Abstract
Trace models such as Finite State Machines (FSMs) are widely used in the area of analysis and synthesis of discrete event systems. FSM minimization is a well-known optimization problem which allows to reduce the number of FSM states by deriving the canonical form that is unique up to isomorphism. In particular, the latter is a base for FSM-based ‘black-box’ test derivation methods such as W-method and its modifications. Since nowadays the behavior of many software and hardware systems significantly depends on time aspects, classical FSMs are extended by clock variables including input and output timeouts. The minimization of a Timed Finite State Machine (TFSM) includes both state and time aspects reduction. Existing approaches allow to derive the canonical representation for non-initialized deterministic TFSMs while for initialized TFSMs, i.e., TFSMs with the designated initial state, several pair-wise non-isomorphic minimal forms can exist. In this paper, we determine initialized TFSM classes for which the minimal form is unique up to isomorphism.
Highlights
Finite State Machines (FSM) [1, 2] are widely used for synthesis and analysis of discrete components of telecommunication and other hardware and software systems [3, 4, 5]
In this work, we have investigated the uniqueness of the minimal form for initialized FSMs with timeouts
The first class contains initialized timed FSM (TFSM) for which all states are reachable from initial state under a timed input sequence
Summary
Finite State Machines (FSM) [1, 2] are widely used for synthesis and analysis of discrete components of telecommunication and other hardware and software systems [3, 4, 5]. From classical FSMs, a timed FSM can have several non-isomorphic state reduced forms and time aspects should be taken into account when minimizing a TFSM. Such minimal form is not unique for an initialized complete FSM with timeouts while such machines are widely used for modeling timed systems with a reliable reset signal. 125-134 techniques are developed for initialized FSMs and the absence of the unique reduced form for Timed FSMs do not allow to directly apply W-methods and its derivatives to initialized TFSMs [14]. We determine classes of initialized FSMs with timeouts for which the unique minimal form can be derived.
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