Alexander Okhotin

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: PostScript, PDF, HTML. (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. (September 2012)

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.

State-of-the-art survey: “Conjunctive and Boolean grammars: the true general case of the context-free grammars” (submitted). (April 2012)
Nine open problems for conjunctive and Boolean grammars (#2 solved in 2007, #3 solved in 2009).
Recent new manuscripts: “Unambiguous conjunctive grammars over a one-letter alphabet” (with Artur Jeż, DLT 2013), “Grammars with two-sided contexts” (with Mikhail Barash, manuscript), “Improved normal form for grammars with one-sided contexts” (DCFS 2013), “Linear grammars with one-sided contexts and their automaton representation” (with Mikhail Barash, submitted). (April 2013)
Recent full versions: “An extension of context-free grammars with one-sided context specifications” (with Mikhail Barash, presented at LATA 2012), “Parsing by matrix multiplication generalized to Boolean grammars” (presented at DLT 2010). (October 2012)

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.

Handbook chapter “Language equations” by Michal Kunc and myself. (Final version, July 2012)
Selected papers on language equations and computability: “Decision problems for language equations” (ICALP 2003; final version in JCSS), “On the computational completeness of equations over sets of natural numbers” (with Artur Jeż; ICALP 2008, full version submitted), “Equations over sets of natural numbers with addition only” (with Artur Jeż; STACS 2009, full version submitted), “On language equations XXK=XXL and XM=N over a unary alphabet” (with Tommi Lehtinen; DLT 2010, full version in progress).
“Language equations: a story of computational completeness” (slides from a Dagstuhl seminar, 2010).

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).

Recent new papers: “Making graph-walking automata reversible” (with M. Kunc, technical report; slides of a seminar talk in Russian), (September 2012)
Recently published papers: “State complexity of operations on two-way deterministic finite automata over a unary alphabet” (with M. Kunc, published in TCS), “Unambiguous finite automata over a unary alphabet” (published in I&C).

Current teaching

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).

Other duties

Current conference programme committees: CSR 2012, CIAA 2012, CIAA 2013, CAI 2013, SOFSEM 2014; see also earlier PC membership.

Programming

Whale Calf, a parser generator for conjunctive grammars. (March 2010)
dfalib, a C++ class library for basic operations on finite automata. (Announced in July 2012)

Various

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: animals, churches, Good Friday procession (Tarragona, Spain, April 14, 2006), other subjects.
Places visited (in kml format), view in Google Maps.

E-mail:

Last updated: April A.D. 2013.