DocumentCode
1959332
Title
Notice of Retraction
Kronecker products of lattice-valued finite automata
Author
Jun Liu ; Su-qin Sun ; Xiao-hua Ou
Author_Institution
Dept. of Math., Sichuan Univ. for Nat., Kangding, China
Volume
3
fYear
2010
fDate
9-11 July 2010
Firstpage
617
Lastpage
620
Abstract
Notice of Retraction
After careful and considered review of the content of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE´s Publication Principles.
We hereby retract the content of this paper. Reasonable effort should be made to remove all past references to this paper.
The presenting author of this paper has the option to appeal this decision by contacting TPII@ieee.org.
In order to solve the structure problem of product automata, the matrix theory is used in this paper. By introducing Kronecker product, product structure of automata can be translated into matrix product. Applying lattice-fuzzy matrix theory, the concepts of lattice-fuzzy transition matrixes, lattice-valued transformation matrix semigroups, as well as coverings for lattice-valued finite automata are introduced. The equivalence relation is defined in the set of input symbols. For each lattice-valued finite state automaton, we have showed that there exists a lattice-valued transformation matrix semigroup associated with it. The definitions of products of lattice-valued fuzzy finite state machines are given by application of Kronecker product. Furthermore, the properties of lattice-fuzzy transition matrix for three kinds Kronecker products of lattice-valued fuzzy finite state machines are discussed. The covering relationships and associative properties among Kronecker products of lattice-valued transformation matrix semigroup associated with lattice-valued fuzzy finite state machines are studied. These results show that Kronecker product is compatible with the product of lattice-valued finite automata. Also Kronecker product can effectively describe and simplify the product structure of automata.
After careful and considered review of the content of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE´s Publication Principles.
We hereby retract the content of this paper. Reasonable effort should be made to remove all past references to this paper.
The presenting author of this paper has the option to appeal this decision by contacting TPII@ieee.org.
In order to solve the structure problem of product automata, the matrix theory is used in this paper. By introducing Kronecker product, product structure of automata can be translated into matrix product. Applying lattice-fuzzy matrix theory, the concepts of lattice-fuzzy transition matrixes, lattice-valued transformation matrix semigroups, as well as coverings for lattice-valued finite automata are introduced. The equivalence relation is defined in the set of input symbols. For each lattice-valued finite state automaton, we have showed that there exists a lattice-valued transformation matrix semigroup associated with it. The definitions of products of lattice-valued fuzzy finite state machines are given by application of Kronecker product. Furthermore, the properties of lattice-fuzzy transition matrix for three kinds Kronecker products of lattice-valued fuzzy finite state machines are discussed. The covering relationships and associative properties among Kronecker products of lattice-valued transformation matrix semigroup associated with lattice-valued fuzzy finite state machines are studied. These results show that Kronecker product is compatible with the product of lattice-valued finite automata. Also Kronecker product can effectively describe and simplify the product structure of automata.
Keywords
finite state machines; fuzzy set theory; matrix algebra; Kronecker product; equivalence relation; finite state machine; lattice fuzzy transition matrix; lattice valued finite automata; lattice valued transformation matrix semigroup; Automata; Least squares approximation; OWL; covering; kronecker product; lattice-valued finite automaton;
fLanguage
English
Publisher
ieee
Conference_Titel
Computer Science and Information Technology (ICCSIT), 2010 3rd IEEE International Conference on
Conference_Location
Chengdu
Print_ISBN
978-1-4244-5537-9
Type
conf
DOI
10.1109/ICCSIT.2010.5565103
Filename
5565103
Link To Document