### Abstract

There are different ways of quantifying the nondeterminism used by a nondeterministic finite automaton (NFA). The amount of nondeterminism is measured as a function of the input length. For most nondeterminism measures the possible growth rates of the measure have been characterized, but this question remains open for the branching of an NFA. Here, we consider a close variant of the branching measure which we call the minimum branching. We show that the minimum branching of an NFA is always either bounded or grows exponentially.

Original language | English |
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Pages (from-to) | 281-292 |

Number of pages | 12 |

Journal | Journal of Automata, Languages and Combinatorics |

Volume | 23 |

Issue number | 1-3 |

Publication status | Published - 2018 Jan 1 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Cite this

*Journal of Automata, Languages and Combinatorics*,

*23*(1-3), 281-292.

}

*Journal of Automata, Languages and Combinatorics*, vol. 23, no. 1-3, pp. 281-292.

**Growth rate of minimum branching.** / Palioudakis, Alexandros; Han, Yo-Sub; Salomaa, Kai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Growth rate of minimum branching

AU - Palioudakis, Alexandros

AU - Han, Yo-Sub

AU - Salomaa, Kai

PY - 2018/1/1

Y1 - 2018/1/1

N2 - There are different ways of quantifying the nondeterminism used by a nondeterministic finite automaton (NFA). The amount of nondeterminism is measured as a function of the input length. For most nondeterminism measures the possible growth rates of the measure have been characterized, but this question remains open for the branching of an NFA. Here, we consider a close variant of the branching measure which we call the minimum branching. We show that the minimum branching of an NFA is always either bounded or grows exponentially.

AB - There are different ways of quantifying the nondeterminism used by a nondeterministic finite automaton (NFA). The amount of nondeterminism is measured as a function of the input length. For most nondeterminism measures the possible growth rates of the measure have been characterized, but this question remains open for the branching of an NFA. Here, we consider a close variant of the branching measure which we call the minimum branching. We show that the minimum branching of an NFA is always either bounded or grows exponentially.

UR - http://www.scopus.com/inward/record.url?scp=85062074358&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062074358&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85062074358

VL - 23

SP - 281

EP - 292

JO - Journal of Automata, Languages and Combinatorics

JF - Journal of Automata, Languages and Combinatorics

SN - 1430-189X

IS - 1-3

ER -