Table of Contents Previous Chapter NOTATIONS

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i, j, k, l, m, n,    general indices;                                                
t                                                                                    
a                    an arrow;                                                       
B(OA)                behavior function of atomic objects;                            
B(OC)                behavior function of container objects;                         
c                    a color;                                                        
ctk                  a container token;                                              
C                    a finite non-empty set of token colors;                         
CP                   a control place;                                                
ds                   a data type;                                                    
dsij                 port place j of data type i;                                    
dsfi                 Petri nets representation of dsi;                               
D                    linear transition time function;                                
DS                   a finite set of data types;                                     
DSF                  a finite set of Petri nets representations of DS;               
e                    a component box;                                                
E                    a set of edges, branches;                                       
I-                   input function;                                                 
I+                   output function;                                                
IP                   input function, <lni, pij>;                                     
l                    a label, which is a set of tokens;                              
L                    a finite non-empty set of labels;                               
ln                   a link, which is defined as <oi, lk, oj>;                       
LF                   mapping function of input and output links;                     
LN                   a finite non-empty set of links;                                
LN-                  a finite set of input links;                                    
LN+                  a finite set of output links;                                   
m                    a marking                                                       
mb                   a message buffer;                                               
md                   a message dispatcher;                                           
ms                   a self-manipulated method;                                      
mbf                  a Petri nets representation of message buffer mb;               
mdf                  a Petri nets representation of message dispatcher md;           
M                    a finite non-empty set of methods;                              
MC                   a finite non-empty set of object control methods;               
MI                   a set of messages that an object can receive;                   
MO                   a set of messages that an object can send;                      
o                    an object;                                                      
oa                   an atomic object;                                               
oc                   a container object;                                             
OA                   a finite non-empty set of atomic objects;                       
OC                   s finite none-empty set of container objects;                   
OP                   output function, <poi, lnj>;                                    
OS                   an object structure                                             
p                    a place;                                                        
pi                   an input place;                                                 
po                   an output place;                                                
post(t)              a post-condition of the transition t;                           
pre(t)               a pre-condition of the transition t;                            
ptk                  a primitive token;                                              
P                    a finite non-empty set of places;                               
PI                   a set of input places;                                          
PO                   a set of output places;                                         
R                    a finite non-empty set of firing operations;                    
RM                   is a one-to-one request mapping function between MO and M;      
RP                   a mapping function between a place in a method and the corre    
                     sponding link;                                                  
SM                   is a one-to-one service mapping function between MI and M;      
SP                   a mapping function between an input link and the place in the   
                     method;                                                         
t                    a transition;                                                   
tk                   a token;                                                        
T                    a finite non-empty set of transitions;                          
TTK(p, tk)           token time stamp;                                               
V                    a set of nodes, objects;                                        
~                    a transition with 0 time delay between parts in an object;      
t                    token time stamp;                                               
D                                                 time;                              
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