codes**

Interior algebras and varieties; **Journal of Algebra**

Invariant radicals; **Proceedings of the Royal Society of Edinburgh**

Inverse automata and monoids and the undecidability of the Cayley subgraph problem for groups: by A Oliveira and P Silva (Glasgow Math. J. (2000))

Labeled directed graphs and FSA as classifiers of strings; **Australasian Workshop on Combinatorial Algorithms**

Labelled Cayley graphs and minimal automata; **27th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing**

Labelled Cayley graphs and minimal automata; **Australasian Journal of Combinatorics**

Languages Recognised by a Class of Finite Automata; **Acta Cybernetica**

Languages recognized by two-sided automata of graphs; **Estonian Academy of Sciences. Proceedings. Physics. Mathematics**

Linear time universal coding and time reversal of tree sources via FSM closure

Mathematics of information and coding (T.S.Han, K.Kobayashi)

Maximising the Shannon capacity of constrained systems with two constraints

Minimum distances and information rates for matrix extensions of BCH codes; **Proceedings WITSP'04 The 3rd Workshop on the Internet, Telecommunications and Signal Processing**

Minimum Distances of Error-Correcting Codes in Incidence Rings; **International Journal of Mathematics and Mathematical Sciences**

MR2003a:68076, H.K. Hsiao, C.C. Huang, S.S. Yu, Word operation closure and primitivity of languages Advances and trends in automata and formal languages

MR2003a:68102, Symeon Bozapalidis, Transduction in polypodes

MR2003a:94005, V.N. Gridin, R.B. Mazepa, B.V. Roshchin, Majority multiplexing and coding of binary signals

MR2003a:94020, V.K. Leont'ev, Yu.G. Smetanin, Problems of information on the set of words

MR2003b:20061, M. Delgado, S. Margolis, B. Steinberg, Combinatorial group theory, inverse monoids, automata, and global semigroup theory

MR2003d:94053, P. Bradford, M.J. Golin, L.L. Larmore, W. Rytter, Optimal prefix-free codes for unequal letter costs: dynamic programming with the Monge property J

MR2003d:94114, G. Skersys, Computing permutation groups of error-correcting codes

MR2003d:94130 Michael E. O'Sullivan, The key equation for one-point codes and efficient error evaluation

MR2003e:68085, Ferenc Gecseg, On quasi-products of tree automata

MR2003h:68101, Symeon Bozapalidis, Olympia Louscou-Bozapalidou, Polytopic codes

MR2003h:68107, Julien Cassaigne, Juhani Karhumaki, Jan Manuch, On conugacy of languages

MR2003i:16065, Li, Huishi, Noncommutative Grobner bases and filtered-graded transfer

MR2003i:94001, Han, Te Sun, 'Information-spectrum methods in information theory

MR2003k:94013, R Togneri, C.J.S. de Silva, Fundamentals of Information Theory and Coding Design

MR2003k:94028, Hoffstein, Jeffrey: Silverman, Joseph H., Polynomial rings and efficient public key authentication

MR2003m:68092, Werner Kuich, Automata on power series and tree automata on tree series

MR2004c:05203, J. Korner, A Monti, Compact representations of the intersection structure of families of finite sets

MR2004c:68064, Decision procedures for inductive Boolean functions based on alternating automata

MR2004e:94040 Norton, G.H., Salagean, A., Strong Grobner bases and cyclic codes over a finite-chain ring

MR2004g:94108, Properties of codes with one check symbol from a quasigroup point of view

MR2004h:94064,VLSI architecture of modified Euclidean algorithm for Reed-Soloman code

MR2146569 (2006d:94047) Goubault-Larrecq, Jean; Roger, Muriel; Verma, Kumar Neeraj 'Abstraction and resolution modulo AC: how to verify Diffie-Hellman-like protocols automatically

MR2147510 (2006d:94052) Joux, Antoine ' Multicollisions in iterated hash functions. Application to cascaded constructions'

MR2153228 (2006b:11162) Hu, Lei 'Maximal periodic two-dimensional arrays over Galois rings'

MR2153691 (2006b:16074) Abramov, S A; Le, Kh K; Li, Z 'Ore polynomial rings in one variable in computer algebra'

MR2156522(2006d:94021) Golomb, Soloman W.; Gong, Guang 'Signal Design for Good Correlation. For Wireless Communication, Cryptography, and Radar', Cambridge Press, Cambridge, 2005

MR2167701 (20063:13038) Torstensson, Anna; Ufnarovski, Victor; Ofverbeck, Hans 'Using resultants for SAGBI basi verification in the univariate polynomial ring'

New results on combinatorial properties of sequences of semigroup elements.; **CANT'95**

Non-commutative Modal Rings and Internalized Equality; **Algebra Colloquium**

Omega rings, their flat and projective acts with some applications; by Olga Sokratova (Dissertationes Mathematicae Universitatis Tartuensis)

On a class of functions computable by index grammars

On a theorem of Cohen and Montgomery for graded rings; **Proceedings of the Royal Society of Edinburgh, Section A**

On Associative Superalgebras of Matrices; **Rocky Mountain Journal of Mathematics**

On Cayley Graphs of Inverse Semigroups; **Semigroup Forum**

On classical Krull dimension of group-graded rings; **Bulletin of the Australian Mathematical Society**

On complete and bipartite Cayley graphs; **Arbeitstagung Allgemeine Algebra 62**

On congruences of automata defined by directed graphs; **Theoretical Computer Science**

On Cyclic Codes in Incidence Rings; **Studia Scientiarum Mathematicarum Hungarica**

On Dehn functions of finitely presented bi-automatic monoids: by Friedrich Otto (J.Autom. Lang. Comb)

On error-correcting codes as ideals in group rings; **46th Annual Meeting of the Australian Mathematical Society**

On finite principal ideal rings; **Acta Mathematicae Universitatis Comenianae**

On fuzzy regular languages; **AISAT 2000**

On genetic algorithms minimizing a class of FSA with fuzzy automata; **AISAT 2004 The 2nd International Conference on Artificial Intelligence in Science and Technology**

On Graded Rings and Varieties; **Fundamental and Applied Mathematics**

On group automata over finite fields; **Finite Fields and their Applications**

On group graded rings satisfying polynomial identities; **Glasgow Mathematical Journal**

On groupoid graded rings; **Journal of Algebra**

On Incidence Rings of Group Automata; **Bulletin of the Australian Mathematical Society**

On information rates and weights of codes in structural matrix rings; **Applied Algebra, Algebraic Algorithms and Error Correcting Codes**

On left self distributive rings; **Acta Mathematicae Hungaricae**

On maximum length convolutional codes under a trellis complexity constraint

On rings with invariant radicals; **Bulletin of the Australian Mathematical Society**

On rings with inverse adjoint semigroup; **Southeast Asian Bulletin of Mathematics**

On some polynomial GCD algorithms: by Drago Pop (Stud. Univ. Babes-Bolyai Inform.)

On the computation of Hilbert series and Poincare series for algebras with Grobner bases: by Jonas Mansson (Comput. Sci. J. Moldovia)

On the description of radicals of semigroup rings of commutative semigroups; **Izvestiya Vysshikh Uchebnykh Zavedenii Matematika**

On the Jacobson radical of graded rings; **Communications in Algebra**

On the nilpotency of the Jacobson radical of semigroup rings; **Acta Mathematicae Universitatis Comenianae**

On the Structure of Incidence Rings of Group Automata; **International Journal of Algebra and Computation**

On the structure of the Jacobson radical of graded rings; **Quaestiones Mathematicae**

On transitive Cayley graphs of groups and semigroups; **European Journal of Combinatorics**

On undirected Cayley graphs; **Australasian Journal of Combinatorics**

One-sided noncommutative Grobner bases with applications to computing Green's relations (A.Heyworth)

Polynomial codes and principal ideal rings; **International Symposium on Information Theory**

Power graphs and semigroups of matrices; **Bulletin of the Australian Mathematical Society**

Radicals of algebras graded by cancellative linear semigroups; **Proceedings of the American Mathematical Society**

Radicals of contracted graded rings; **Journal of Algebra**

Recent results and open questions on semigroup-graded rings; **Fundamental and Applied Mathematics**

Recent results on Ring Constructions for Error-Correcting Codes; **Contemporary Mathematics**

Relative duality in MacWilliams identity

Rewriting as a special case of non-commutative Grobner basis theory: by Anne Heyworth (London Math. Soc. Lecture Note Ser. 275) Series

Ring Constructions and Applications; **World Scientific**

Rings Used in Modal Logic and Their Radicals; **Vietnam Journal of Mathematics**

Rings which are sums of finite fields; **Finite Fields and their Applications**

Semigroup gradings of full matrix rings; **Communications in Algebra**

Semigroup gradings of upper triangular matrix rings; **Revue Roumaine de Mathematiques Pures et Appliquees**

Semigroup rings in semisimple varieties; **Bulletin of Australian Mathematical Society**

Semigroup rings which are finite direct products of Galois rings; **Semigroup Forum**

Semigroup varieties and semigroup algebras; **Semigroup Forum**

Semigroups of matrices

Semisimple Artinian graded rings; **Communications in Algebra**

Semisimple ring graded by inverse semigroups; **Journal of Algebra**

Shortest paths and d-cycle problem; **AWOCA 99**

Slender matrix languages (R. Stiebe)

Soluble and linear repetitive groups; **Bulletin of the Australian Mathematical Society**

Solution of a system of polynomial equations over the Galois-Eisenstein ring using a canonical system of generators of a polynomial ideal

Some new results on primitive words and language classes (M. Kudlek)

Syntactic semigroups and graph algebras; **Bulletin of the Australian Mathematical Society**

The Jacobson Radical of Graded PI-Rings and Related Classes of Rings; **Journal of Algebra**

The minimum number of idempotent generators of an upper triangular matrix algebra; **Journal of Algebra**

The Theory of Information and Coding

Triangular matrix representations (G.F.Birkenmeier, H.E.Heatherly, J.Y.Kim, J.K.Park)

Two algorithms for languages recognized by graph algebras; **International Journal of Computer Mathematics**

Two generalizations of T-nilpotence; **Algebra Colloquium**

Two ring constructions and sums of fields; **New Zealand Journal of Mathematics**

Two versions of graded rings; **Publicationes Mathematicae - Debrecen**

Varieties and sums of rings; **Contributions to Algebra and Geometry**

## Research Projects

Algorithms for computing the radical of abelian group graded rings; **Australian Research Council (ARC)**

Applications of Inverse Semigroups to Error-correcting Codes; **Australian Research Council (ARC)**

Classification Rules and Algorithms for Analysis of DNA Sequences; **University of Tasmania (UTAS)**

Graded rings and applications to codes.; **Australian Research Council (ARC)**

Graph Algebras, Shortest Path Algorithms and Applications to Geographic Information Systems; **Australian Research Council (ARC)**

Matrix Ring Approach To Efficient Error-Correcting Codes; **University of Tasmania (UTAS)**

Nullstellensatz for graded PI-algebras; **University of Tasmania (UTAS)**

Ring Constructions and Algorithms for Enhancing Performance of BCH Codes; **Australian Research Council (ARC)**

## Research Candidate Supervision

An investigation of the Jacobson radical of epigroup graded rings

Artinian rings, finite principal ideal rings and algebraic error-correcting codes

Directed graphs and combinatorial properties of groups and semigroups

In Silico Detection and Characterisation of Biological Regulatory Elements

Structural and Combinatorial Aspects of Graded Rings with Applications