Efficient algorithm to decide the periodicity of b-recognisable sets using MSDF convention

Victor Marsault
University of Liège
Friday, 24 February, 2017 - 16:00
Salle Solvay (NO, 5th floor)
Given an integer base b>1, a set of integers is represented in base b by a
language over {0,1,...,b-1}.  The set is said b-recognisable if its
representation is a regular language.  It is known that eventually periodic sets
are b-recognisable in every base b, and Cobham theorem imply the converse:
no other set is b-recognisable in every base b.

We are interested here in deciding whether a b-recognisable set of integers
(given as a finite automaton) is eventually periodic.  Honkala first showed this
problem decidable in 1986 and recent developments give efficient decision
algorithms.  However, they only work when the integers are written with the
least significant digit first.

On the contrary, we consider here the natural order of digits (Most Significant
Digit First) and give a quasi-linear algorithm to solve the problem in this
case.