Sequence binary decision diagram: Minimization, relationship to acyclic automata, and complexities of Boolean set operations

Shuhei Denzumi, Ryo Yoshinaka, Hiroki Arimura, Shin ichi Minato

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

The manipulation of large sequence data is one of the most important problems in string processing. In this paper, we discuss a new data structure for storing and manipulating sets of strings, called Sequence Binary Decision Diagrams (sequence BDDs), which has recently been introduced by Loekito et al. (2010) as a descendant of both acyclic DFAs (ADFAs) and binary decision diagrams (BDDs). Sequence BDDs can compactly represent sets of sequences similarly to minimal ADFAs, and allow efficient set operations inherited from BDDs. We study fundamental properties of sequence BDDs, such as the characterization of minimal sequence BDDs by reduced sequence BDDs, non-trivial relationships between sizes of minimal sequence BDDs and minimal ADFAs, the complexities of minimization, Boolean set operations, and sequence BDD construction. We also show experimental results for real and artificial data sets.

Original languageEnglish
Pages (from-to)61-80
Number of pages20
JournalDiscrete Applied Mathematics
Volume212
DOIs
Publication statusPublished - 2016 Oct 30
Externally publishedYes

Keywords

  • Boolean set operation
  • Deterministic finite automaton
  • Minimization
  • Persistent data structure
  • Sequence binary decision diagram

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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