TY - JOUR
T1 - Sequence binary decision diagram
T2 - Minimization, relationship to acyclic automata, and complexities of Boolean set operations
AU - Denzumi, Shuhei
AU - Yoshinaka, Ryo
AU - Arimura, Hiroki
AU - Minato, Shin ichi
N1 - Funding Information:
The authors are grateful to anonymous reviewers of this paper and anonymous referees of PSC’11 of the earlier version of this paper for many useful comments and suggestions, which have improved the quality of this paper. They would like to thank Takashi Horiyama, Takeru Inoue, Jun Kawahara, Takuya Kida, Toshiki Saitoh, Yasuyuki Shirai, Kana Shimizu, Yasuo Tabei, Koji Tsuda, Takeaki Uno, and Thomas Zeugmann for their discussions and valuable comments. This research was partly supported by MEXT Grant-in-Aid for Scientific Research (A), 20240014 , FY2008–2011, MEXT / JSPS Global COE Program, FY2007–2011, and ERATO MINATO Discrete Structure Manipulation System Project, JST .
Publisher Copyright:
© 2014 Elsevier B.V.
PY - 2016/10/30
Y1 - 2016/10/30
N2 - 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.
AB - 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.
KW - Boolean set operation
KW - Deterministic finite automaton
KW - Minimization
KW - Persistent data structure
KW - Sequence binary decision diagram
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U2 - 10.1016/j.dam.2014.11.022
DO - 10.1016/j.dam.2014.11.022
M3 - Article
AN - SCOPUS:84919346253
SN - 0166-218X
VL - 212
SP - 61
EP - 80
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -