Post-doctoral position: ERC grant GALE (Games, Automata and Logic's Extensions)

Subject: Verification of regular cost functions.

Regular cost functions extend the notion of regular languages with counting capabilities, while retaining many important decibility properties [C09a,b,CL10]. It prolongates the theory of distance automata [H82,L87] and extensions [K05].

A cost function is a function from words (or infinite words, trees, or infinite trees) to non-negative integers or infinitity, which is considered modulo an equivalence relation which does not preserve exact values, but preserves the existence of a bound on each subset of the domain. This abstraction allows to recover all the effective equivalences and decidability results which are usually lost when moving to a quantitative setting. In particular the effective equivalence between automata, monoids and monadic logic are preserved in this setting, and the corresponding decision procedures still exist (extending the classical one).

The theory of regular cost functions is now better understood. The subject of this post-doctoral position is to study the applications of this theory in the context of verification.

[CL10] T.Colcombet and Christof Loeding. Regular cost functions over finite trees. In LICS, pages 70-79, 2010.

[C09a] T.Colcombet. The Theory of Stabilisation Monoids and Regular Cost Functions. In 36th ICALP, number 5556 of LNCS, pages 139-150, 2009. Springer.

[C09b] T.Colcombet. Regular cost functions, Part I: logic and algebra over words. Note: Submitted, 2009.

[K05] Daniel Kirsten. Distance desert automata and the star height problem. RAIRO, 3(39):455-509, 2005.

[L87] Hing Leung. An Algebraic Method for Solving Decision Problems in Finite Automata Theory. PhD thesis, 1987.

[H82] K.Hashiguchi. Limitedness theorem on finite automata with distance functions. J. Comput. Syst. Sci., 24(2):233-244, 1982.

Background

The candidate should have a strong background in theoretical computer science. In particular he/she should have a knowledge in one or more subjects among

• formal language theory,
• algebra,
• logic,
• verification.

Founding

The post-doctoral position will be paid around 2000 euros, free of charges, per month.

Location

Liafa, Paris.

Dates of the position

The start of the position is to be decided with the applicant, and the duration is a priori of one year, also subject to discussion.

Application procedure

The applicants should send in electronic form:

1. a Curriculum Vitae
2. title and summary of the PHD
3. list of publications
4. official reports on PHD (preferably in French or English or German),
5. recommandation letters are welcome.

Any particular situation (PHD not yet defended, starting date too early , etc ...) should be clearly explained by a joint letter. The applications should be sent, by email, to T.Colcombet (thomas.colcombet@liafa.jussieu.fr).

• Submission before the 30th of September 2011.
• Decision before the 7th of October 2011.