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Statements

Subject Item
n2:RIV%2F00216224%3A14310%2F11%3A00050220%21RIV12-GA0-14310___
rdf:type
skos:Concept n7:Vysledek
dcterms: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 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. 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.
dcterms:title
State complexity of union and intersection for two-way nondeterministic finite automata State complexity of union and intersection for two-way nondeterministic finite automata
skos:prefLabel
State complexity of union and intersection for two-way nondeterministic finite automata State complexity of union and intersection for two-way nondeterministic finite automata
skos:notation
RIV/00216224:14310/11:00050220!RIV12-GA0-14310___
n7:predkladatel
n8:orjk%3A14310
n3:aktivita
n15:P
n3:aktivity
P(GA201/09/1313)
n3:cisloPeriodika
1-4
n3:dodaniDat
n10:2012
n3:domaciTvurceVysledku
n12:6751881
n3:druhVysledku
n17:J
n3:duvernostUdaju
n11:S
n3:entitaPredkladatele
n14:predkladatel
n3:idSjednocenehoVysledku
232151
n3:idVysledku
RIV/00216224:14310/11:00050220
n3:jazykVysledku
n18:eng
n3:klicovaSlova
finite automata; two-way automata; state complexity; partitions into sums of primes
n3:klicoveSlovo
n5:finite%20automata n5:state%20complexity n5:partitions%20into%20sums%20of%20primes n5:two-way%20automata
n3:kodStatuVydavatele
NL - Nizozemsko
n3:kontrolniKodProRIV
[24D6D1C07644]
n3:nazevZdroje
Fundamenta Informaticae
n3:obor
n20:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n4:GA201%2F09%2F1313
n3:rokUplatneniVysledku
n10:2011
n3:svazekPeriodika
110
n3:tvurceVysledku
Okhotin, Alexander Kunc, Michal
n3:wos
000294764900018
s:issn
0169-2968
s:numberOfPages
9
n6:doi
10.3233/FI-2011-540
n19:organizacniJednotka
14310