Geodesic
Fuzzy linear automata testing
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 19 (2019) no. 2, pp. 233-240

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The article deals with the problem of synthesis of tests for fuzzy linear automata (FLA). Now several varieties of FLA are used as models of real fuzzy systems. The article introduces and investigates one particular type of FLA. The fuzziness of the behavior of the automaton is suggested to appear due to the use of elements of a special type in the characteristic matrices. Each such element is a certain set of elements of the field over which the FLA is given. During the functioning of the FLA (at each clock cycle) an alternative matrix element is replaced randomly by one of the elements of the alternative set. The notion of the FLA acceptable fault is introduced. Substantially it means replacing the alternative elements of matrices by one element of the sets corresponding to them. The method of the tests synthesis for detecting faults of this type is proposed. This method reduces to solving systems of linear algebraic equations. The method is oriented to $\mu$-definite and synchronized FLA and synthesizes tests of sufficiently short length (not more than FLA dimension). 
@article{ISU_2019_19_2_a9,
     author = {D. V. Speranskiy},
     title = {Fuzzy linear automata testing},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {233--240},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2019_19_2_a9/}
}
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D. V. Speranskiy. Fuzzy linear automata testing. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 19 (2019) no. 2, pp. 233-240. http://geodesic.mathdoc.fr/item/ISU_2019_19_2_a9/