Abstract
The state complexity of basic operations on finite languages (considering complete DFAs) has been extensively studied in the literature. In this paper we study the incomplete (deterministic) state and transition complexity on finite languages of boolean operations, concatenation, star, and reversal. For all operations we give tight upper bounds for both descriptional measures. We correct the published state complexity of concatenation for complete DFAs and provide a tight upper bound for the case when the right automaton is larger than the left one. For all binary operations the tightness is proved using family languages with a variable alphabet size. In general the operational complexities depend not only on the complexities of the operands but also on other refined measures.
This work was partially funded by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT under projects PEst-C/MAT/UI0144/2011 and CANTE-PTDC/EIA-CCO/101904/2008.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beesley, K.R., Karttunen, L.: Finite State Morphology. CSLI Publications, Stanford University (2003)
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)
Cassandras, C.G., Lafortune, S.: Introduction to discrete event systems. Springer (2006)
Gao, Y., Salomaa, K., Yu, S.: Transition complexity of incomplete DFAs. Fundam. Inform. 110(1-4), 143–158 (2011)
Han, Y.S., Salomaa, K.: State complexity of union and intersection of finite languages. Int. J. Found. Comput. Sci. 19(3), 581–595 (2008)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley (1979)
Maia, E., Moreira, N., Reis, R.: Incomplete transition complexity of some basic operations. In: van Emde Boas, P., Groen, F.C.A., Italiano, G.F., Nawrocki, J., Sack, H. (eds.) SOFSEM 2013. LNCS, vol. 7741, pp. 319–331. Springer, Heidelberg (2013)
Maurel, D., Guenthner, F.: Automata and Dictionaries. College Publications (2005)
Owens, S., Reppy, J.H., Turon, A.: Regular-expression derivatives re-examined. J. Funct. Program. 19(2), 173–190 (2009)
Salomaa, K., Yu, S.: NFA to DFA transformation for finite languages over arbitrary alphabets. J. of Aut., Lang. and Comb. 2(3), 177–186 (1997)
Shallit, J.: A Second Course in Formal Languages and Automata Theory. CUP (2008)
Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, pp. 41–110. Springer (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maia, E., Moreira, N., Reis, R. (2013). Incomplete Transition Complexity of Basic Operations on Finite Languages. In: Konstantinidis, S. (eds) Implementation and Application of Automata. CIAA 2013. Lecture Notes in Computer Science, vol 7982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39274-0_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-39274-0_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39273-3
Online ISBN: 978-3-642-39274-0
eBook Packages: Computer ScienceComputer Science (R0)