Publications

Manuscripts

• Dmitry Berdinsky, Prohrak Kruengthomya, "Finite Automata Encoding Functions: A Representation Using B–splines" // [arXiv]

Accepted

• Prohrak Kruengthomya, Dmitry Berdinsky, "Extending the Synchronous Fellow Traveler Property", to appear in Asian-European Journal of Mathematics // [publisher] [arXiv]

Published

• Prohrak Kruengthomya, Dmitry Berdinsky, "Cayley Linear–Time Computable Groups", journal of Groups, Complexity, Cryptology, V. 15, Issue 2 (2024), pp. 1–22 // [publisher] [arXiv] 

• Berdinsky D., Jain S., Khoussainov B., Stephan F., "String Compression in FA–Presentable Structures", Theoretical Computer Science, 947 (2023) 113705, pp. 1-10 //  [publisher] [arXiv] 

• Berdinsky D., Elder M., Kruengthomya P., "Cayley Polynomial-Time Computable Groups", Information and Computation, 288 (2022) 104768, pp. 1-15 // [publisher] [arXiv]

• Berdinsky D., Elder M., Taback J., "On the geometry of Cayley automatic groups", International Journal of Algebra and Computation, 32, No. 03, pp. 383-409 (2022) // [publisher] [arXiv]  

• Berdinsky D., Elder M., Taback J., "Being Cayley automatic is closed under taking wreath product with virtually cyclic groups", Bulletin of the Australian Mathematical Society, 104, pp. 464–474 (2021) // [publisher] [arXiv]  

• Berdinsky D., Kruengthomya P., "Nonstandard Cayley Automatic Representations for Fundamental Groups of Torus Bundles over the Circle", Lecture Notes in Computer Science, Springer, Cham, V. 12038, pp. 115-127 (2020) // [publisher] [arXiv]

• Berdinsky D., Trakuldit P., "Towards quantitative classification of Cayley automatic groups", East-West Journal of Mathematics, V. 20, N 2, pp. 107-124 (2018) // [publisher] [arXiv]

• Berdinsky D., Trakuldit P., "Measuring Closeness Between Cayley Automatic Groups and Automatic Groups" In: Klein S., Martín-Vide C., Shapira D. (Eds.): Language and Automata Theory and Applications 2018. Lecture Notes in Computer Science, Springer, Cham, V. 10792, pp. 245-257 (2018) // [publisher] [arXiv]

• Berdinsky D., Vyatkin Y., "Willmore-like functionals for surfaces in 3-dimensional Thurston geometries", Osaka Journal of Mathematics 2017, V. 54, N 1, pp. 75-83 // [publisher] [arXiv]

• Berdinsky D., "Cayley automatic groups and numerical characteristics of Turing transducers", S. Brlek and C. Reutenauer (Eds.): Developments in Language Theory 2016, Lecture Notes in Computer Science, V. 9840, pp. 26-37 (2016) // [publisher] [arXiv] 

• Berdinsky D., Khoussainov B., "Cayley automatic representations of wreath products", International Journal of Foundations of Computer Science, V. 27, N 2, pp. 147-159 (2016) // [publisher] [arXiv]  

• Berdinsky D., Kim T., Cho D., Bracco C., Kiatpanichgij S., "Bases of T-meshes and the refinement of hierarchical B-splines", Computer Methods in Applied Mechanics and Engineering 2015, V. 283, pp. 841-855 // [publisher] [arXiv] 

• Berdinsky D., Khoussainov B., "On automatic transitive graphs", A.M. Shur and M.V. Volkov (Eds.): Developments in Language Theory 2014, Lecture Notes in Computer Science, V. 8633, pp. 1-12 (2014) // [publisher] [HAL] 

• Bracco C., Berdinsky D., Cho D., Oh M., Kim T., "Trigonometric Generalized T-splines", Computer Methods in Applied Mechanics and Engineering 2014, V. 268, pp. 540–556 // [publisher] 

• Berdinsky D., Kim T., Bracco C., Cho D., Mourrain B., Oh M., Kiatpanichgij S., "Dimensions and bases of hierarchical tensor-product splines", Journal of Computational and Applied Mathematics 2014, V. 257, pp. 86–104 // [publisher] [HAL] 

• Berdinsky D., Kim T., Bracco C., Cho D., Oh. M, Seo Y., Kiatpanichgij S., "Iterative refinement of hierarchical T-meshes for bases of spline spaces with highest order smoothness", Computer-Aided Design 2014, V. 47, pp. 96-107 // [publisher] [HAL] 

• Berdinsky D., Oh M., Kim T., Mourrain B., "On the problem of instability in the dimension of a spline space over a T-mesh", Computers & Graphics 2012, V. 36, N 5, pp. 507–513 // [publisher] [HAL] 

• Berdinsky D., "On constant mean curvature surfaces in the Heisenberg group", Siberian Advances in Mathematics 2012, V. 22, N 2, pp. 75-79 // [publisher] [pdf] 

• Berdinsky D., "On minimal surfaces in the Heisenberg group", A collection of papers of the International Conference "Geometry and Analysis", Kemerovo, Russia, 2011, Bulletin of Kemerovo State University 2011, V. 3/1 (47), pp. 34–38 // (in Russian) [publisher] (English translation [to be updated]) [pdf] 

• Berdinsky D., Rybnikov I., "On orthogonal curvilinear coordinate systems in constant curvature spaces", Siberian Math. Journal 2011, V. 52, pp. 394-401 // [publisher] [pdf]

• Berdinsky D., "On some generalization of the Willmore functional for surfaces in SL2", Siberian Electronic Mathematical Reports 2010, V. 7, pp. 140-149 // (in Russian) [publisher] (English translation [to be updated]) [pdf] 

• Berdinsky D., Taimanov I., "Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional", Siberian Math. Journal 2007, V. 48, N 3, pp. 395-407 // [publisher] [pdf]

• Berdinsky D., Taimanov I., "Surfaces in three-dimensional Lie groups", Siberian Math. Journal 2005, V. 46, N 6, pp. 1005-1019 // [publisher] [pdf]

Reports

• Berdinsky D. and Taimanov I., Oberwolfach reports. 2007, V. 4, N 2, pp. 1353–1358 // [publisher]

Theses

• Berdinsky D., "Representations of transitive graphs by automata", PhD Thesis (Computer Science), The University of Auckland 2017 // [archive] [pdf] 

• Berdinsky D., "The Weierstrass representation of surfaces in three-dimensional Lie groups and its applications", PhD Thesis (Mathematics), Sobolev Institute of Mathematics 2009 // [synopsis] [pdf]