How expressions can code for automata

Issue		RAIRO-Theor. Inf. Appl. Volume 39, Number 1, January-March 2005 Imre Simon, the tropical computer scientist


Page(s)		217 - 237
DOI		10.1051/ita:2005013

Theoret. Informatics Appl. 39, 217-237 (2005)
DOI: 10.1051/ita:2005013

Sylvain Lombardy¹ and Jacques Sakarovitch²

¹ LIAFA (UMR 7089), Université Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France; lombardy@liafa.jussieu.fr
² LTCI (UMR 5141), CNRS/ENST, 46 rue Barrault, 75634 Paris Cedex 13, France; sakarovitch@enst.fr

Abstract
In this paper we investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton. The notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem. The second important ingredient is the co-minimization of an automaton, a dual and generalized Moore algorithm on non-deterministic automata.

We show here that if an automaton is then sufficiently "decorated", the combination of these two algorithms gives the desired result. Reducing the amount of "decoration" is still the object of ongoing investigation.

Mathematics Subject Classification. 68Q45, 68Q70

Key words: Finite automata -- regular expression -- derivation of expressions -- quotient of automata.

© EDP Sciences 2005

What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.

If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.