Abstract
Partial words are sequences of characters from an alphabet in which some positions may be marked with a “hole” symbol, ⋄. We can create a ⋄-substitution mapping this symbol to a subset of the alphabet, so that applying such a substitution to a partial word results in a set of full words (ones without holes). This setup allows us to compress regular languages into smaller partial languages. Deterministic finite automata for such partial languages, referred to as ⋄-DFAs, employ a limited non-determinism that can allow them to have lower state complexity than the minimal DFAs for the corresponding full languages. Our paper focuses on algorithms for the construction of minimal partial languages, associated with some ⋄-substitution, as well as approximation algorithms for the construction of minimal ⋄-DFAs.
This material is based upon work supported by the National Science Foundation under Grant No. DMS–1060775.
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
Balkanski, E., Blanchet-Sadri, F., Kilgore, M., Wyatt, B.J.: Partial word DFAs. In: Konstantinidis, S. (ed.) CIAA 2013. LNCS, vol. 7982, pp. 36–47. Springer, Heidelberg (2013)
Björklund, H., Martens, W.: The tractability frontier for NFA minimization. Journal of Computer and System Sciences 78, 198–210 (2012)
Blanchet-Sadri, F.: Algorithmic Combinatorics on Partial Words. Chapman & Hall/CRC Press, Boca Raton (2008)
Dassow, J., Manea, F., Mercaş, R.: Regular languages of partial words. Information Sciences 268, 290–304 (2014)
Groz, B., Maneth, S., Staworko, S.: Deterministic regular expressions in linear time. In: 31th ACM Symposium on Principles of Database Systems, PODS 2012, pp. 49–60 (2012)
Holzer, M., Jakobi, S., Wendlandt, M.: On the computational complexity of partial word automata problems. IFIG Research Report 1404, Institut für Informatik, Justus-Liebig-Universität Gießen, Arndtstr. 2, D-35392 Gießen, Germany (May 2014)
Hopcroft, J.E.: An n log n algorithm for minimizing states in a finite automaton. Tech. rep., DTIC Document (1971)
Jiang, T., Ravikumar, B.: Minimal NFA problems are hard. SIAM Journal on Computing 22, 1117–1141 (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Blanchet-Sadri, F., Goldner, K., Shackleton, A. (2014). Minimal Partial Languages and Automata. In: Holzer, M., Kutrib, M. (eds) Implementation and Application of Automata. CIAA 2014. Lecture Notes in Computer Science, vol 8587. Springer, Cham. https://doi.org/10.1007/978-3-319-08846-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-08846-4_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08845-7
Online ISBN: 978-3-319-08846-4
eBook Packages: Computer ScienceComputer Science (R0)