On equations for regular languages, finite automata, and sequential networks

We consider systems of equations of the form where A is the underlying alphabet, the Xi are variables, the Pi,a are boolean functions in the variables Xi, and each δi is either the empty word or the empty set. The symbols υ and denote concatenation and union of languages over A. We show that any such system has a unique solution which, moreover, is regular. These equations correspond to a type of automation, called boolean automation, which is a generalization of a nondeterministic automation. The equations are then used to determine the language accepted by a sequential network; they are obtainable directly from the network.

加工深度、记忆材料类型对FOK和FOnK判断的影响

Predecessors’ research found that feeling-of-knowing and feeling-of-not-knowing was two different cognitional processes. Processing depth had more good effects on FOK judgment, but it had little effects on FOnK judgment, furthermore, it perhaps decreased the accuracy of FOnK judgment. On the base of predecessors’ research the experiment discussed the different effects on FOK judgment and FOnK judgment by processing depth and memory materials of different kinds. The first purpose was to find that the effects of processing depth on FOK judgment and FOnK judgment were different or not. The second purpose was to reveal the two different memory materials of the Paired-Chinese-words and the Paired- Chinese-phonetic-alphabet would cause difference on the grade and accuracy of FOK judgment or not, and if the two different kinds of memory materials took different effects on FOK judgment and FOnK judgment. The third purpose was to search if there was interaction on processing depth and different kinds of memory materials. The experiment used the Paired-Chinese-words and the Paired- Chinese-phonetic-alphabet as the materials, and regarded processing depth in the time of encoding stage and different kinds of memory materials as the independent variable. The experiment regarded validity of memory; the grade of FOK judgment; the accuracy of FOK judgment; the accuracy of FOnK judgment as the dependent variable. The experiment adopted the “RJR” normal researching form of FOK judgment projected by Hart. The result of the researching proved that in the condition of deep processing in the time of encoding stage, the validity of memory; the grade of FOK judgment; the accuracy of FOK judgment were higher than in the condition of superficial processing, but processing depth had little effect on accuracy of FOnK judgment. FOK judgment and FOnK judgment were two different cognitional processes. Memory materials of different kinds led clear difference on the dependent variable of the validity of memory; the grade of FOK judgment; the accuracy of FOK judgment, and also had little effect on accuracy of FOnK judgment. Processing depth and different kinds of memory materials had interaction on their effects on FOK judgment. Regard the accuracy of recall, the percentage of “feeling of knowing”, the percentage of “feeling of not knowing”, and the grade of FOK judgment as the dependent variables, memory materials of different kinds make little effect in the condition of superficial processing in the time of encoding stage, but in the condition of deep processing in the time of encoding stage, Chinese characters was higher than Chinese phonetic alphabet.