Let 3V denote the set of all possible transfer function matrices of weakly invertible linear finite automata over a given finite field F. A classification and an enumeration on the infinite set are given.
We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various ...We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. We present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, we give a negative answer to a problem posed by Gao and Hou on characterizing spectrum-preserving elementary operators. Several open problems are also mentioned.展开更多
FAPKC4, a public key cryptosystem based on automata theory, is generalized so that component automata of compound automata in user’s public key would not be restricted to memory finite automata. The generalized FAPKC...FAPKC4, a public key cryptosystem based on automata theory, is generalized so that component automata of compound automata in user’s public key would not be restricted to memory finite automata. The generalized FAPKCA can be used in encryption and implementing digital signatures as well.展开更多
基金supported by the National Natural Science Foundation of China.
文摘Let 3V denote the set of all possible transfer function matrices of weakly invertible linear finite automata over a given finite field F. A classification and an enumeration on the infinite set are given.
文摘We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. We present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, we give a negative answer to a problem posed by Gao and Hou on characterizing spectrum-preserving elementary operators. Several open problems are also mentioned.
文摘FAPKC4, a public key cryptosystem based on automata theory, is generalized so that component automata of compound automata in user’s public key would not be restricted to memory finite automata. The generalized FAPKCA can be used in encryption and implementing digital signatures as well.
