K.G. Larsen. A context dependent equivalence between processes. Theoretical Computer Science, 49:185--215, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....than semantically as we have done in the current paper. Among many advantages, this would allow fault tolerance to 11 be verified automatically, e.g. using [RCS93] We would also like to study the use of other bisimilarity like relations, like the partial [Mil81, Wal90] and the context dependent [Lar86, Lar87] bisimilarities, for fault tolerance. By constraining transitions which a process can undergo in a given context, the latter can be seen as complementary to F bisimilarities which provide additional, faulty transitions for a process to perform. Acknowledgements I am indebted to my supervisor, ....

K.G. Larsen. A context dependent equivalence between processes. Theoretical Computer Science, 49:185--215, 1987.

....from its behaviour in the absence of faults, a correctness condition is necessary. The correctness criterion distinguishes faulty behaviour from non faulty behaviour. When relating two processes only the correct behaviour needs to be matched. This indicates the need for an indexed relation. [16] introduces the idea of equivalences induced by contexts called relativised bisimulation. For example, P OE C Q relates the behaviours of P and Q in the context C. We use this idea with a different interpretation in developing the fault preorders. The preorders we consider do not directly deal ....

K. G. Larsen. A Context Dependent Equivalence Between Processes. Theoretical Computer Science, 49:185--215, 1987.

....# doneg Since the go i can be heard both by p i and by b i or d i , there is no need to relay the information by new signals. The following relation is a strong bisimulation upto , and so OEs 0 OE (s (1; The example suggests work on the notion equivalent in a context , studied for CCS in [Lar87]. nD OE (s (i; X) OE i i c j Q j2X;j 6=i j b j Q j = 2X j d jE fi fi fi i 2 X o [ nD OE (s (i; X) OE i i a j Q j = 2X;j 6=i j d j Q j2X j b jE fi fi fi i = 2 X o In a communication model that has to relay the go i s, the bisimulation would be weak. 21 ....

Kim Larsen. A context-dependent equivalence between processes. Theoretical Computer Science, 49, 1987.

....of faults, and conditional, given the maximal number of times they can occur successively. There is a number of directions that we plan to develop this work. We plan to study the use of other bisimulation like relations, like the partial [Wal90] the terminating [AH92] and the context dependent [Lar87] bisimilarities for fault tolerance. In the presence of faulty transitions, a convergent process may diverge and the one which terminates (successfully) may deadlock. We plan to relate our theory with modal specifications [LT88] which constrain possible implementations by two kinds of transitions, ....

K.G. Larsen. A context dependent equivalence between processes. Theoretical Computer Science, 49:185--215, 1987.

....be relevant. Our proof technique based on polymorphic types yields a simple proof of equivalence between processes whose untyped behaviors have incomparable sets of traces. Proof techniques with this property are rare in the literature. Perhaps the best known is Larsen s relativised bisimulation [Lar87]; indeed, our method can be seen as a disciplined instance of Larsen s, in which one uses types to express constraints on the behaviors of the observers, rather than explicitly writing all their possible behaviors. RR n Sigma3042 26 Benjamin C. Pierce , Davide Sangiorgi 11 Discussion We close ....

K. G. Larsen. A context dependent equivalence between processes. Theoretical Computer Science, 49:185215, 1987.

....may be relevant. Our proof techniques based on polymorphic types yield proofs of equivalence between processes whose untyped behaviors have incomparable sets of traces. Proof techniques with this property are rare in the literature. Perhaps the best known is Larsen s relativized bisimulation [Lar87]; indeed, our method can be seen as a disciplined instance of Larsen s, in which one uses types to express constraints on the behaviors of the observers, rather than explicitly writing all their possible behaviors. Types allow a more compact representation of the constraints, and hence proof ....

K. G. Larsen. A context dependent equivalence between processes. Theoretical Computer Science, 49:185--215, 1987.

....Corollary 11. S 1 F S 2 implies F [S 1 ] E F [S 2 ] 3.1 A discrimination ordering on programs Once we have a context sensitive notion of approximation, it seems natural to attempt to distinguish contexts with respect to their discriminating power. For CCS, for example, this was done in [Lar87]. The program F 1 j ( tt; Var : tt; tt] for instance, can do any transition at any time. The program F 2 j ( tt; inv x) however, can only do those transitions that leave the value of x unchanged. Every approximation that holds with respect to F 1 will also hold with respect to F 2 , ....

....local(F ) or augmenting the set of initial states init(F ) or the capabilities of the statement stmt(F ) makes F more discriminating. Proposition 14. 1: L; I ; S) v (L 0 ; I ; S) iff L 0 L 2: L; I ; S) v (L; I 0 ; S) iff I ) I 0 3: L; I ; S) v (L; I ; S 0 ) if S C S 0 In [Lar87], Larsen introduces a discrimination ordering on CCS contexts and presents a characterization result. Unfortunately, the fairness requirement prevented us from obtaining a similar result for our setting. Note, however, that Proposition 14.3 can be strengthened to an equivalence in case S 1 and S 2 ....

K. G. Larsen. A context dependent equivalence between processes. Theoretical Computer Science, 49(2):185--216, 1987.

.... such as CCS [19] and CSP [11] operational semantics can be given by structural inference rules [24] as labeled transition systems (lts) 14] Usually lts s are a too detailed model: they make unnecessary distinctions between systems. Therefore several behavioural equivalences [4] 5] [15] [19] 20] 21] 25] have been defined. These often distinguish an unobservable or internal action from observable actions. We will here consider observation equivalence [17] 23] 19] We only briefly recall the basic definitions. A good introduction to observation equivalence can be ....

Larsen, K., A Context Dependent Equivalence between Processes. Lecture Notes in Computer Science 194 (1985), 373 -- 382.

....be relevant. Our proof technique based on polymorphic types yields a simple proof of equivalence between processes whose untyped behaviors have incomparable sets of traces. Proof techniques with this property are rare in the literature. Perhaps the best known is Larsen s relativised bisimulation [Lar87]; indeed, our method can be seen as a disciplined instance of Larsen s, in which one uses types to express constraints on the behaviors of the observers, rather than explicitly writing all their possible behaviors. 11 Discussion We close with a brief discussion of some additional technical ....

K. G. Larsen. A context dependent equivalence between processes. Theoretical Computer Science, 49:185--215, 1987.

....by the other program in the same context. Typically, we want to reason about a program in a fixed context and thus it suffices to show approximation with respect to that particular context. So, one would like to parameterize the approximation relation with information about the context. In [Lar87] Larsen demonstrates how this can be done for CCS and bisimulation. Let I range over state predicates. A possibly infinite trace ff j (s 0 ; s 0 0 ) s i ; s 0 i ) is called interference free, i free(ff) for short, if s j = s 0 j Gamma1 for all 0 j length(ff) The ....

K. G. Larsen. A context dependent equivalence between processes. Theoretical Computer Science, 49(2):185--216, 1987.

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