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# å½¢å¼åŒ–æ–¹æ³•0051

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5.2 Temporal Logic          In this chapter, we introduce the language of temporal logic as a tool for the specification of reactive systems. By specification we mean the description of the desired behavior or operation of the system, while avoiding references to the method or details of its implementation.

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Viewing a program as a generator of a set of computations. The language of temporal logic defines predicates over infinite sequences of states. Thus each formula of temporal logic is satisfied by some sequences and falsified by some other sequences. Interpreted over a computation, such a formula expresses a property of the computation.
Example Consider a program P implementing  mutual exclusion between processes P1  and P2.  p 0 :   For all states of the computation, it is  never  the case that P1 and P2 occupy  their critical sections at the same state. p 1 :   If a computation  σ  contains a state at  position j 0 in which P1 is waiting to  enter.

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the critical section, then  σ  also contains a state  at a position   j  in which P 1 is inside the  critical section. That is, whenever P wishes to  enter its critical section, it will eventually do so. p 2 : The same requirement as p 1  but for process  P 2 . These properties are true of some sequences  and false of others.
If a property  p  is true of all computations  generated by a program P, then we call  p  a  valid property  of P. If p 0 , p 1 , p 2  are valid properties of a program  P, then P should be considered an  acceptable  solution to the mutual exclusion  program. This suggests that the set of properties p 0 p 1 , p 2  can be viewed as a  specification  of the  mutual exclusion  program.

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P   Satisfies   p 0  p  p 2  . We may view a property ( a set of  properties) as a  specification  for a  program.  It specifies any program all of whose  computations satisfy (or have) the  property.
Let  sat(p)  be the set of all sequences  that satisfy property  and  (P)  the  set of all sequences that are  computations of P.  We say that P implements the  specification   p , or P satisfies  p  , if  the set of computation of P is  contained in the set of sequences  satisfying  , i.e.,                             (P)     sat(p)  .

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State Formulas A state formula can be evaluated at a  certain position   0  in a sequence, and it  expresses properties of the state  s occurring at this position.  State Language Vocabulary  :  a countable set of typed  variables; Data variables ( booleans,  integers, lists, and sets.); Control variables  ( values locations in programs).
Other Symbols

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