The least significant digit first decomposition of integer vectors into words of digit vectors provides a natural way for representing sets of integer vectors by automata. In this paper, the minimal automata representing Presburger sets are proved structurally Presburger: automata obtained by moving the initial state and replacing the accepting condition represent Presburger sets. 相似文献
This paper establishes an axiomatic foundation and a representation theorem for the rigorous, constructive process, called sequence-based specification, of deriving precise specifications from ordinary (informal) statements of functional requirements. The representation theorem targets a special class of Mealy state machines, and algorithms are presented for converting from the set of sequences that define the specification to the equivalent Mealy machine, and vice versa. Since its inception, sequence-based specification has been effectively used in a variety of real applications, with gains reported in quality and productivity. This paper establishes the mathematical foundation independently of the process itself. 相似文献
The exponent of a word is the quotient of its length over its smallest period. The exponent and the period of a word can be computed in time proportional to the word length. We design an algorithm to compute the maximal exponent of all factors of an overlap-free word. Our algorithm runs in linear-time on a fixed-size alphabet, while a naive solution of the question would run in cubic time. The solution for non-overlap-free words derives from algorithms to compute all maximal repetitions, also called runs, occurring in the word.We also show there is a linear number of occurrences of maximal-exponent factors in an overlap-free word. Their maximal number lies between 0.66n and 2.25n in a word of length n. The algorithm can additionally locate all of them in linear time. 相似文献
PID control has widely used in the field of process control and a lot of methods have been used to design PID parameters.
When the characteristic values of a controlled object are changed due to a change over the years or disturbance, the skilled
operators observe the feature of the controlled responses and adjust the PID parameters using their knowledge and know-how,
and a lot of labors are required to do it. In this research, we design a learning type PID control system using the stochastic
automaton with learning function, namely learning automaton, which can autonomously adjust the control parameters updating
the state transition probability using relative amount of controlled error. We show the effectiveness of the proposed learning
type PID control system by simulations.
This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January
31–February 2, 2008 相似文献
This paper presents a system-theoretic approach to the general problem of autonomous planning under uncertainty. The autonomous planning problem involves an automaton (an autonomous machine) which interacts with an environment via a set of unreliable control and sensing operations. The task assigned to the automaton is to plan and execute a sequence of control and sensing operations which changes the state of the environment in a desirable way.
The paper introduces the concept of an Uncertainty Machine which models the propagation of the information from the environment to the automaton during the execution of the plans. Based on the concept of an uncertainty machine, mathematical expressions are presented for the active-sensing, the passive-sensing and the control (sensorless) entropies of an arbitrary execution instance. These entropies are shown to be useful measures of the automaton's ability to utilize its control and sensing resources in reducing its uncertainty.
In a companion paper,7 the concept of an uncertainty machine is utilized to synthesize strategies which enable the automaton to actively explore the environment. 相似文献