### Abstract

We investigate the state complexities of basic operations for prefix-free regular languages. The state complexity of an operation for regular languages is the number of states that are necessary and sufficient in the worst-case for the minimal deterministic finite-state automaton (DFA) that accepts the language obtained from the operation. We know that a regular language is prefix-free if and only if its minimal DFA has only one final state and the final state has no out-transitions whose target state is not a sink state. Based on this observation, we reduce the state complexities for prefix-free regular languages compared with the state complexities for (general) regular languages. For both catenation and Kleene star operations of (general) regular languages, the state complexities are exponential in the size of given minimal DFAs. On the other hand, if both regular languages are prefix-free, then the state complexities are at most linear. We also demonstrate that we can reduce the state complexities of intersection and union operations based on the structural properties of prefix-free minimal DFAs.

Original language | English |
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Pages | 165-176 |

Number of pages | 12 |

Publication status | Published - 2006 Jan 1 |

Event | 8th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2006 - Las Cruces, NM, United States Duration: 2006 Jun 21 → 2006 Jun 23 |

### Other

Other | 8th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2006 |
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Country | United States |

City | Las Cruces, NM |

Period | 06/6/21 → 06/6/23 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*State complexity of prefix-free regular languages*. 165-176. Paper presented at 8th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2006, Las Cruces, NM, United States.

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**State complexity of prefix-free regular languages.** / Han, Yo Sub; Salomaa, Kai; Wood, Derick.

Research output: Contribution to conference › Paper

TY - CONF

T1 - State complexity of prefix-free regular languages

AU - Han, Yo Sub

AU - Salomaa, Kai

AU - Wood, Derick

PY - 2006/1/1

Y1 - 2006/1/1

N2 - We investigate the state complexities of basic operations for prefix-free regular languages. The state complexity of an operation for regular languages is the number of states that are necessary and sufficient in the worst-case for the minimal deterministic finite-state automaton (DFA) that accepts the language obtained from the operation. We know that a regular language is prefix-free if and only if its minimal DFA has only one final state and the final state has no out-transitions whose target state is not a sink state. Based on this observation, we reduce the state complexities for prefix-free regular languages compared with the state complexities for (general) regular languages. For both catenation and Kleene star operations of (general) regular languages, the state complexities are exponential in the size of given minimal DFAs. On the other hand, if both regular languages are prefix-free, then the state complexities are at most linear. We also demonstrate that we can reduce the state complexities of intersection and union operations based on the structural properties of prefix-free minimal DFAs.

AB - We investigate the state complexities of basic operations for prefix-free regular languages. The state complexity of an operation for regular languages is the number of states that are necessary and sufficient in the worst-case for the minimal deterministic finite-state automaton (DFA) that accepts the language obtained from the operation. We know that a regular language is prefix-free if and only if its minimal DFA has only one final state and the final state has no out-transitions whose target state is not a sink state. Based on this observation, we reduce the state complexities for prefix-free regular languages compared with the state complexities for (general) regular languages. For both catenation and Kleene star operations of (general) regular languages, the state complexities are exponential in the size of given minimal DFAs. On the other hand, if both regular languages are prefix-free, then the state complexities are at most linear. We also demonstrate that we can reduce the state complexities of intersection and union operations based on the structural properties of prefix-free minimal DFAs.

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M3 - Paper

SP - 165

EP - 176

ER -