### Abstract

This paper concerns new characterizations of language classes in the Chomsky hierarchy in terms of a new type of computing device called FAMM (Finite Automaton with Multiset Memory) in which a multiset of symbol objects is available for the storage of working space. Unlike the stack or the tape for a storage, the multiset might seem to be less powerful in computing task, due to the lack of positional (structural) information of stored data. We introduce the class of FAMMs of degree d (for non-negative integer d) in general form, and investigate the computing powers of some subclasses of those FAMMs. We show that the classes of languages accepted by FAMMs of degree 0, by FAMMs of degree 1, by exponentially-bounded FAMMs of degree 2, and by FAMMs of degree 2 are exactly the four classes of languages REG, CF, CS and RE in the Chomsky hierarchy, respectively. Thus, this unified view from multiset-based computing provides new insight into the computational aspects of the Chomsky hierarchy.

Original language | English |
---|---|

Pages (from-to) | 31-44 |

Number of pages | 14 |

Journal | Fundamenta Informaticae |

Volume | 138 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2015 |

### Fingerprint

### Keywords

- Chomsky hierarchy of languages
- computation power
- finite automata
- multiset memory

### ASJC Scopus subject areas

- Information Systems
- Computational Theory and Mathematics
- Theoretical Computer Science
- Algebra and Number Theory

### Cite this

*Fundamenta Informaticae*,

*138*(1-2), 31-44. https://doi.org/10.3233/FI-2015-1196

**Finite automata with multiset memory : A new characterization of chomsky hierarchy.** / Okubo, Fumiya; Yokomori, Takashi.

Research output: Contribution to journal › Article

*Fundamenta Informaticae*, vol. 138, no. 1-2, pp. 31-44. https://doi.org/10.3233/FI-2015-1196

}

TY - JOUR

T1 - Finite automata with multiset memory

T2 - A new characterization of chomsky hierarchy

AU - Okubo, Fumiya

AU - Yokomori, Takashi

PY - 2015

Y1 - 2015

N2 - This paper concerns new characterizations of language classes in the Chomsky hierarchy in terms of a new type of computing device called FAMM (Finite Automaton with Multiset Memory) in which a multiset of symbol objects is available for the storage of working space. Unlike the stack or the tape for a storage, the multiset might seem to be less powerful in computing task, due to the lack of positional (structural) information of stored data. We introduce the class of FAMMs of degree d (for non-negative integer d) in general form, and investigate the computing powers of some subclasses of those FAMMs. We show that the classes of languages accepted by FAMMs of degree 0, by FAMMs of degree 1, by exponentially-bounded FAMMs of degree 2, and by FAMMs of degree 2 are exactly the four classes of languages REG, CF, CS and RE in the Chomsky hierarchy, respectively. Thus, this unified view from multiset-based computing provides new insight into the computational aspects of the Chomsky hierarchy.

AB - This paper concerns new characterizations of language classes in the Chomsky hierarchy in terms of a new type of computing device called FAMM (Finite Automaton with Multiset Memory) in which a multiset of symbol objects is available for the storage of working space. Unlike the stack or the tape for a storage, the multiset might seem to be less powerful in computing task, due to the lack of positional (structural) information of stored data. We introduce the class of FAMMs of degree d (for non-negative integer d) in general form, and investigate the computing powers of some subclasses of those FAMMs. We show that the classes of languages accepted by FAMMs of degree 0, by FAMMs of degree 1, by exponentially-bounded FAMMs of degree 2, and by FAMMs of degree 2 are exactly the four classes of languages REG, CF, CS and RE in the Chomsky hierarchy, respectively. Thus, this unified view from multiset-based computing provides new insight into the computational aspects of the Chomsky hierarchy.

KW - Chomsky hierarchy of languages

KW - computation power

KW - finite automata

KW - multiset memory

UR - http://www.scopus.com/inward/record.url?scp=84927647164&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84927647164&partnerID=8YFLogxK

U2 - 10.3233/FI-2015-1196

DO - 10.3233/FI-2015-1196

M3 - Article

AN - SCOPUS:84927647164

VL - 138

SP - 31

EP - 44

JO - Fundamenta Informaticae

JF - Fundamenta Informaticae

SN - 0169-2968

IS - 1-2

ER -