scholarly journals Bisimulations for weighted automata over an additively idempotent semiring

2014 ◽  
Vol 534 ◽  
pp. 86-100 ◽  
Author(s):  
Nada Damljanović ◽  
Miroslav Ćirić ◽  
Jelena Ignjatović
Keyword(s):  
Idempotent Semiring ◽  
Weighted Automata

scholarly journals Modeling of safe time Petri nets by interval weighted automata

2020 ◽  
Vol 53 (4) ◽  
pp. 187-192
Author(s):  
Jan Komenda ◽  
Aiwen Lai ◽  
José Godoy Soto ◽  
Sébastien Lahaye ◽  
Jean-louis Boimond
Keyword(s):  
Petri Nets ◽  
Time Petri Nets ◽  
Weighted Automata

scholarly journals Nested Weighted Automata

2017 ◽  
Vol 18 (4) ◽  
pp. 1-44 ◽  
Author(s):  
Krishnendu Chatterjee ◽  
Thomas A. Henzinger ◽  
Jan Otop
Keyword(s):  
Weighted Automata

scholarly journals PATH-EQUIVALENT DEVELOPMENTS IN ACYCLIC WEIGHTED AUTOMATA

2007 ◽  
Vol 18 (04) ◽  
pp. 799-811
Author(s):  
MATHIEU GIRAUD ◽  
PHILLIPE VEBER ◽  
DOMINIQUE LAVENIER
Keyword(s):  
Surface Area ◽  
Finite Automata ◽  
Clock Frequency ◽  
Partial Removal ◽  
Frequency Constraints ◽  
Weighted Automata ◽  
Weighted Finite Automata ◽  
Special Case

Weighted finite automata (WFA) are used with FPGA accelerating hardware to scan large genomic banks. Hardwiring such automata raises surface area and clock frequency constraints, requiring efficient ∊-transitions-removal techniques. In this paper, we present bounds on the number of new transitions for the development of acyclic WFA, which is a special case of the ∊-transitions-removal problem. We introduce a new problem, a partial removal of ∊-transitions while accepting short chains of ∊-transitions.

Derivations of matrix semirings

2020 ◽  
pp. 2150150
Author(s):  
Dimitrinka Vladeva
Keyword(s):  
Differential Equations ◽  
The Other ◽  
Idempotent Semiring ◽  
Inner Derivation ◽  
Commutative Case ◽  
Linear Map ◽  
Algebra Ii ◽  
Matrix Calculus ◽  
Derivation Formula ◽  
Matrix Formula

It is well known that if [Formula: see text] is a derivation in semiring [Formula: see text], then in the semiring [Formula: see text] of [Formula: see text] matrices over [Formula: see text], the map [Formula: see text] such that [Formula: see text] for any matrix [Formula: see text] is a derivation. These derivations are used in matrix calculus, differential equations, statistics, physics and engineering and are called hereditary derivations. On the other hand (in sense of [Basic Algebra II (W. H. Freeman & Company, 1989)]) [Formula: see text]-derivation in matrix semiring [Formula: see text] is a [Formula: see text]-linear map [Formula: see text] such that [Formula: see text], where [Formula: see text]. We prove that if [Formula: see text] is a commutative additively idempotent semiring any [Formula: see text]-derivation is a hereditary derivation. Moreover, for an arbitrary derivation [Formula: see text] the derivation [Formula: see text] in [Formula: see text] is of a special type, called inner derivation (in additively, idempotent semiring). In the last section of the paper for a noncommutative semiring [Formula: see text] a concept of left (right) Ore elements in [Formula: see text] is introduced. Then we extend the center [Formula: see text] to the semiring LO[Formula: see text] of left Ore elements or to the semiring RO[Formula: see text] of right Ore elements in [Formula: see text]. We construct left (right) derivations in these semirings and generalize the result from the commutative case.

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