State complexity of union and intersection for two-way nondeterministic finite automata

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F11%3A00050220" target="_blank" >RIV/00216224:14310/11:00050220 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.3233/FI-2011-540" target="_blank" >http://dx.doi.org/10.3233/FI-2011-540</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3233/FI-2011-540" target="_blank" >10.3233/FI-2011-540</a>

Result language
angličtina
Original language name
State complexity of union and intersection for two-way nondeterministic finite automata
Original language description
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 numberof 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 afew more exceptions) into sums of pairwise distinct primes is established as well.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GA201%2F09%2F1313" target="_blank" >GA201/09/1313: Algebraic Methods in Automata and Formal Language Theory II</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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