In this paper, we propose a matrix-based approach for finite automata and then study the reachability conditions. Both the deterministic and nondeterministic automata are expressed in matrix forms, and the necessary a...In this paper, we propose a matrix-based approach for finite automata and then study the reachability conditions. Both the deterministic and nondeterministic automata are expressed in matrix forms, and the necessary and sufficient conditions on reachability are given using semitensor product of matrices. Our results show that the matrix expression provides an effective computational way for the reachability analysis of finite automata.展开更多
In this papert weights of output set and of input set for finiteautomata are discussed. For a weakly invertible finite automaton, we proye thatfor states with minimal output weight, the distribution of input sets is u...In this papert weights of output set and of input set for finiteautomata are discussed. For a weakly invertible finite automaton, we proye thatfor states with minimal output weight, the distribution of input sets is uniform.Then for a kind of compound finite automata, we give weights of output set and ofinput set explicitly, and a characterization of their input-trees. For finite automatonpublic key cryptosystems, of which automata in public keys belong to such a kind ofcompound finite automata, we evaluate search amounts of exhaust search algorithmsin average case and in worse case for both encryption and signature, and successfulprobabilities of stochastic search algorithms for both encryption and signature. Inaddition, a result on mutual invertibility of finite automata is also given.展开更多
Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions ar...Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms.Based on this algebraic description, a necessary and sufficient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to find all the control sequences of an arbitrary length. Moreover, the stabilizability of finite automata is considered, and a necessary and sufficient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples verifies the correctness of the presented results/algorithms.展开更多
基金supported by the National Natural Science Foundation of China (No. 61174071)
文摘In this paper, we propose a matrix-based approach for finite automata and then study the reachability conditions. Both the deterministic and nondeterministic automata are expressed in matrix forms, and the necessary and sufficient conditions on reachability are given using semitensor product of matrices. Our results show that the matrix expression provides an effective computational way for the reachability analysis of finite automata.
文摘In this papert weights of output set and of input set for finiteautomata are discussed. For a weakly invertible finite automaton, we proye thatfor states with minimal output weight, the distribution of input sets is uniform.Then for a kind of compound finite automata, we give weights of output set and ofinput set explicitly, and a characterization of their input-trees. For finite automatonpublic key cryptosystems, of which automata in public keys belong to such a kind ofcompound finite automata, we evaluate search amounts of exhaust search algorithmsin average case and in worse case for both encryption and signature, and successfulprobabilities of stochastic search algorithms for both encryption and signature. Inaddition, a result on mutual invertibility of finite automata is also given.
基金supported by the National Natural Science Foundation of China(61174094)the Tianjin Natural Science Foundation of China(13JCYBJC1740014JCYBJC18700)
文摘Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms.Based on this algebraic description, a necessary and sufficient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to find all the control sequences of an arbitrary length. Moreover, the stabilizability of finite automata is considered, and a necessary and sufficient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples verifies the correctness of the presented results/algorithms.
