Abstract
We investigate the state complexity of union and intersection for finite languages. Note that the problem of obtaining the tight bounds for both operations was open. First we compute upper bounds using structural properties of minimal deterministic finite-state automata for finite languages. Then, we show that the upper bounds are tight if we have a variable sized alphabet that can depend on the size of input deterministic finite-state automata. In addition, we prove that the upper bounds are unreachable for any fixed sized alphabet.
| Original language | English |
|---|---|
| Pages (from-to) | 581-595 |
| Number of pages | 15 |
| Journal | International Journal of Foundations of Computer Science |
| Volume | 19 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2008 Jun 1 |
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All Science Journal Classification (ASJC) codes
- Computer Science (miscellaneous)
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State complexity of union and intersection of finite languages. / Han, Yo-Sub; Salomaa, Kai.
In: International Journal of Foundations of Computer Science, Vol. 19, No. 3, 01.06.2008, p. 581-595.Research output: Contribution to journal › Article
TY - JOUR
T1 - State complexity of union and intersection of finite languages
AU - Han, Yo-Sub
AU - Salomaa, Kai
PY - 2008/6/1
Y1 - 2008/6/1
N2 - We investigate the state complexity of union and intersection for finite languages. Note that the problem of obtaining the tight bounds for both operations was open. First we compute upper bounds using structural properties of minimal deterministic finite-state automata for finite languages. Then, we show that the upper bounds are tight if we have a variable sized alphabet that can depend on the size of input deterministic finite-state automata. In addition, we prove that the upper bounds are unreachable for any fixed sized alphabet.
AB - We investigate the state complexity of union and intersection for finite languages. Note that the problem of obtaining the tight bounds for both operations was open. First we compute upper bounds using structural properties of minimal deterministic finite-state automata for finite languages. Then, we show that the upper bounds are tight if we have a variable sized alphabet that can depend on the size of input deterministic finite-state automata. In addition, we prove that the upper bounds are unreachable for any fixed sized alphabet.
UR - http://www.scopus.com/inward/record.url?scp=44849090524&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=44849090524&partnerID=8YFLogxK
U2 - 10.1142/S0129054108005838
DO - 10.1142/S0129054108005838
M3 - Article
VL - 19
SP - 581
EP - 595
JO - International Journal of Foundations of Computer Science
JF - International Journal of Foundations of Computer Science
SN - 0129-0541
IS - 3
ER -