Giuseppina Rindone

REVERSE ENGINEERING PREFIX TABLES

The Prefix table of a string reports for each position the maximal length of its prefixes starting here. The Prefix table and its dual Suffix table are basic tools used in the design of the most efficient string-matching and pattern extraction algorithms. These tables can be computed in linear time independently of the alphabet size. We give an algorithmic characterisation of a Prefix table (it can be adapted to a Suffix table). Namely, the algorithm tests if an integer table of size

Acyclic, connected and tree sets

n

Maximal bifix decoding

is the Prefix table of some word and, if successful, it constructs the lexicographically smallest string having it as a Prefix table. We show that the alphabet of the string can be bounded to

Recent results on syntactic groups of prefix codes

\log_2 n

Return words of linear involutions and fundamental groups

letters. The overall algorithm runs in

Bifix codes and Sturmian words

O(n)

Bifix codes and interval exchanges

time.

The finite index basis property

Given a set

On the groups of codes with empty kernel

S