Abstract
This paper addresses the problem of minimizing a Finite State Machine (FSM) augmented with input and output timeouts, since almost all methods for deriving complete test suites are developed for reduced (minimal) timed machines, i.e., FSMs where every two states are not equivalent. If at some state no input is applied until the corresponding (input) timeout expires then the FSM can spontaneously move to another prescribed state. An output timeout describes the time that is necessary for executing a transition that is the number of time instances needed for producing an output after an input has been applied. A technique for minimizing such machines based on corresponding classical FSMs is proposed; it is also shown that differently from classical FSMs, an FSM with timeouts can have minimal forms which are not pair-wise isomorphic.
Highlights
This paper addresses the problem of minimizing a Finite State Machine (FSM) augmented with input and output timeouts, since almost all methods for deriving complete test suites are developed for reduced timed machines, i.e., FSMs where every two states are not equivalent
If at some state no input is applied until the corresponding timeout expires the FSM can spontaneously move to another prescribed state
An output timeout describes the time that is necessary for executing a transition that is the number of time instances needed for producing an output after an input has been applied
Summary
Модель конечного автомата широко используются при анализе и синтезе дискретных систем. Однако в ряде случаев при описании поведения реальных систем необходимо учитывать временные аспекты, и соответственно, понятие конечного автомата необходимо расширить. Известно несколько способов введения временной переменной в конечный автомат [1, 2]. Поскольку сложность решения многих задач в теории автоматов существенно зависит от числа состояний рассматриваемого автомата, большое внимание уделяется задаче минимизации временного автомата, т. Е. построению эквивалентного автомата с наименьшим числом состояний. В данной работе мы предлагаем алгоритм минимизации конечного автомата с входными и выходными таймаутами
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