07/06/98 知的インタフェース特論 1 Operational Semantics Again, the question? Operational Model = Labeled Transition System If P and Q yields a same LTS. How to define.

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Presentation transcript:

07/06/98 知的インタフェース特論 1 Operational Semantics Again, the question? Operational Model = Labeled Transition System If P and Q yields a same LTS. How to define LTS formally This semantics is not abstract enough Equivalences over LTS

07/06/98 知的インタフェース特論 2 Structural Operational Semantics SOS = How to define an LTS formally along with the calculus. If holds for all I, holds.

07/06/98 知的インタフェース特論 3 SOS for Process Languages : Term constructed by : Set of actions This rule (partially) defines the semantics of f.

07/06/98 知的インタフェース特論 4 SOS rules for CSP

07/06/98 知的インタフェース特論 5 SOS rules for CSP (Cnt’d)

07/06/98 知的インタフェース特論 6 SOS rules for CSP (Cnt’d) Or empty

07/06/98 知的インタフェース特論 7 SOS rules for CSP (Cnt’d)

07/06/98 知的インタフェース特論 8 How Concrete is LTS? The operational semantics of P : LTS(P) Thus, P=Q iff LTS(P)=LTS(Q) LTS(P)=LTS(Q) iff State is labeled by an expression No abstraction for empty labeled transition

07/06/98 知的インタフェース特論 9 Unwanted Difference aa Both behave same, but different.

07/06/98 知的インタフェース特論 10 Equivalences over LTS Bisimulation (Park, 1981) A relation R over states is a bisimulation if implies p R q R a a

07/06/98 知的インタフェース特論 11 Bisimulation Equivalence Generally, bisimulation is not an equivalence, since the empty relation satisfies the condition. The largest bisimulation is suitable for the behavior definition. is a strong bisimulation is an equivalence. Show this by proving the reflexitity, the asymetricity, and the transitivity.

07/06/98 知的インタフェース特論 12 But, bisimulation is still too concrete d dc bb aa a bb c P Q P is NOT bisimulation equivalent to Q, but P is Failures/Divergent equivalent to Q.

07/06/98 知的インタフェース特論 13 Full Abstractness Thus, the bisimulation equivalence is not fully abstract to F/D model. F/D model is more abstract than the bisimulation equivalence. For convergent processes, F/D model is fully abstract to Testing Equivalence. (DeNicola and Hennessy, 1988)

07/06/98 知的インタフェース特論 14 Other Topics Other Calculus and Semantics (complete) Axiomatization Time Probability Meta-theory Make this model more usable!! There is a large/big/wide gap between the reality and the theories.

07/06/98 知的インタフェース特論 15 Summary We have been discussing: The Communicating Process Model Hoare’s CSP (1978, 1985) Which is a calculus to express A theoretical framework for concurrency. In the theory, concurrency is captured as a theory of non-determinism. Similar investigation by Milner(CCS), Baeten(ACP), and many more….