Abstract
We study the state complexity of the set of subwords and superwords of regular languages, and provide new lower bounds in the case of languages over a two-letter alphabet. We also consider the dual interior sets, for which the nondeterministic state complexity has a doubly-exponential upper bound. We prove a matching doubly-exponential lower bound for downward interiors in the case of an unbounded alphabet.
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References
Sheng, Y.: State complexity: Recent results and open problems. Fundamenta Informaticae 64(1-4), 471–480 (2005)
Abdulla, P.A., Collomb-Annichini, A., Bouajjani, A., Jonsson, B.: Using forward reachability analysis for verification of lossy channel systems. Formal Methods in System Design 25(1), 39–65 (2004)
Haase, Ch., Schmitz, S., Schnoebelen, Ph.: The power of priority channel systems. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013. LNCS, vol. 8052, pp. 319–333. Springer, Heidelberg (2013)
Baeza-Yates, R.A.: Searching subsequences. Theoretical Computer Science 78(2), 363–376 (1991)
Haines, L.H.: On free monoids partially ordered by embedding. Journal of Combinatorial Theory 6(1), 94–98 (1969)
Gruber, H., Holzer, M., Kutrib, M.: More on the size of Higman-Haines sets: Effective constructions. Fundamenta Informaticae 91(1), 105–121 (2009)
Birget, J.-C.: Partial orders on words, minimal elements of regular languages and state complexity. Theoretical Computer Science 119(2), 267–291 (1993)
Okhotin, A.: On the state complexity of scattered substrings and superstrings. Fundamenta Informaticae 99(3), 325–338 (2010)
Brzozowski, J.A., Jirásková, G., Li, B.: Quotient complexity of ideal languages. Theoretical Computer Science 470, 36–52 (2013)
Héam, P.-C.: On shuffle ideals. RAIRO Theoretical Informatics and Applications 36(4), 359–384 (2002)
Bertrand, N., Schnoebelen, Ph.: Computable fixpoints in well-structured symbolic model checking. Formal Methods in System Design 43(2), 233–267 (2013)
Pin, J.-É., Weil, P.: Polynomial closure and unambiguous product. Theory of Computing Systems 30(4), 383–422 (1997)
van Leeuwen, J.: Effective constructions in well-partially-ordered free monoids. Discrete Mathematics 21(3), 237–252 (1978)
Courcelle, B.: On constructing obstruction sets of words. EATCS Bulletin 44, 178–185 (1991)
Gruber, H., Holzer, M.: Finding lower bounds for nondeterministic state complexity is hard. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 363–374. Springer, Heidelberg (2006)
Arfi, M.: Polynomial operations on rational languages. In: Brandenburg, F.J., Wirsing, M., Vidal-Naquet, G. (eds.) STACS 1987. LNCS, vol. 247, pp. 198–206. Springer, Heidelberg (1987)
Elzinga, C.H., Rahmann, S., Wang, H.: Algorithms for subsequence combinatorics. Theoretical Computer Science 409(3), 394–404 (2008)
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Karandikar, P., Schnoebelen, P. (2014). On the State Complexity of Closures and Interiors of Regular Languages with Subwords. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2014. Lecture Notes in Computer Science, vol 8614. Springer, Cham. https://doi.org/10.1007/978-3-319-09704-6_21
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DOI: https://doi.org/10.1007/978-3-319-09704-6_21
Publisher Name: Springer, Cham
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