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 Systems1; 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