DETERMINATIONS OF WEIGHTED FINITE AUTOMATA OVER COMMUTATIVE IDEMPOTENT MF-SEMIRINGS
2012 ◽
Vol 22
(03)
◽
pp. 1250020
Keyword(s):
The semirings admitting maximal factorizations of any finite dimension are called MF-semirings. We first show that a commutative semiring K is an MF-semiring if and only if K admits a maximal factorization of dimension n ≥ 2, and if and only if K is a multiplicatively cancellative semiring satisfying the g.c.d. condition. And then, by using above result, we prove that a weighted finite automaton [Formula: see text] over a commutative idempotent MF-semiring has a determination if [Formula: see text] has the victory property and twins property. Also, some special cases are considered.
2007 ◽
Vol 18
(06)
◽
pp. 1407-1416
◽
2007 ◽
Vol 18
(04)
◽
pp. 799-811
Keyword(s):
2018 ◽
Vol 9
(1)
◽
pp. 115-133
◽
2020 ◽
Vol 31
(04)
◽
pp. 527-538