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      A virtual finite-state machine (VFSM) is a finite-state machine (FSM) defined in a virtual environment. 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.
      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.


      Why


      Implementing a state machine necessitates the generation of logical conditions (state transition conditions and action conditions). 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:

      Temperature could be Low, OK, High
      Commands may have several values: Init, Start, Stop, Break, Continue
      In a hierarchical control system the subordinate state machines can have many states that are used as conditions of the superior state machine
      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


      A state 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 or RUNNING.


      Actions


      Other state variables 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.


      Virtual environment



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

      input names represent the control properties of all available variables
      output names represent the available actions on the variables
      state names, as defined for each of the states of the FSM.
      The input names build virtual conditions to perform state transitions or input actions. The virtual conditions are built using the positive logic algebra. The output names trigger actions; entry actions, exit actions, input actions or transition actions.


      Positive logic algebra


      The rules to build a virtual condition are as follows:


      = Input names and virtual input

      =
      A state of an input is described by Input Names which create a set:

      input A: Anames = {A1, A2, A3}
      input B: Bnames = {B1, B2}
      input C: Cnames = {C1, C2, C3, C4, C5}
      etc.
      Virtual input VI is a set of mutually exclusive elements of input names. A VI always contains the element always:

      VI = {always}
      VI = {always, A1}
      VI = {always, A1, B2, C4}


      = Logical operations on input names

      =
      & (AND) operation is a set of input names:
      A1 & B3 & C2 => {A1, B3, C2}

      | (OR) operation is a table of sets of input names:
      A1 | B3 | C2 =>





      [



      {


      A
      1


      }




      {


      B
      3


      }




      {


      C
      2


      }



      ]




      {\displaystyle {\begin{bmatrix}\{&A1&\}\\\{&B3&\}\\\{&C2&\}\\\end{bmatrix}}}


      ~ (Complement) is a complement of a set of input names:
      ~A2 = {A1, A3}


      = Logical expression

      =
      A logical expression is an OR-table of AND-sets (a disjunctive normal form):
      A1 & B3 | A1 & B2 & C4 | C2 =>





      [



      {


      A
      1


      B
      3


      }




      {


      A
      1


      B
      2


      C
      4


      }




      {


      C
      2


      }



      ]




      {\displaystyle {\begin{bmatrix}\{&A1&B3&\}\\\{&A1&B2&C4&\}\\\{&C2&\}\\\end{bmatrix}}}


      Logical expressions are used to express any logical function.


      = Evaluation of a logical expression

      =
      The logical value (true, false) of a logical expression is calculated by testing whether any of the AND-sets in the OR-table is a subset of VI.


      = Output names and virtual output

      =
      A state of an output is described by Output Names which create a set:

      output X: Xnames = {X1, X2}
      output Y: Ynames = {Y1, Y2, Y3}
      Virtual output VO is a set of mutually exclusive elements of output names.


      = Virtual environment

      =
      The Virtual Name and Virtual Output completed by State Names create the Virtual Environment VE where the behaviour is specified.


      VFSM execution model



      A subset of all defined input names, which can exist only in a certain situation, is called virtual input or 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 or VO. This is built by the current action(s) of the VFSM.
      The behavior specification is built by a state table which describes all details of all states of the VFSM.
      The VFSM executor is triggered by VI and the current state of the VFSM. In consideration of the behavior 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 behavior characteristics must be considered.


      State table



      A state table defines all details of the behavior of a state of a VFSM. 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. 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 cases only where input actions are used, but no state transitions are defined. The transition action can be replaced by the proper use of other actions.


      Tools


      StateWORKS: an implementation of the VFSM concept
      PlayMaker: implements the VFSM concept as a method of "visual scripting" the Unity game engine


      References


      Wagner, F., "The Virtual Finite State Machines: Executable Control Flow Specification", Rosa Fischer-Löw Verlag, 1994, ISBN 3-929465-04-3
      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
      State machine misunderstandings, IEE journal "Computing and Control Engineering", 1997
      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
      [1], Wagner, T., "VFSMML - XML standard for VFSM", 2004

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    Virtual finite-state machine - Wikipedia

    A virtual finite-state machine (VFSM) is a finite-state machine (FSM) defined in a virtual environment. The VFSM concept provides a software specification method to describe the behaviour of a control system using assigned names of …

    Virtual Finite State Machine - StateWORKS

    A virtual finite state machine (VFSM) is a finite state machine defined in a virtual environment. The virtual environment is created by three sets of names: input names, output names and state names. The input and output names can be transferred by a …

    The Virtual Finite-State Machine Design and Implementation …

    This paper discusses the virtual finite-state machine (VFSM) design and implementa- tion paradigm and our experience in introducing VFSM on software development projects for several Lucent Technologies products.

    Papers - StateWORKS

    The paper presents a software design method based on the virtual finite state machine (VFSM) concept. The concept defines a virtual environment that allows the finite state machine to be an entire table driven software module. A hybrid finite state model is …

    Virtual State Machines in Cellular Automata - Wolfram

    Feb 1, 2018 · A finite state machine (FSM) consists of a finite set of states E, a finite input alphabet a, and a transition function !'> that maps a (state,input) pair to the next state: !'>: (E x c] -+ E.

    The virtual finite state machine - Open Library

    The virtual finite state machine executable control flow specification by Ferdinand Wagner

    VFSM executable specification | IEEE Conference Publication

    May 8, 1992 · A software design method is presented, based on a virtual finite state machine (VFSM) concept. The concept defines a virtual environment that allows the finite state machine to be an entirely table driven software module. A hybrid finite state model is used to achieve a superior design clarity.

    Misunderstandings about state machines | StateWORKS

    A virtual finite state machine (VFSM) is a state machine which operates in a virtual environment. This virtual environment (VI) is created defining all control-relevant information about inputs and outputs of a control system.

    Finite State Machine Meaning, Working, and Examples - Spiceworks

    Sep 12, 2023 · Finite state machines provide a systematic way of controlling and managing systems with discrete and sequential behavior. By defining states, transitions, and output actions, FSMs allow for clear and structured design and analysis of complex systems, making them easier to understand and implement.

    The virtual finite-state machine design and implementation …

    This paper discusses the virtual finite-state machine (VFSM) design and implementation paradigm and our experience in introducing VFSM on software development projects for several Lucent Technologies products.