Abstract
In this paper, we propose a new data structure sequence sentential decision diagram (SSDD) that represents sets of strings. SSDD is a generalized data structure of Sequence Binary Decision Diagram (SeqBDD), that is a similar data structure to a deterministic finite automaton, but the size can be exponentially smaller than the SeqBDD for the same string set. We also provide algorithms to manipulate sets of strings on SSDD. These algorithms allow operations such as intersection, union, and concatenation to be executed on SSDDs under their compressed representations without expanding. We analyzed the size complexity of SSDD and the time complexity of proposed algorithms.
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References
Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Boston (1974)
Crochemore, M., Hancart, C., Lecroq, T.: Algorithms on Strings. Cambridge University Press, Cambridge (2007)
Daciuk, J., Mihov, S., Watson, B.W., Watson, R.: Incremental construction of minimal acyclic finite state automata. Comput. Linguist. 26(1), 3–16 (2000)
Darwiche, A.: SDD: a new canonical representation of propositional knowledge bases. In: Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI 2011, vol. 22, pp. 819–826. AAAI Press (2011)
Denzumi, S., Yoshinaka, R., Arimura, H., Minato, S.-I.: Sequence binary decision diagram: minimization, relationship to acyclic automata, and complexities of boolean set operations. Discret. Appl. Math. 212, 61–80 (2016)
Gusfield, D.: Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press, Cambridge (1997)
Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, 3rd edn. Addison-Wesley, Boston (2006)
Loekito, E., Bailey, J., Pei, J.: A binary decision diagram based approach for mining frequent subsequences. Knowl. Inf. Syst. 24(2), 235–268 (2010)
Minato, S.-I.: Zero-suppressed BDDs for set manipulation in combinatorial problems. In: Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, pp. 1058–1066 (2016)
Minato, S.-I., Ishiura, N., Yajima, S.: Shared binary decision diagram with attributed edges for efficient Boolean function manipulation. In: Proceedings of the 27th ACM/IEEE Design Automation Conference, pp. 52–57 (1990)
Nishino, M., Yasuda, N., Minato, S.-I., Nagata, M.: Zero-suppressed sentential decision diagrams. In: Proceedings of the 30th ACM/IEEE Design Automation Conference, pp. 272–277 (2016)
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Denzumi, S. (2018). Sequence Sentential Decision Diagrams. In: Kim, D., Uma, R., Zelikovsky, A. (eds) Combinatorial Optimization and Applications. COCOA 2018. Lecture Notes in Computer Science(), vol 11346. Springer, Cham. https://doi.org/10.1007/978-3-030-04651-4_40
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DOI: https://doi.org/10.1007/978-3-030-04651-4_40
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