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 Löding. 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
http://www.liafa.jussieu.fr/

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).
The decision will be notified by the 7th of September.


Contact: Thomas Colcombet
Email: thomas.colcombet@liafa.jussieu.fr
URL: http://www.liafa.jussieu.fr/colcombe

Important Dates:
Applications must be sent, by email, before 30/09/2011.
The answer will be given the 07/10/11.