Tight Bounds for Cut-Operations on Deterministic Finite Automata
2015 (English)In: Machines, Computations, and Universality: 7th International Conference, MCU 2015, Famagusta, North Cyprus, September 9-11, 2015, Proceedings / [ed] J. Durand-Lose and B. Nagy, Springer Publishing Company, 2015, Vol. 9288, 45-60 p.Conference paper (Refereed)
We investigate the state complexity of the cut and iterated cut operation for deterministic finite automata (DFAs), answering an open question stated in [M. Berglund, et al.: Cuts in regular expressions. In Proc. DLT, LNCS 7907, 2011]. These operations can be seen as an alternative to ordinary concatenation and Kleene star modelling leftmost maximal string matching. We show that the cut operation has a matching upper and lower bound of (n−1)⋅m+n(n−1)⋅m+n states on DFAs accepting the cut of two individual languages that are accepted by n- and m-state DFAs, respectively. In the unary case we obtain max(2n−1,m+n−2)max(2n−1,m+n−2) states as a tight bound. For accepting the iterated cut of a language accepted by an n-state DFA we find a matching bound of 1+(n+1)⋅F(1,n+2,−n+2;n+1∣−1)1+(n+1)⋅F(1,n+2,−n+2;n+1∣−1) states on DFAs, where FF refers to the generalized hypergeometric function. This bound is in the order of magnitude Θ((n−1)!)Θ((n−1)!). Finally, the bound drops to 2n−12n−1 for unary DFAs accepting the iterated cut of an n-state DFA and thus is similar to the bound for the cut operation on unary DFAs.
Place, publisher, year, edition, pages
Springer Publishing Company, 2015. Vol. 9288, 45-60 p.
, Lecture Notes in Computer Science, ISSN 0302-9743
Research subject Computer Science
IdentifiersURN: urn:nbn:se:umu:diva-104114DOI: 10.1007/978-3-319-23111-2_4ISI: 000363670900004ISBN: 978-3-319-23111-2ISBN: 978-3-319-23110-5OAI: oai:DiVA.org:umu-104114DiVA: diva2:817777
7th Conference on Machines, Computations and Universality (MCU 2015)