J. C. M. Baeten and F. W. Vaandrager. An Algebra for Process Creation. Acta Inf., 29(4):303-334, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....be distinguished by the way they treat the formalisation of successful and unsuccessful termination. In a sequential composition of B1 and B2, B2 may only start when B1 has successfully terminated. Several different alternatives for rules formalising sequential composition exist (see for instance [6]) The version which matches our solution most closely is the following: x x x x y y (1) x; y x; y x; y y where x x denotes that x can terminate successfully and thereby becomes x (and; denotes ordinary sequential composition) Besides these two rules for sequen tial composition, ....

J. C. M. Baeten and F. W. Vaandrager. An Algebra for Process Creation. Acta Inf., 29(4):303-334, 1992.

....of dynamic types but it has not yet been related to any operationally based equivalence. An operational semantics is also given for a language called FPI. This contains many CML features but the author notes that accommodating any spawn or fork operator would be difficult. In (Havelund, 1994; Baeten Vaandrager, 1992) the spawn operator is studied within the context of process algebras. The former gives a two level operational semantics for a simple pure process algebra with fork and uses this to develop a semantic equivalence based on strong bisimulation; an axiomatisation is also given using an auxiliary ....

Baeten, J. C. M., & Vaandrager, F. W. (1992). An algebra for process creation. Acta informatica, 29(4), 303--334.

....action a should be refined by a term t, there is no obvious way to denote the resulting behaviour t:b:0 without resorting to sequential composition. The interaction of process creation and sequential composition in the setting of process algebra has been studied before by Baeten and Vaandrager in [3] and by Havelund and Larsen in [14,15] Only the latter address higher order features as well, also through name passing. Their solution to the scoping problem, however, is quite restrictive, since they essentially return to action prefixing for input actions, which implies all terms that raise ....

....a g t; u Gamma t 0 ; u 0 R 9 Fig. 1. Transition rules for the basic calculus. The termination predicate extends the usual notion, in that terminated terms may at the same time still perform actions, namely if they are spawned off as parallel processes. A similar approach is seen in [3]. Note that we need no rule for the termination of choice, since the restriction to guarded choice guarantees that in t u, neither t nor u can be terminated. This simplifies matters greatly and is, in fact, precisely the reason for the restriction to guarded choice. Since there appears to be ....

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Jos C. M. Baeten and Frits W. Vaandrager. An Algebra for Process Creation. Acta Informatica, 29(4):303--334, 1992.

....Then E(G) corresponds to the events of E. Also, any configuration of E is a configuration of E 0 or of E 1 , as no mixed configuration is possible. This is exactly the state set of G. There is no universally accepted definition of sequential composition for event structures. Baeten and Vaandrager[BV92] define sequential composition, and our definition does agree with theirs operationally. They define a special event, a p which is interpreted as the last event of the process executing the event structure. Sequential composition E 0 ; E 1 is then defined by refining each p of E 0 with E 1 . ....

J.C.M. Baeten and F.W. Vaandrager. An algebra for process creation. Acta Informatica, 29(4):303--334, 1992.

....added a spawn operator for introducing new threads of computation. To enable these threads to cooperate a range of constructs, based on those of CCS, for receiving and sending values is also added. The resulting language is more powerful than the fork calculus, 7] and the language considered in [1] as computation threads have the ability to exchange data. It is also more powerful than the value passing process algebra of [9] as not only can expressions exchange values as data but the evaluation of expressions can terminate in the production of values. More importantly in [9] the calculation ....

....v implies e 1 ; e 2 Gamma e 2 . Intuitively spawn(e 1 ) e 2 should proceed by creating a new processor to handle the evaluation of e 1 which could proceed at the same time as the evaluation of e 2 . However this requires a reinterpretation of the sequential composition operator ; as in [1]; e 1 ; e 2 no longer means when the evaluation of e 1 is finished start with the evaluation of e 2 . Instead we interpret e 1 ; e 2 as start the evaluation of e 2 as soon as an initialisation signal has been received from e 1 . This initialisation signal is of course a p move and the above ....

J.C.M. Baeten and F.W. Vaandrager. An algebra for process creation. Acta Informatica, 29(4):303-- 334, 1992.

....models for CCS like languages where action prefixing is the only form of sequential composition; in this context, the distinction is not necessary. As explained in the introduction, dealing with action refinement incorporates sequential composition, and the distinction becomes relevant. In [BV] this distinction is achieved, in the context of prime event structures, by introducing a special event label p . The occurrence of a p event models successful termination. A system run deadlocks iff it does not contain a p event and cannot be prolonged. Another way of establishing this ....

....prime event structure representation of the resulting behaviour is c b # d b : It is not possible to represent this behaviour by a prime event structure with only one b event. Exactly the same problem occurs when refining a by c#d in a b. A definition of sequential composition (cf. [BV]) or of a refinement operator on prime event structures allowing conflicts in refinements, would require duplications of events, as illustrated above. This would lead to undesirable complications when using these constructions. We will consider more general forms of event structures that do not ....

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J.C.M. Baeten & F.W. Vaandrager (1992): An algebra for process creation. Acta Informatica 29(4), pp. 303--334.

....nondeterministically chosen order rather than (truly) concurrently. We now formalise these intuitions operationally. First consider sequential composition. Examples of operational rules for normal sequential composition are the following from Baeten and Weijland [4] for a detailed discussion see [3]) B Gamma a B 0 B Delta C Gamma a B 0 Delta C B Gamma a p B Delta C Gamma a C where B Gamma a p denotes that B can terminate successfully by executing a. The rules state that either B has not terminated yet, in which case the sequential composition can only ....

J. C. M. Baeten and F. W. Vaandrager. An algebra for process creation. In J.W. de Bakker, 25 Jaar Semantiek --- Liber Amicorum. Stichting Mathematisch Centrum, Amsterdam, Apr. 1989. Also availabe as: Report CS-R8907, CWI, Amsterdam.

....the relative position of the expressiveness of the stalk format. In particular a characterization of completed trace congruences in terms of a special bisimulation would facilitate the comparison with general GSOS and pure tyft. On the other hand, for particular cases it seems possible, following [BV92a] to discard the many sortedness of the format. It therefore may very well be the case that the restrictions of the format (contexts in the shape of smooth stalks) can be relaxed. Also, if the congruence result of the paper can be generalized (which seems to require amendments as just indicated) to ....

....we do not consider them in the comparison below. A first difference, in comparing the stalk format to the three formats given above, concerns the many sortedness of the former vs. the single sortedness of the latter three. The manysortedness is not an essential distinction, since following [BV92a], many sortedness can be, so to speak, coded into the transition schemes by ensuring the well sortedness of the x 1 ; x by adding extra premises x i X sort(S i ) and rules x i X sort(S i ) 1 i k) f(x 1 ; x k ) X sort(S) for f :S 1 Theta Delta Delta Delta ....

J.C.M. Baeten and F.W. Vaandrager. An algebra for process creation. Acta Informatica, 29:303--334, 1992.

....morphisms is routine. If we restrict P 1 k P 2 to the events from A Theta B, then we get the synchronous product of P 1 and P 2 , and this is the product in the category Hgr. There is no universally accepted definition of sequential composition for event structures. Baeten and Vaandrager[BV92] define sequential composition, and our definition does agree with theirs operationally. They define a special event, a p which is interpreted as the last event of the process represented by the event structure. Sequential composition E 0 ; E 1 is then defined by refining each p of E 0 with E ....

J.C.M. Baeten and F.W. Vaandrager. An algebra for process creation. Acta Informatica, 29(4):303--334, 1992.

....all we still have to be careful with coding of predicates by relations since this can lead to non intuitive situations. Next, we will give some examples of operational semantics that are better understood with than without predicates. Two examples can be found in a paper of Baeten and Vaandrager [7] in which several operational semantics are given for the simple language Basic Process Algebra (BPA) this consists of the first five laws of the theory PA of Bergstra and Klop [10] The language BPA has only atomic actions and alternative and sequential composition. First, Baeten and Vaandrager ....

....a function and ordinary transitions. We claim that this function is, in fact, a mixfix predicate and that the resulting operational semantics is well founded and in path format. We promised in the introduction to return to the operational semantics with negative premises that Baeten and Vaandrager [7] give for BPA. We recall that they extend the signature of BPA with an auxiliary constant ffi and that they have ffix = x. They have this property because they model the sequential composition as a sequencing operator. If x is sequenced with y, notation xy, the process xy starts with the execution ....

J. C. M. Baeten and F. W. Vaandrager, An algebra for process creation, Acta Informatica 29, pp. 303--334, 1992.

....on process graphs. A first contribution of this section is a precise definition of the transformation from a calculus to operations on graphs. Although the result is the same, the definition of the transformation that we present here is quite different from the definition in Baeten and Vaandrager [7]. Our definition, which in spirit is very close to De Simone s notion of FHbisimulation, turns out to be useful for proving that an operation from one calculus is a derived operation from another calculus. Technically, a key role is played by the notion of an action transducer: to each function ....

J.C.M. Baeten and F.W. Vaandrager. An algebra for process creation. Acta Informatica, 29(4):303--334, 1992.

.... obtain an axiomatization for the sequencing operation described in (28) Besides the law (30) it consists of: x y) 1 z = x; 1 z y; 1 z x; 2 (y z) x; 2 y x; 2 z ax; 1 y = a(x; y) 0; 2 ay = ay (ax y) 2 z = 0 0; 1 x = 0 x; 2 0 = 0 This is somewhat inferior to the axiomatization of [9], which does not require auxiliary operations. However, finding the latter axiomatization required a lot of thinking whereas the one presented here is produced automatically. 4.2 General GSOS Operations In this subsection we show how to axiomatize non smooth operations. An operation can fail to ....

J.C.M. Baeten and F.W. Vaandrager. An algebra for process creation. Acta Informatica, 29(4):303--334, 1992.

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