Factor automata of automata and applications

Mehryar Mohri, Pedro Moreno, Eugene Weinstein

Research output: Chapter in Book/Report/Conference proceedingConference contribution


An efficient data structure for representing the full index of a set of strings is the factor automaton, the minimal deterministic automaton representing the set of all factors or substrings of these strings. This paper presents a novel analysis of the size of the factor automaton of an automaton, that is the minimal deterministic automaton accepting the set of factors of a finite set of strings, itself represented by a finite automaton. It shows that the factor automaton of a set of strings U has at most 2|Q| - 2 states, where Q is the number of nodes of a prefix-tree representing the strings in U, a bound that significantly improves over 2||U|| - 1, the bound given by Blumer et al. (1987), where ||U|| is the sum of the lengths of all strings in U. It also gives novel and general bounds for the size of the factor automaton of an automaton as a function of the size of the original automaton and the maximal length of a suffix shared by the strings it accepts. Our analysis suggests that the use of factor automata of automata can be practical for large-scale applications, a fact that is further supported by the results of our experiments applying factor automata to a music identification task with more than 15,000 songs.

Original languageEnglish (US)
Title of host publicationImplementation and Application of Automata - 12th International Conference, CIAA 2007, Revised Selected Papers
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783540763352
StatePublished - 2007
Event12th International Conference on Implementation and Application of Automata, CIAA 2007 - Prague, Switzerland
Duration: Jul 16 2007Jul 18 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4783 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other12th International Conference on Implementation and Application of Automata, CIAA 2007


  • Factor automata
  • Finite automata
  • Information retrieval
  • Inverted files
  • Music identification
  • Suffix automata
  • Suffix trees
  • Text indexing

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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