%0 Conference Proceedings
%T Square on Deterministic, Alternating, and Boolean Finite Automata
%+ Slovak Academy of Sciences (SAS)
%A Krajňáková, Ivana
%A Jirásková, Galina
%Z Part 2: Contributed Papers
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 19th International Conference on Descriptional Complexity of Formal Systems (DCFS)
%C Milano, Italy
%Y Giovanni Pighizzini
%Y Cezar Câmpeanu
%I Springer International Publishing
%3 Descriptional Complexity of Formal Systems
%V LNCS-10316
%P 214-225
%8 2017-07-03
%D 2017
%R 10.1007/978-3-319-60252-3_17
%Z Computer Science [cs]Conference papers
%X We investigate the state complexity of the square operation on languages represented by deterministic, alternating, and Boolean automata. For each k such that $1 \le k \le n-2$, we describe a binary language accepted by an n-state DFA with k final states meeting the upper bound $n2^n - k2^{n-1}$ on the state complexity of its square. We show that in the case of $k=n-1$, the corresponding upper bound cannot be met. Using the DFA witness for square with $2^n$ states where half of them are final, we get the tight upper bounds on the complexity of the square operation on alternating and Boolean automata.
%G English
%Z TC 1
%Z WG 1.2
%2 https://inria.hal.science/hal-01657005/document
%2 https://inria.hal.science/hal-01657005/file/440206_1_En_17_Chapter.pdf
%L hal-01657005
%U https://inria.hal.science/hal-01657005
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC1
%~ IFIP-WG
%~ IFIP-DCFS
%~ IFIP-WG1-2
%~ IFIP-LNCS-10316