Subsequence versus substring constraints in sequence pattern languages
Tóm tắt
A family of logics for expressing patterns in sequences is investigated. The logics are all fragments of first-order logic, but they are variable-free. Instead, they can use substring and subsequence constraints as basic propositions. Propositions expressing constraints on the beginning or the end of the sequence are also available. Also wildcards can be used, which is important when the alphabet is not fixed, as is typical in database applications. The maximal logic with all four features of substring, subsequence, begin–end constraints, and wildcards, turns out to be equivalent to the family of star-free regular languages of dot-depth at most one. We investigate the lattice formed by taking all possible combinations of the above four features, and show it to be strict. For instance, we formally confirm what might intuitively be expected, namely, that boolean combinations of substring constraints are not sufficient to express subsequence constraints, and vice versa. We show an expressiveness hierarchy results from allowing multiple wildcards. We also investigate what happens with regular expressions when concatenation is replaced by subsequencing. Finally, we study the expressiveness of our logic relative to first-order logic.
Tài liệu tham khảo
Büchi, J.R.: Weak second-order arithmetic and finite automata. Zeitschrift für Mathematische Logic und Grundlagen der Mathematik 6, 66–92 (1960)
Brzozowski, J.A., Knast, R.: The dot-depth hierarchy of star-free languages is infinite. J. Comput. Syst. Sci. 16, 37–55 (1978)
Baeza-Yates, R., Ribeiro-Neto, B.: Modern Information Retrieval. Addison-Wesley, Boston (1999)
Cohen, R.S., Brzozowski, J.A.: Dot-depth of star-free events. J. Comput. Syst. Sci. 5(1), 1–16 (1971)
Dong, G., Pei, J.: Sequence Data Mining. Springer, Berlin (2007)
Faloutsos, Ch., Ranganathan, M., Manolopoulos, Y.: Fast subsequence matching in time-series databases. In: Proceedings ACM SIGMOD International Conference on Management of Data, pp. 419–429 (1994)
Genkin, D., Kaminski, M., Peterfreund, L.: Closure Under Reversal of Languages over Infinite Alphabets. In: Fomin, E., Podolskii, V. (eds.),Computer Science Symposium in Russia, Proceedings (CSR), volume 10846 of Lecture Notes in Computer Science, Springer, pp. 145–156 (2018)
Jagadish, H.V., et al.: Making database systems usable. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 13–24 (2007)
Kaminski, M., Tan, T.: Regular expressions for languages over infinite alphabets. Fundam. Inf. 69, 301–318 (2006)
Loeffen, A.: Text databases: a survey of text models and systems. SIGMOD Record 23(1), 97–106 (1994)
McNaughton, R., Papert, S.: Counter-Free Automata. MIT Press, Cambridge (1971)
Neven, F., Schwentick, T., Vianu, V.: Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Logic 5(3), 403–435 (2004)
Patel, J.M.: Special issue on querying biological sequences. IEEE Data Eng. Bull. 27(3), (2004)
Peterfreund, L.: Closure under reversal of languages over infinite alphabets: a case study. Master thesis, Department of Computer Science, Technion—Israel Institute of Technology (2015)
Pin, J.E.: Syntactic semigroups. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, chapter 10. Springer (1997)
Pin, J.E.: The dot-depth hierarchy, 45 years later. The role of theory in computer science, pp. 177–202 (2017)
Place, T., van Rooijen, L., Zeitoun, M.: Separating regular languages by locally testable and locally threshold testable languages. Logical Methods Comput. Sci. 10(3) (2014)
Segoufin, L.: Automata and logics for words and trees over an infinite alphabet. In: Ésik, Z. (ed.) Computer Science Logic, Proceedings (CSL), volume 4207 of Lecture Notes in Computer Science, Springer, pp. 41–57 (2006)
Simon, I.: Piecewise testable events. In: Barkhage, H. (ed.) Automata Theory and Formal Languages, Proceedings, volume 33 of Lecture Notes in Computer Science, Springer, pp. 214–222 (1975)
Tan, T.: On pebble automata for data languages with decidable emptiness problem. J. Comput. Syst. Sci. 76(8), 778–791 (2010)
Tan, T.: Graph reachability and pebble automata over infinite alphabets. ACM Trans. Comput. Logic 14(3), 19 (2013)
Thomas, W.: A concatenation game and the dot-depth hierarchy. In: Computation Theory and Logic, volume 270 of Lecture Notes in Computer Science, Springer-Verlag, pp. 415–426 (1987)
Thomas, W.: Languages, automata, and logic. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, chapter 7. Springer (1997)
Wang, J.T.L., Shapiro, B.A., Shasha, D. (eds.): Pattern Discovery in Biomolecular Data. Oxford University Press, Oxford (1999)