Juris Viksna - Research interests

Currently the main area of my research. The topics in which I am particularly interested/involved include:

Computational Learning
This is the subject I have started my research carrier with (I have been fortunate to work on my Dr.sc. thesis as one of the students of Rusins Freivalds) and the one in which I still feel interested. My research is mainly focussed on probabilistic aspects of inductive inference - on realations between classes of functions identifiable with different probabilities according to some criterion of identification. The focus of interest in computational learning has somewhat changed since the time I have been very active in the field, however probabilistic identification of limiting functions and identification up to small (according to measure) sets probably still might be of some interest.

Automated verification of formal systems
I have never been an expert in this field in general, however I have enjoyed working on several problems related to reachability of particular states in some kind of formal systems. In joint work with K.Cerans we genaralized a famous result by O.Maler and A.Pnueli for multi-polynomial systems.
Another subfield of this area in which I have been involved is the use of Higman lemma to prove that reachability problem in particular systems is decidable (this research was originated by A.Parosh, B.Jonsson and K.Cerans). Unfortunately, the attempts to generalize Higmans result to other practically interesting cases so far have led only to negative results.
Somewhat unexpectedly state reachability problems become an important topic also in recent work also in recent work in bioinformatics in applying Finite State Linear Models for modelling the behaviour of gene regulatory networks.

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