Abstract
We investigate the descriptional and computational complexity of boundary sets of regular and context-free languages. The right (left, respectively) a-boundary set of a language L are those words that belong to L, where the a-predecessor or the a-successor of these words w.r.t. the prefix (suffix, respectively) relation is not in L. For regular languages described by deterministic finite automata (DFAs) we give tight bounds on the number of states for accepting boundary sets. Moreover, the question whether the boundary sets of a regular language is finite is shown to be NL-complete for DFAs, while it turns out to be PSPACE-complete for nondeterministic devices. Boundary sets for context-free languages are not necessarily context free anymore. Here we find a subtle difference of right and left a-boundary sets. While right a-boundary sets of deterministic context-free languages stay deterministic context free, we give an example of a deterministic context-free language the left a-boundary set of which is already non context free. In fact, the finiteness problem for a-boundary sets of context-free languages becomes undecidable.
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References
Badr, A., Geffert, V., Shipman, I.: Hyper-minimizing minimized deterministic finite state automata. RAIRO–Informatique Théorique et Applications Theoretical Informatics and Applications 43(1), 69–94 (2009)
Gawrychowski, P., Jeż, A., Maletti, A.: On minimising automata with errors. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 327–338. Springer, Heidelberg (2011)
Harrison, M.A.: Introduction to Formal Language Theory. Addison-Wesley (1978)
Holzer, M., Jakobi, S.: From equivalence to almost-equivalence, and beyond—minimizing automata with errors (extended abstract). In: Yen, H.-C., Ibarra, O.H. (eds.) DLT 2012. LNCS, vol. 7410, pp. 190–201. Springer, Heidelberg (2012)
Holzer, M., Kutrib, M.: Descriptional complexity—an introductory survey. In: Martín-Vide, C. (ed.) Scientific Applications of Language Methods, pp. 1–58. World Scientific (2010)
Jones, N.: Space-bounded reducibility among combinatorial problems. Journal of Computer and System Sciences 11, 68–85 (1975)
Willard, S.: General Topology. Addison-Wesley (1970)
Yu, S.: On the state complexity of combined operations. In: Ibarra, O.H., Yen, H.-C. (eds.) CIAA 2006. LNCS, vol. 4094, pp. 11–22. Springer, Heidelberg (2006)
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Holzer, M., Jakobi, S. (2014). Boundary Sets of Regular and Context-Free Languages. 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_15
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DOI: https://doi.org/10.1007/978-3-319-09704-6_15
Publisher Name: Springer, Cham
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