I am a Russian mathematician in the Finnish service.
I have been working
at the Department of Mathematics
of the University of Turku,
first as a research fellow of the Academy of Finland (2006–2011),
and then as a researcher of the Turku Collegium of Science and Medicine (since 2012).
My research interests belong to the area
of formal language and automata theory,
and my main subjects are
formal grammars and their parsing algorithms,
language equations in connection with computability,
and descriptional complexity of finite automata.
I received my education
at Moscow State University, Russia (1996–2001),
and at Queen's University, Canada (2001–2004),
and got a habilitation from the University of Turku (2009).
- My curriculum vitae:
(21 May 2013)
- Current status of my refereeing queue:
4 papers under review.
- My office is Kasarmi 10, 101.
The front door of the building is locked;
visitors are requested to knock at my window
(the northernmost window to the east side)
- In the current semester (January-May 2013),
my main occupation is teaching a course on formal grammars
and preparing lecture notes.
- Current status of the Formal Grammars draft:
167 pages, 19 figures.
- My personal page, in Russian.
Research on formal grammars
My research on grammars
began with understanding context-free grammars
as a logic for representing syntax,
which prompted me to investigate
the power of Boolean connectives in this logic.
This outlook led me
to conjunctive grammars,
which allow a conjunction operation in their rules,
and to Boolean grammars,
which further allow the negation.
My subsequent research has shown
that the main practically relevant properties of context-free grammars,
including most of the parsing algorithms,
equally hold for Boolean grammars.
These developments significantly change
the perspective on formal grammars in general,
and now my mission is to work out
an up-to-date theory of formal grammars.
Research on language equations
Equations with formal languages as unknowns
naturally arise when reasoning about sets of strings,
and they have been used in many applied areas of computer science.
These applications would benefit
from a general theory of language equations.
I have been working towards such a theory,
exploring the relations between language equations and computation,
and tracing the border between their decidability and undecidability.
The latest findings are that, in short,
almost all language equations are computationally complete,
including those over a one-letter alphabet
and with concatenation as the only operation.
Research on descriptional complexity of automata
It is well-known that
converting a nondeterministic finite automaton (NFA)
to an equivalent deterministic one (DFA)
requires exponentially many states;
representing a Kleene star of a DFA
also leads to an exponential blowup
in the size of the description.
For ordinary DFAs and NFAs,
all problems of this kind have long been solved.
I am occasionally investigating similar problems
for a few related models, such as
unambiguous finite automata (UFA),
two-way finite automata (2DFA, 2NFA)
and input-driven pushdown automata (IDPDA).
- Formal grammars, University of Turku, Spring 2013.
(daily updates in January-April A.D. 2013)
Students, current and former
- Dr. Artur Jeż
(Ph. D. student at the University of Wrocław, Poland;
supervised jointly with Krzysztof Loryś),
defended on 14 September 2010, with distinction;
Polish Prime Minister's Award for an Outstanding Ph. D. thesis (2011).
- Tommi Lehtinen
(Ph. D. student at the University of Turku since 2007),
thesis "Numbers and languages"
defended on 15 March 2013,
awaiting confirmation of the degree.
- Mikhail Barash
(Ph. D. student at the University of Turku since 2011;
supervised jointly with Tero Harju).
- Whale Calf, a parser generator for conjunctive grammars.
- dfalib, a C++ class library for basic operations on finite automata.
(Announced in July 2012)
- Photographs from conferences:
- From CIAA 2004 conference, Kingston, Ontario, Canada, July 22–24, 2004.
- From AFL 2005 conference, Dobogoko, Hungary, May 17–20, 2005.
- From DCFS 2005 workshop, Como, Italy, June 30–July 2, 2005.
- From DLT 2005
(second part) conference, Palermo, Italy, July 4–8, 2005.
- From Workshop on Fibonacci Words, Turku, Finland, September 27–30, 2006.
- From DLT 2007 conference, Turku, Finland, June 3–6, 2007.
- From UC 2011 conference, Turku, Finland, June 6–10, 2011.
- From RuFiDiM 2012 conference, Turku, Finland, September 25–28, 2012.
- Selected photographs:
Good Friday procession (Tarragona, Spain, April 14, 2006),
- Places visited (in kml format),
view in Google Maps.
Last updated: April A.D. 2013.