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A finite state machine (FSM) defined in a virtual environment is called virtual finite state machine (VFSM). VFSM is a software specification method used to describe the behaviour of a control system using assigned names of input control properties and of output actions.

The VFSM method introduces an execution model and facilitates the idea of an executable specification. This technology is mainly used in complex machine control, instrumentation and telecommunication applications.

Contents 1 Control Properties 2 Actions 3 Virtual Environment 4 Positive Logic Algebra 5 VFSM Execution Model 6 State Table 7 Tools 8 References

A variable in the VFSM environment may have one or more values which are relevant for the control – in such a case it is an input variable. Those values are the control properties of this variable. Control properties are not necessarily specific data values but are rather certain states of the variable. For instance, a digital variable could provide three control properties: TRUE, FALSE and UNKNOWN according to its possible boolean values. A numerical (analog) input variable has control properties such as: LOW, HIGH, OK, BAD, UNKNOWN according to its range of desired values. A timer can have its OVER state (time-out occurred) as its most significant control value; other values could be STOPPED, RUNNING etc...

A variable in the VFSM environment may be activated by actions - in such a case it is an output variable. For instance, a digital output has two actions: True and False. A numerical (analog) output variable has an action: Set. A timer which is both: an input and output variable can be triggered by actions like: Start, Stop or Reset.

The virtual environment characterises the environment in which a VFSM operates. It is defined by three sets of names:

• input names, represented by the control properties of all available variables
• output names, represented by all the available actions on the variables
• state names, as defined for each of the states of the FSM.

The input names are used to build virtual conditions to perform state transitions or input actions. The virtual conditions are built using the positive logic algebra. The output names are used to trigger actions (entry actions, exit actions, input actions or transition actions).

To build a virtual condition using input names the boolean operations AND and OR are allowed. The NOT operator is not possible because the input names can not be negated, even when they apparently describe boolean values. They simply exist or not.

A subset of all defined input names, which can exist only in a certain situation, is called virtual input (VI). For instance temperature can be either "too low", "good" or "too high". Although there are three input names defined, only one of them can exist in a real situation. This one builds the VI.

A subset of all defined output names, which can exist only in a certain situation is called virtual output (VO). VO is built by the current action(s) of the VFSM.

The behaviour specification is built by a state table which describes all details of a single state of the VFSM.

The VFSM executor is triggered by VI and the current state of the VFSM. In consideration of the behaviour specification of the current state, the VO is set.

Figure 2 shows one possible implementation of a VFSM executor. Based on this implementation a typical behaviour characteristics must be considered.

main page: state transition table.

A state table defines all details of the behaviour of a state of a VFSM. It consists of three columns: in the first column state names are used, in the second the virtual conditions built out of input names using the positive logic algebra are placed and in the third column the output names appear:

State Name	Condition(s)	Actions(s)
Current state	Entry action	Output name(s)
	Exit action	Output name(s)
	Virtual condition	Output name(s)
	...	...
Next state name	Virtual condition	Output name(s)
Next state name	Virtual condition	Output name(s)
...	...	...

Read the table as following: the first two lines define the entry and exit actions of the current state. The following lines which do not provide the next state represent the input actions. Finally the lines providing the next state represent the state transition conditions and transition actions. All fields are optional. A pure combinatorial VFSM is possible in case only input actions are used, but no state transitions are defined. The transition action can be replaced by the proper use of other actions.

• StateWORKS: an implementation of the VFSM concept

• Wagner, F., "Modeling Software with Finite State Machines: A Practical Approach", Auerbach Publications, 2006, ISBN 0-8493-8086-3
• VFSM Executable Specification, CompEuro 1992 Proceedings
• The Virtual Finite State Machine Design and Implementation Paradigm, Bell Labs Technical Journal, 1997
• A Modern Real-Time Software Design Tool: Applying Lessons from Leo, IEE journal "Computing and Control Engineering", 2003
• Modelling and Building Reliable, Re-usable Software., Engineering of Computer -Based Software 2003 (ECBS'03) Proceedings
• Closing the Gap Between Software Modelling and Code, Engineering of Computer -Based Software 2004 (ECBS'04) Proceedings
• State machine misunderstandings, IEE journal "Computing and Control Engineering", 2004