Virtual finite-state machine
The VFSM concept provides a software specification method to describe the behaviour of a control system using assigned names of input control properties and output actions.
This technology is mainly used in complex machine control, instrumentation, and telecommunication applications.
In the hardware environment, where state machines found their original use, this is trivial: all signals are Boolean.
In contrast state machines specified and implemented in software require logical conditions that are per se multivalued: In addition input signals can be unknown due to errors or malfunctions, meaning even digital input signals (considered as classical Boolean values) are in fact 3 values: Low, High, Unknown.
A Positive Logical Algebra solves this problem via virtualization, by creating a Virtual Environment which allows specification of state machines for software using multivalued variables.
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 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 conditions are built using the positive logic algebra.
A logical expression is an OR-table of AND-sets (a disjunctive normal form):
In consideration of the behavior specification of the current state, the VO is set.
It consists of three columns; the first column names the state, the second lists virtual conditions built out of input names using the positive logic algebra, and the third column contains the output names: Read the table as following: the first two lines define the entry and exit actions of the current state.
A pure combinatorial VFSM is possible in cases only where input actions are used, but no state transitions are defined.
