 -         
 


          DLAA,               ,      (C++, C#)             .        DLAA.    DLAA     ,   ,   ,     SysML  UML,  .. ,  DEVS.   ,           DLAA.





 

 -         



    

    

 ..

    

   -, -,    -

_____________________________________________________________________________



. . , . . , . . , . . 



 -          



  



         02.00.00             ,    :     ,      ,    



  2026

 519.713(075.8)

 22.182.373

 74

         :

..   -. , ..-.., ,    ;

..   ..., ...   ..



 . .,  . .,  . .,  . . 

 74

 -          :  / .. , .. , .. , .. .   : ;   -, 2026.  100 c.

ISBN  978-5-521-25037-0

https://doi.org/10.25559/978-5-521-25037-0



          DLAA[1 -  ..,  ..       DLAA //     -. 2025. . 21,  1. . 76-89. https://doi.org/10.25559/SITITO.021.202501.76-89; Gapanovich D.A., Sukhomlin V.A. Tools for Constructing Production Digital Twin Models Based on an Algebraic Approach and a Graphical State Language Extended by Functional and Operational Semantics // Mathematical Modeling and Supercomputer Technologies. MMST 2024. Communications in Computer and Information Science ; ed. by D. Balandin, K. Barkalov, I. Meyerov. Vol. 2363. Cham: Springer, 2025. P. 3-16. https://doi.org/10.1007/978-3-031-80457-1_1],               ,      (C#, C++)             .        DLAA.

   DLAA     ,   ,   ,     SysML  UML,  .. ,  DEVS.

  ,           DLAA, :  ,           ;  ,          DLAA; ,           ,  .     DLAA.

         -    ,        .



 :   , DLAA,  , - ,  ,  ,    , ,  ,  ,  .



    .Time and Space.       ,         -   ,      OSA     ,     .



 519.713(075.8)

 22.182.373



ISBN 978-5-521-25037-0                                                                         . .,  . .,  . .,  . ., 2026

   -, 2026





5

 1.                   7

1.1.          7

1.2.           9

1.3.        10

1.4.   ..       10

1.5.     SysML  UML      11

1.6. DEVS                  12

      15

 2.   DLAA,   ,          16

2.1.        16

2.2.      DLAA      17

 3.    DLAA      22

 4.   DLAA        26

 5.         29

 6.    DLAA.        32

6.1        32

6.2    DLAA      34

 7.     DLAA          43

7.1.  OSA      43

7.2.    DLAA      44

 8.          DLAA      48

8.1       DLAA      49

8.2                50

8.3         52

       54

 A      56

  AADL      56

       59

            59

       75

 ,         75







    4.0     ,  ,        ,          ,         ,           .

          (Digital Twin)   ,             ( , , :  ,  , , ,   ..).         , , -,           , -,         ,     -  (Cyber-Physical System - CPS)    ,   ,     [1, 2].

                 ,      .             :

   ,   ,    ,     .

               .

         (),      .

                          - ,     ,    .

               , :   ,     ,   (Statecharts) . , -   .. ,     SysML  UML, DEVS (Discrete-Event Modelling and Simulation)              .

         DLAA,         *.

           , ,   SysML, .     ,     ,     DLAA     .

                     DTA (Digital Twin Algebra)     [3],   ,                .

                DLAA,     ,   ,    .

       DLAA,        ,      .

         DLAA    .

         DLAA       , :      DLAA             (++),        OSA,             (++),   ,  .

 A.   AADL.

 .       .

 . .   .

 .    (   ).

 .








 1.             



                     .                   .




1.1.    


         [5, 6].      (   q0)        :

M = <A, B, Q, ?, ?, q


>

:

A          (  , ,   ),

B          (,     ),

Q            ( ),

?        : Q?A?Q

?       : Q?A?B

q


   q


.

    ,        : Q?A?B, ..        ,       ( ).       ,     ,    , ..    ?   : Q?B.

 ,  ,           ,        .       ,          ,      , ,         .    ,       ,    ?,  ,  , ,   -   .

      ,               [7].

  ,   ,      ,    .     ,    ?(q, a)    (q, a) ?Q ? A, ..  ?(q, a)= q   .

,   ,      , ..   ?(q, a)     

(q, a) ?Q ? A.

         ,   .     ,   ,    ,     -  Q,      E,    (  ).      ,     ,   .       E?A?B,        -   a?A    b?B.  ,    q   q?,    a,     q,  q?   a,           b= ?(q, a).

           ,     .

  M = <A, B, Q, ?, ?, q


>,  :

A={0, 1},

B={0, 1},

Q={q


, q


, q


},

{?(q


, 0)=q


, ?(q


, 1)=q


, ?(q


, 0)=q


, ?(q


, 1)=q


, ?(q


, 0)=q


, ?(q


, 1)=q


},

{?(q


, 0)=0, ?(q


, 1)=1, ?(q


, 0)=0, ?(q


, 1)=1, ?(q


, 0)=1, ?(q


, 1)=0,)}.

 ,       ,       .

 . 1    ,       ,   ,     .








 1.    ,      

              .                 .




1.2.     


                   [8].         ,     (Coupling Recipe)   - ,    .

         :

? = {??, ??, ??, ??, ??}, :

Z   

SZ    

IZ    

OZ     

NZ     (   ,          )

RZ    (),       .

  ,       ,        .

,      [9],         . 1,      Z* = RES(K)   K  Zi  i = {1-4}    ,   K.    /    Z1, Z2, Z3, Z4      Z* = RES(K),   . 2.








 2.    [9]

      ;                      .             ,     ,    ,      ,      .




1.3.  


.            (Statecharts),            ,      ,       [10].

         :

               (Clustering)  (   (XOR- decomposition))   (Superstate),

            (-  AND-decomposition,),    (orthogonality),    ,

   (communication)  ,   ,

   (refinement) ,

                     ,           ,

         .




1.4.   .. 


       (Statecharts)  ,   ,  ..  [11].          .      ,      ,    ,       .

     ,          (    ),       ,      .           ,          ,        (      ).          .             ,     .

         :

-        (   )       (   ),               Statecharts,           

-                   ,     

-           C    [12, 13]

-      ,   -  .


1.5.     

SysML

 

UML

  UML/SysML     (Finite State Machine)      (State Machine Diagram), ,   ,        ,       [14, 15].

     :

1)  ,    , :

,       ( entry),

,     ( do),

,      ( exit).

2) ,     ,       ,

3)     ,   ,   ,   ,

4)    ,         ,       -,      (      ),

5)      , ..         ,     ,   ,           (         ),

6) ,        ,        ,      (  ),    ,

7)        (-),

8)  ,          (Guards),      ,    ,

9)                       ,

10)    -      

11)      ,           ,    .


1.6. 

DEVS

           

DEVS (Discrete-Event Modelling and Simulation)              ,        [16, 17, 18, 19]. ,  DEVS      ,      , : , ,    ().

     DEVS,      .

 DEVS    :

(i)  ,     

(ii)  ,  ,      (     ) ,    

          (coupling)  DEVS [18].

  DEVS          ,          .     ,            .    ,     ,     .        (time advance function).          .

      .     :

1)    (S)

2)   (ta) (Time Advance)

    -  ,         ,         .       ,  .  DEVS    ,   ,    . (,        ,      ).

3)    (?


)

?


: S ? S

   ?





     ,        ,   .          (,        +?),      .

4)    (q


).

    ,      (s


),    ,       ,         .          (Elapsedtime),       .   ,         .

q


: (s, e)| s  S, 0=< e =<ta(s)

5)   (Y)

    ,    .         ,  ,    .      .   ,       .        ,    .

Y: ?








Y




6)   (?)

     .          (  ).  ,       , ..     .

      ,         ?, 

?: S ? Y ? {?}

7)   (X)   

 ,     ,       .

X = ?








X




8)   (?


)

      ,     .         ;     .   ,            (  ).           (. .    ),    .

    ,       .    ,   .    ,    ,   .

 ,          :

<X, Y, S, q


, ?


, ?


 ?, ta>

    DEVS   ,    ,    .     ,        .      .

        .

1)   (D)

    ,      :

(MS = {M


 |i?D})

2)   (MS),

 M





-


 i  .   ,   D,    ,   .

MS = {M


 |i ? D} = {<X


, Y


, S


, q


,


 , ?


 , ?


, ?


 , ta


> |i ? D}

     DEVF       DEVS    (abstract simulator),     .

 ,    DEVS      ( ,      ).

3)   (Model influencees) - (IS = {I


|i ? D ? {self }})

      ,     .       (influenceesets):        ,     .    ,      :       , ..        . ?i ? D : i < I


.      , ..            ,    ,        ,   ,             . ?i?D: I


?D.

 ,        :

<D, MS, IS>

,        ,        ,      .       Xself  Yself,      ,       5 :

<X


, Y


, D, MS, IS>

     DEVS:

4)     (select),       ,          .         ,     ,    .

select: 2


 ? D

5)   (ZS),       ,        .      ,          .

ZS = {Zi,j |i?D? {self }, j?Ii} 

     ,    .      ,         .

         :

<X


, Y


, D, MS, IS, ZS, select>







             ,                  .

          ,  DLAA,    , ,    ,        ,    .  ,                   .







 2.   

DLAA

,   ,    

         ,      .   ,     DLAA,   :

-       ,         (  ),

-     ,       ,

-          ,

-    ,     ,

-          ,           ,    ,               ,

-             -  ,        ,

-                 ,               ,

-        ( ,   ),

-      ,        .




2.1.  


  ,          .          ,    [3].

               , ..  , -,  ,      , , -,      (   ).  ,         -          .  ,   ,          .

         ,          ,        ,       (  ),    (),   . ,          ,  ,     ,     .

       ,       :      ,     .

   , -,         , , -,     .

         .


2.2.      

DLAA

     [3]           [19, 20].              .

         :      ,     .         * (  ),        DAVS [16, 17, ],      .

   * :

 1:     ,  *,    :

FSM=<Ex, Ey, E


, S, F, q





?





?





?








?


, Ta, TS>,       (1)

Ex      

Ey -     

E


={i, *, **} -    

S -   

F -    

q


 -   

?


-   

?


-   

?


-    

?


 -    

Ta      

TS


-   

        :

1)        (   )   (E).

2)     E      (Ex)   (Ey).

3)     :

i -   ,           ;

*     ,       () ;

** -    ,       .

4)        (?


)     :

?


: S ? S,  S    .

          ,  .       .      .    F.           .      ,     ,   ,          .           .

5)        (?


):

?


: SxEx ? S

              .             .

6)        (ta) (Time Advance)        DEVS [16, 17],         .        (    ),  ,      TS.   ,  ,    .

7)     DEVS         -     (?


)      (?


).    ,  ,     .

 ?


,  ,        ,      .   ,       , ,      ?.

 ?





 ( )     ?





 ,  ,    S,        E       **,       .

8)           ,       .          ,         .  ,                  ,    ,    ,    .        - *,         - **.

9)          TS





   ,    ,     ,     ,            .       ,    ,    , ,      .

      *         - ,  DLAA.                .

 2:             :

SM=< N, D, E, SPM, Q, TS, G, R>,       (2)



N -    SM (System_Model)

D = {d


} -  /   (FSM),    ,

i ? [1 - k],  k -  

E -      -     (  ) -  E=?(Ex


?Ey


), i?[1 - k],

SPM = {SP_FSM


} -   ,   ,  SP_FSM





-   d


?D,

FSM


=<Ex


, Ey


, E


, S


, F


, q








 ?











?








 ?








?





, Ta


, TS>,

Q={S


} -      

TS -   ,

G     S (      ) -   ,

R -    (      ) -   .

         (*)      ,         DLAA (Diagrams Language of Automata Algebra).     ,      ,       .

             . ,            .  ,         ,      .

 ,  wait/signal,     () , , ,  ,    ,    ,    .       x     (,      ),                .         (wait)      ,     (signal), .. t


 < t


.-     x.

     ,     ,    - x.    ,            (,    ).      -        , .. [t


, t


) -     x.

                    - ,   , ..          .       .  ,       ,        ,    .

 ,      S  A   wait   x, ,   A     ?


   ?


(S, x)=S,       S    (Ta(S)=?).          x     wait/signal.

        x  -      ?


     , ..  ?


(S, x)=S,       x   [t


, t


).

 ,  ,    ,        .      ,    .       ,       *      ,     .

           , ..     ,  ,   .

 ,       DLAA,     ,    ,     .




  .


   .

   ,     (https://www.litres.ru/book/vladimir-aleksandrov-33429295/modelirovanie-diskretno-sobytiinykh-sistem-sredstvami-74532817/)  .

      Visa, MasterCard, Maestro,    ,   ,     ,  PayPal, WebMoney, ., QIWI ,       .



notes








1


 ..,  ..       DLAA //     -. 2025. . 21,  1. . 76-89. https://doi.org/10.25559/SITITO.021.202501.76-89; Gapanovich D.A., Sukhomlin V.A. Tools for Constructing Production Digital Twin Models Based on an Algebraic Approach and a Graphical State Language Extended by Functional and Operational Semantics // Mathematical Modeling and Supercomputer Technologies. MMST 2024. Communications in Computer and Information Science ; ed. by D. Balandin, K. Barkalov, I. Meyerov. Vol. 2363. Cham: Springer, 2025. P. 3-16. https://doi.org/10.1007/978-3-031-80457-1_1


