Abstract
We investigate context-free languages with respect to the measure Prod of descriptional complexity, which gives the minimal number of productions necessary to generate the language. In particular, we consider the behaviour of this measure with respect to operations. For given natural numbers c 1,c 2,…,c n and an n-ary operation τ on languages, we discuss the set g τ (c 1,c 2,…,c n ) which is the range of Prod(τ(L 1,L 2,…, L n )) where, for 1 ≤ i ≤ n, L i is a context-free language with Prod(L i ) = c i . The operations under discussion are union, concatenation, reversal, and Kleene closure.
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References
Câmpeanu, C., Culik, K., Salomaa, K., Yu, S.: State Complexity of Basic Operations on Finite Languages. In: Boldt, O., Jürgensen, H. (eds.) WIA 1999. LNCS, vol. 2214, pp. 60–70. Springer, Heidelberg (2001)
Dassow, J., Stiebe, R.: Nonterminal Complexity of Some Operations on Context-Free Languages. Fundamenta Informaticae 83, 35–49 (2008)
Domaratzki, M., Salomaa, K.: Transition complexity of language operations. In: Proc. Intern. Workshop Descriptional Complexity of Formal Systems 2006, New Mexico State Univ. Las Cruces, pp. 141–152 (2006)
Ellul, K.: Descriptional complexity measures of regular languages. Master Thesis, University of Waterloo (2002)
Gruska, J.: Some classifications of context-free languages. Information and Control 14, 152–179 (1969)
Gruska, J.: Generation and approximation of finite and infinite languages. In: Internat. Symp. Summer School Math. Found. Comp. Sci., Warsaw, pp. 1–7 (1972)
Gruska, J.: On the size of context-free grammars. Kybernetika 8, 213–218 (1972)
Gruska, J.: Descriptional complexity of context-free languages. In: Proc. Math. Found. Comp. Sci., Strebske Pleso, pp. 71–83 (1973)
Harbich, R.: Beschreibungskomplexität kontextfreier Sprachen bezüglich der AFL-Operationen. Dissertation, Otto-von-Guericke-Universität Magdeburg, Fakultät für Informatik (2012)
Holzer, M., Kutrib, M.: Nondeterministic descriptional complexity of regular languages. Intern. J. Found. Comp. Sci. 14, 1087–1102 (2003)
Jirásek, J., Jirásková, G., Szabari, A.: State Complexity of Concatenation and Complementation of Regular Languages. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds.) CIAA 2004. LNCS, vol. 3317, pp. 178–189. Springer, Heidelberg (2005)
Jiraskova, G., Okhotin, A.: State Complexity of cyclic shift. In: Proc. Descriptional Complexity of Formal Systems, Univ. Milano, pp. 182–193 (2005)
Păun, G.: On the smallest number of nonterminals required to generate a context-free language. Mathematica 18, 203–208 (1976)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. I–III. Springer (1997)
Yu, S.: State complexity of regular languages. J. Automata, Languages and Combinatorics 6, 221–234 (2001)
Yu, S.: State complexity of finite and infinite regular languages. Bulletin of the EATCS 76, 142–152 (2002)
Yu, S., Zhuang, Q., Salomaa, K.: The state complexity of some basic operations on regular languages. Theor. Comp. Sci. 125, 315–328 (1994)
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Dassow, J., Harbich, R. (2012). Production Complexity of Some Operations on Context-Free Languages. In: Kutrib, M., Moreira, N., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2012. Lecture Notes in Computer Science, vol 7386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31623-4_11
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DOI: https://doi.org/10.1007/978-3-642-31623-4_11
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