Abstract
State identification is the well-known problem in the theory of Finite State Machines (FSM) where homing sequences (HS) are used for the identification of a current FSM state, and this fact is widely used in the area of software and hardware testing and verification. For various kinds of FSMs, such as partial, complete, deterministic, non-deterministic, there exist sufficient and necessary conditions for the existence ofpreset and adaptive HS and algorithms for their derivation. Nowadays timed aspects become very important for hardware and software systems and for this reason classical FSMs are extended by clock variables. In this work, we address the problem of checking the existence and derivation of homing sequences for FSMs with timed guards and show that the length estimation for timed homing sequence coincides with that for untimed FSM. The investigation is based on the FSM abstraction of a Timed FSM, i.e. on a classical FSM which describes behavior of corresponding TFSM and inherits some of its properties. When solving state identification problems for timed FSMs, the existing FSM abstraction is properly optimized.
Highlights
State identi cation is the well-known problem in the theory of Finite State Machines (FSM) where homing sequences (HS) are used for the identi cation of a current FSM state, and this fact is widely used in the area of so ware and hardware testing and veri cation
Nowadays timed aspects become very important for hardware and so ware systems and for this reason classical FSMs are extended by clock variables
We address the problem of checking the existence and derivation of homing sequences for FSMs with timed guards and show that the length estimation for timed homing sequence coincides with that for untimed FSM. e investigation is based on the FSM abstraction of a Timed FSM, i.e. on a classical FSM which describes behavior of corresponding TFSM and inherits some of its properties
Summary
Если в автомате P для любой пары ( , ) ∈ × существует переход ( , , , ′) ∈ hP, то автомат называется полностью определённым, иначе – частичным. Если в автомате P для любой пары ( , ) ∈ × существует не более одного перехода ( , , , ′) ∈ hP, то автомат называется детерминированным, иначе – недетерминированным. / в состоянии 1 называется вход-выходной последовательностью в состоянии 1, если в P существует соответствующая последовательность переходов ( 1, 1, 1, 2), ( 2, 2, 2, 3), . Вход-выходная последовательность в этом случае может быть обозначена как / , и в автомате существует переход ( 1, , , +1). Для состояния p и вход-выходной пары / вводится понятие / -преемника состояния p: / преемник состояния p в автомате P содержит каждое состояние ′ такое, что в автомате существует переход ( , , , ′).
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