### Abstract

A finance automaton is a sixtuple 〈Σ, Q, δ, S, F, f〉, where 〈Σ, Q, δ, S, F〉 is a (non-deterministic) finite automaton, f : Q × Σ × Q → R ∪ {- ∞} is a finance function, R is the set of real numbers and f(q, a, q′) = -∞ if and only if q′ ∉ δ(q, a). The function f is extended to f : 2^{Q} × Σ* × 2^{Q} → R ∪ {- ∞} by the plus-max principle. For any ω ∈ Σ*, f(S, ω, F) is the profit of ω. It is shown that the equivalence problem for finitely ambiguous finance automata is decidable.

Original language | English |
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Pages (from-to) | 445-461 |

Number of pages | 17 |

Journal | International Journal of Algebra and Computation |

Volume | 12 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2002 |

### Fingerprint

### Keywords

- Finance automata
- Plus-max principle
- Transducer
- Tropical semiring

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*International Journal of Algebra and Computation*,

*12*(3), 445-461. https://doi.org/10.1142/S0218196702000845

**Decidability of the equivalence problem for finitely ambiguous finance automata.** / Hashiguchi, Kosaburo; Ishiguro, Kenichi; Jinbo, Shuji.

Research output: Contribution to journal › Article

*International Journal of Algebra and Computation*, vol. 12, no. 3, pp. 445-461. https://doi.org/10.1142/S0218196702000845

}

TY - JOUR

T1 - Decidability of the equivalence problem for finitely ambiguous finance automata

AU - Hashiguchi, Kosaburo

AU - Ishiguro, Kenichi

AU - Jinbo, Shuji

PY - 2002

Y1 - 2002

N2 - A finance automaton is a sixtuple 〈Σ, Q, δ, S, F, f〉, where 〈Σ, Q, δ, S, F〉 is a (non-deterministic) finite automaton, f : Q × Σ × Q → R ∪ {- ∞} is a finance function, R is the set of real numbers and f(q, a, q′) = -∞ if and only if q′ ∉ δ(q, a). The function f is extended to f : 2Q × Σ* × 2Q → R ∪ {- ∞} by the plus-max principle. For any ω ∈ Σ*, f(S, ω, F) is the profit of ω. It is shown that the equivalence problem for finitely ambiguous finance automata is decidable.

AB - A finance automaton is a sixtuple 〈Σ, Q, δ, S, F, f〉, where 〈Σ, Q, δ, S, F〉 is a (non-deterministic) finite automaton, f : Q × Σ × Q → R ∪ {- ∞} is a finance function, R is the set of real numbers and f(q, a, q′) = -∞ if and only if q′ ∉ δ(q, a). The function f is extended to f : 2Q × Σ* × 2Q → R ∪ {- ∞} by the plus-max principle. For any ω ∈ Σ*, f(S, ω, F) is the profit of ω. It is shown that the equivalence problem for finitely ambiguous finance automata is decidable.

KW - Finance automata

KW - Plus-max principle

KW - Transducer

KW - Tropical semiring

UR - http://www.scopus.com/inward/record.url?scp=0035998625&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035998625&partnerID=8YFLogxK

U2 - 10.1142/S0218196702000845

DO - 10.1142/S0218196702000845

M3 - Article

VL - 12

SP - 445

EP - 461

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

SN - 0218-1967

IS - 3

ER -