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@article{961274,
author = {Kunc, Michal and Okhotin, Alexander},
article_location = {Amsterdam},
article_number = {1-4},
doi = {http://dx.doi.org/10.3233/FI-2011-540},
keywords = {finite automata; two-way automata; state complexity; partitions into sums of primes},
language = {eng},
issn = {0169-2968},
journal = {Fundamenta Informaticae},
title = {State complexity of union and intersection for two-way nondeterministic finite automata},
volume = {110},
year = {2011}
}
TY - JOUR
ID - 961274
AU - Kunc, Michal - Okhotin, Alexander
PY - 2011
TI - State complexity of union and intersection for two-way nondeterministic finite automata
JF - Fundamenta Informaticae
VL - 110
IS - 1-4
SP - 231-239
EP - 231-239
PB - IOS Press
SN - 01692968
KW - finite automata
KW - two-way automata
KW - state complexity
KW - partitions into sums of primes
N2 - The number of states in a two-way nondeterministic finite automaton (2NFA) needed to represent intersection of languages given by an m-state 2NFA and an n-state 2NFA is shown to be at least m + n and at most m + n + 1. For the union operation, the number of states is exactly m + n. The lower bound is established for languages over a one-letter alphabet. The key point of the argument is the following number-theoretic lemma: for all m,n >= 2 with m, n not equal to 6 (and with finitely many other exceptions), there exist partitions m = p1 +...+ pk and n = q1 +...+ ql, where all numbers p1,...,pk,q1,...,ql >= 2 are powers of pairwise distinct primes. For completeness, an analogous statement about partitions of any two numbers m,n not in {4,6} (with a few more exceptions) into sums of pairwise distinct primes is established as well.
ER -
KUNC, Michal and Alexander OKHOTIN. State complexity of union and intersection for two-way nondeterministic finite automata. \textit{Fundamenta Informaticae}. Amsterdam: IOS Press, 2011, vol.~110, 1-4, p.~231-239. ISSN~0169-2968. Available from: https://dx.doi.org/10.3233/FI-2011-540.
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