Rūsiņš Freivalds#

Short laudatio by Jozef Gruska#

Rūsiņš Freivalds main contributions have been in reserach, education of scientists and in teaching. In all three areas he had very significant achievements.

Rūsiņš Freivalds started his scientific carrier in the area of inductive inference, especially of Boolean and recursive functions, in learning theory and in recursive functions. His main outcomes has been a theory of inductive inference; qualitative theory of inductive inference and introduction of deep mathematics and especially probabilistic methods into the heory of inductive inference. In general his main contribution was to use deep mathematical methods in this area. For example, he used constructive ordinals to measure the complexity of inductive inference and group theory to solve problems of inductive inference.

Second main area of research and of significant contributions of Rusins Freivalds have been probabilistic algorithms and automata. He proved the very first theorem concerning the advantages of randomized algorithms over deterministic ones. Namely, he has proven that randomized Turing machines can use less running time than deterministic ones for computation of certain functions. Very influential have been his randomized algorithms for testing matrix and polynomial operations and various very deep results concerning power of various types of probabilistic automata. Very important is also his powerful method to prove lower bounds for time and space complexity of randomized algorithms. In general, in this area he has produced a variety of deep results and powerful methods.

Using the experience from the area of probabilistic automata, Rūsiņš Freivalds, in cooperation with his student Andris Ambainis, and later with many of other students, he has produced various very basic results concerning quantum automata and their properties, power as well as fundamental results concerning their succinctness comparing with classical models.

Advising PhD students has been another very successful area of sctivities of Rūsiņš Freivalds. As documented in his CV the number of awards of his PhD and Master students is admirable. His former PhD student andris Ambainis is one of the leaders in the area of quantum information processing

Rūsiņš Freivalds has been also an excellent teacher who has always concentrated on deep issues as well as on very modern issues of theoretical, in a broad sense, informatics.

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