Derivation of the cascade parallel composition of timed finite state machines using BALM-II

The paper considers the problem of deriving a cascade parallel composition of timed finite state machines (TFSMs). It can be reduced to a step-by-step derivation of a binary parallel composition. It is known that if each component of the binary parallel composition is a TFSM with constant output delays, then the composition can result in a TFSM with an infinite set of output delays given by a finite set of linear functions. Therefore, the problem of deriving a cascade composition of TFSMs with constant output delays is reduced to deriving a series of binary parallel compositions of TFSMs with output delays given either as constants or as a set of linear functions. In this paper, we refine the definition of the TFSM with particular attention to the description of the output delay. BALM-II is used as an instrument for deriving the composition. Therefore, we consider the transition from a TFSM with output delays given as a set of linear functions to the corresponding automaton. We propose a new procedure for deriving an automaton. Unlike the known procedure, it does not require subsequent determinization of the derived automaton. In addition, we provide a step-by-step description of how to derive the composition of the corresponding automata using BALM-II, discuss the procedure of reverse transformation from the automaton of the composition to the TFSM, and note some aspects associated with the composition of TFSMs with output delays as a set of linear functions. An example that illustrates the derivation of the cascade parallel composition of TFSMs is given

Derivation of the cascade parallel composition of timed finite state machines using BALM-II

The paper considers the problem of deriving a cascade parallel composition of timed finite state machines (TFSMs). It can be reduced to a step-by-step derivation of a binary parallel composition. It is known that if each component of the binary parallel composition is a TFSM with constant output delays, then the composition can result in a TFSM with an infinite set of output delays given by a finite set of linear functions. Therefore, the problem of deriving a cascade composition of TFSMs with constant output delays is reduced to deriving a series of binary parallel compositions of TFSMs with output delays given either as constants or as a set of linear functions. In this paper, we refine the definition of the TFSM with particular attention to the description of the output delay. BALM-II is used as an instrument for deriving the composition. Therefore, we consider the transition from a TFSM with output delays given as a set of linear functions to the corresponding automaton. We propose a new procedure for deriving an automaton. Unlike the known procedure, it does not require subsequent determinization of the derived automaton. In addition, we provide a step-by-step description of how to derive the composition of the corresponding automata using BALM-II, discuss the procedure of reverse transformation from the automaton of the composition to the TFSM, and note some aspects associated with the composition of TFSMs with output delays as a set of linear functions. An example that illustrates the derivation of the cascade parallel composition of TFSMs is given