Real - time Systems

ion The hiding operator P n A makes the events in the set A internal to the process, thus removing them from the control of the environment. The only participants will then be the components of P. From the maximal progress assumption, the internal events will occur as soon as P is ready to perform them. In general, internal events occur as soon as they are ready, unless they are pre-empted because of conflict, such as when there is a choice between events. A print spooler SPOOL and PRINTER communicate via channel print: SPOOL = in 2 ! print 3 ! SPOOL PRINTER = print 30 ! out! PRINTER The parallel combination SPOOL j[ in;print jprint;out ]j PRINTER has print as a visible channel and further processes may participate in it. Since only SPOOL and PRINTER should participate in that synchronization, we make print internal: (SPOOL j[ in;print jprint;out ]j PRINTER) n print 6.1. THE LANGUAGE OF REAL-TIME CSP 153 and the event print will occur as soon as both processes are ready to perform it. The renaming operators f (P) and f 1(P) change the names of events through the alphabet mapping function f . This allows a generic pattern of communication to be defined for use with different events. For example, a waiter responsible for table i might be described by a generic WAITER process and a renaming fi which maps any event a to ai. Thus f1(WAITER) is prepared to show a customer to table 1, but to no other table. Renaming using the inverse function f 1 allows a number of events to trigger a particular communication. If function g has g(credit card) = pay and g(cash) = pay, then the process g 1(WAITER) is prepared to engage in a credit card event or a cash event whenever WAITER is prepared to accept a pay event. The function h satisfying h(tablei) = table allows h 1(WAITER) to show a customer to any table: g (WAITER) = table 2 ! coat 5 ! order 20 ! serve 30 ! (credit card 0:01 ! tip 3 ! coat! SKIP 2 cash 0:01 ! tip 3 ! coat! SKIP) h 1(WAITER) = (table1 2 ! coat 5 ! order 20 ! serve 30 ! credit card 0:01 ! tip 3 ! coat! SKIP) 2 (table2 2 ! coat 5 ! order 20 ! serve 30 ! credit card 0:01 ! tip 3 ! coat! SKIP) .. 2 (tablen 2 ! coat 5 ! order 20 ! serve 30 ! credit card 0:01 ! tip 3 ! coat! SKIP) Recursion A recursive term μX P behaves as P, with every occurrence of X in P representing an immediate recursive invocation. Thus we will have the usual law