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
Some concepts in Fuzzy Generalized Automata （FGA） are established. Then an important new algorithm which would calculate the minimal FGA is given. The new algorithm is composed of two parts： the first is called E-r...Some concepts in Fuzzy Generalized Automata （FGA） are established. Then an important new algorithm which would calculate the minimal FGA is given. The new algorithm is composed of two parts： the first is called E-reduction which contracts equivalent states, and the second is called RE-reduction which removes retrievable states. Finally an example is given to illuminate the algorithm of minimization.展开更多
This paper presents an evolution strategy to induce fuzzy finite-state automata from examples of fuzzy languages. The coding, fitness function of a generated automaton and corresponding mutation operators are given re...This paper presents an evolution strategy to induce fuzzy finite-state automata from examples of fuzzy languages. The coding, fitness function of a generated automaton and corresponding mutation operators are given respectively. The application example given at last shows the effectiveness of the proposed evolution strategy for automata induction.展开更多
The equivalence exists between regular grammar and finite automata in accepting languages. Some complicated conversion algorithms have also been in existence. The simplified forms of the algorithms and their proofs ar...The equivalence exists between regular grammar and finite automata in accepting languages. Some complicated conversion algorithms have also been in existence. The simplified forms of the algorithms and their proofs are given. And the construction algorithm 5 of the equivalent conversion from finite automata to left linear grammar is presented as well as its correctness proof. Additionally, a relevant example is expounded.展开更多
1-way multihead quantum finite state automata (1QFA(k)) can be thought of modified version of 1-way quantum finite state automata (1QFA) and k-letter quantum finite state automata (k-letter QFA) respectively. It has b...1-way multihead quantum finite state automata (1QFA(k)) can be thought of modified version of 1-way quantum finite state automata (1QFA) and k-letter quantum finite state automata (k-letter QFA) respectively. It has been shown by Moore and Crutchfield as well as Konadacs and Watrous that 1QFA can’t accept all regular language. In this paper, we show different language recognizing capabilities of our model 1-way multihead QFAs. New results presented in this paper are the following ones: 1) We show that newly introduced 1-way 2-head quantum finite state automaton (1QFA(2)) structure can accept all unary regular languages. 2) A language which can’t be accepted by 1-way deterministic 2-head finite state automaton (1DFA((2)) can be accepted by 1QFA(2) with bounded error. 3) 1QFA(2) is more powerful than 1-way reversible 2-head finite state automaton (1RMFA(2)) with respect to recognition of language.展开更多
This paper models a biological brain—excluding motivation (e.g., emotions)—as a Finite Automaton in Developmental Network (FA-in-DN), but such an FA emerges incrementally in DN. In artificial intelligence (AI), ther...This paper models a biological brain—excluding motivation (e.g., emotions)—as a Finite Automaton in Developmental Network (FA-in-DN), but such an FA emerges incrementally in DN. In artificial intelligence (AI), there are two major schools: symbolic and connectionist. Weng 2011 [1] proposed three major properties of the Developmental Network (DN) which bridged the two schools: 1) From any complex FA that demonstrates human knowledge through its sequence of the symbolic inputs-outputs, a Developmental Program (DP) incrementally develops an emergent FA itself inside through naturally emerging image patterns of the symbolic inputs-outputs of the FA. The DN learning from the FA is incremental, immediate and error-free;2) After learning the FA, if the DN freezes its learning but runs, it generalizes optimally for infinitely many inputs and actions based on the neuron’s inner-product distance, state equivalence, and the principle of maximum likelihood;3) After learning the FA, if the DN continues to learn and run, it “thinks” optimally in the sense of maximum likelihood conditioned on its limited computational resource and its limited past experience. This paper gives an overview of the FA-in-DN brain theory and presents the three major theorems and their proofs.展开更多
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.
基金Supported by Supported by National Natural Science Foundation of China (No.60074014)
文摘Some concepts in Fuzzy Generalized Automata （FGA） are established. Then an important new algorithm which would calculate the minimal FGA is given. The new algorithm is composed of two parts： the first is called E-reduction which contracts equivalent states, and the second is called RE-reduction which removes retrievable states. Finally an example is given to illuminate the algorithm of minimization.
文摘This paper presents an evolution strategy to induce fuzzy finite-state automata from examples of fuzzy languages. The coding, fitness function of a generated automaton and corresponding mutation operators are given respectively. The application example given at last shows the effectiveness of the proposed evolution strategy for automata induction.
文摘The equivalence exists between regular grammar and finite automata in accepting languages. Some complicated conversion algorithms have also been in existence. The simplified forms of the algorithms and their proofs are given. And the construction algorithm 5 of the equivalent conversion from finite automata to left linear grammar is presented as well as its correctness proof. Additionally, a relevant example is expounded.
文摘1-way multihead quantum finite state automata (1QFA(k)) can be thought of modified version of 1-way quantum finite state automata (1QFA) and k-letter quantum finite state automata (k-letter QFA) respectively. It has been shown by Moore and Crutchfield as well as Konadacs and Watrous that 1QFA can’t accept all regular language. In this paper, we show different language recognizing capabilities of our model 1-way multihead QFAs. New results presented in this paper are the following ones: 1) We show that newly introduced 1-way 2-head quantum finite state automaton (1QFA(2)) structure can accept all unary regular languages. 2) A language which can’t be accepted by 1-way deterministic 2-head finite state automaton (1DFA((2)) can be accepted by 1QFA(2) with bounded error. 3) 1QFA(2) is more powerful than 1-way reversible 2-head finite state automaton (1RMFA(2)) with respect to recognition of language.
文摘This paper models a biological brain—excluding motivation (e.g., emotions)—as a Finite Automaton in Developmental Network (FA-in-DN), but such an FA emerges incrementally in DN. In artificial intelligence (AI), there are two major schools: symbolic and connectionist. Weng 2011 [1] proposed three major properties of the Developmental Network (DN) which bridged the two schools: 1) From any complex FA that demonstrates human knowledge through its sequence of the symbolic inputs-outputs, a Developmental Program (DP) incrementally develops an emergent FA itself inside through naturally emerging image patterns of the symbolic inputs-outputs of the FA. The DN learning from the FA is incremental, immediate and error-free;2) After learning the FA, if the DN freezes its learning but runs, it generalizes optimally for infinitely many inputs and actions based on the neuron’s inner-product distance, state equivalence, and the principle of maximum likelihood;3) After learning the FA, if the DN continues to learn and run, it “thinks” optimally in the sense of maximum likelihood conditioned on its limited computational resource and its limited past experience. This paper gives an overview of the FA-in-DN brain theory and presents the three major theorems and their proofs.
