J.F. Groote. Transition systems specification with negative premises. In CONCUR'90, LNCS 458, pp. 332-341, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Springer, 1996, pp. 502 513. The first systematic study of transition system specifications with negative premises appears in Bloom, Istrail Meyer [2] The concept of a (positive) TSS presented above was introduced in Groote Vaandrager [10] the negative premises t were added in Groote [9]. The notion generalises the GSOS rule systems of [2] and constitutes the first formalisation of Plotkin s Structural Operational Semantics (SOS) 11] that is su#ciently general to cover most of its applications. The premises t t # are added here, mainly for technical reasons. The following ....

....p a closed proof, if T for all literals # that appear as node labels in p. The main purpose of a TSS (#, R) is to specify a transition relation over #. A positive TSS specifies a transition relation in a straightforward way as the set of all provable transitions. But as pointed out in Groote [9], it is much less trivial to associate a transition relation to a TSS with negative premises. Several solutions are proposed in [9] and Bol Groote [3] Here I will present these solutions from a somewhat di#erent point of view, and also review a few others. The TSS P 1 can be ....

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J.F. Groote (1993): Transition system specifications with negative premises. Theoretical Computer Science 118(2), pp. 263--299.

....s in the setting. Ma rkov tra az only possible if ma1 ma progress is a14 red, which is incorpora ed via nega ive premises. Nega ive premises in such rule schema ta ha ve to be trea ted ca refully in genera l, since they ma ya #ect the well definedness of the induced tra nsition rela tion [17]. In this ca se, however, it is not di#cult to showtha t the rule schema ta a re well defined. In the caS of paOS lel composition, it should be noted tha the Ma1 ovia dela y tra sitionsaO interlea ved a if they were sta da rd az ion tr a sitions, in pa rticula r withouta djusting ra tes. This isa ....

J.F. Groote. Transition system specifications with negative premises. Theoretical Computer Science, 118:263--299, 1993.

.... spirit to those in the literature (e.g. 22, 26] In Bloom, Fokkink van Glabbeek [4] a method is given for decomposing formulae from a fragment of HML with infinite conjunctions, with respect to terms from any process algebra that has a structural operational semantics in ntyft ntyxt format [9] without lookahead. This format is a generalisation of the De Simone format, and still guarantees that bisimulation equivalence is a congruence. The decomposition method is not presented in its own right, but is used in the derivation of congruence formats for a range of behavioural equivalences ....

....# literals (transitions) A TSS with only positive premises specifies a transition relation in a straightforward way as the set of all provable transitions. But it is much less trivial to associate a transition relation to a TSS with negative premises. Several solutions are proposed in Groote [9], Bol Groote [5] and van Glabbeek [7] From the latter we adopt the notion of a well supported proof and a complete TSS. Definition 7 (well supported proof) Let P = #, R) be a TSS. A wellsupported proof of a closed literal # from P is a well founded, upwardly branching tree of which the nodes ....

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J. F. Groote (1993): Transition system specifications with negative premises. Theoretical Computer Science 118(2), pp. 263--299.

....[1] for an overview) Some rule formats guarantee that a behavioural equivalence relation is a congruence with respect to the LTS associated with a TSS, meaning that each function symbol respects this equivalence. For bisimulation equivalence there are the De Simone [26] GSOS [9] and ntyft ntyxt [10, 17, 18] formats. Furthermore, congruence formats have been developed for behavioural equivalences based on decorated traces [6, 8, 12, 29] and weak bisimulations [7, 13, 27, 28] Let a TSS and its signature be extended with new transition rules and function symbols, respectively. The rule formats put ....

....Furthermore, congruence formats have been developed for behavioural equivalences based on decorated traces [6, 8, 12, 29] and weak bisimulations [7, 13, 27, 28] Let a TSS and its signature be extended with new transition rules and function symbols, respectively. The rule formats put forward in [11, 17, 18, 31] guarantee that such an extension is (operationally) conservative, meaning that the provable transitions for a term over the original signature are the same both in the original and in the extended TSS. Finally, some rule formats exist to guarantee that the LTS associated to a TSS is bounded ....

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J.F. Groote. Transition system specifications with negative premises. Theoretical Computer Science, 118(2):263--299, 1993.

....rules in Tables 1 and 3. oe d (x) y Table 3: Transition Rules for Discrete Time. 3 The Meaning of TSSs A positive TSS specifies an LTS in a straightforward way as the set of all provable transitions (cf. Def. 2. 14) However, as Groote [107, 108] pointed out, it is much less trivial to associate an LTS with a TSS containing negative premises. Several solutions were investigated in [56, 57, 107, 108] mostly originating from logic programming. This section presents an overview of how to associate one or more LTSs with a TSS. Our ....

....Meaning of TSSs A positive TSS specifies an LTS in a straightforward way as the set of all provable transitions (cf. Def. 2.14) However, as Groote [107, 108] pointed out, it is much less trivial to associate an LTS with a TSS containing negative premises. Several solutions were investigated in [56, 57, 107, 108], mostly originating from logic programming. This section presents an overview of how to associate one or more LTSs with a TSS. Our presentation here is heavily based upon the excellent systematic analysis of the meaning of TSSs by van Glabbeek [100, 102] and we heartily refer the reader to op. ....

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J. F. Groote, Transition system specifications with negative premises (extended abstract), in Baeten and Klop [26], pp. 332--341. Preliminary version of [108].

....very logical. In terms of logic programming, this means that the transition relation is a supported model of the TDS. However, this notion of agreement just defines a general target. It is not operational in the sense that it does not explain how the TR is obtained from the TDS. In [Gro90b, Gro93] J. F. Groote mentions two potential problems. The first risk is that there is no TR agreeing with the TDS. Negative premises can lead to inconsistencies of the form : a transition belongs to the TR if it does not belong to it. Clearly, no TR exists which agrees with this TDS. The second ....

Groote, J. F. : Transition system specification with negative premises. Theoretical Computer Science 118. Elsevier, 1993, 263--299.

....may resolve choices. x x y , x q y x (4) plus a symmetric rule) choice is not resolved: In case both operands terminate w.r.t. an action, the x x y y x q y x q y (5) Note the negative premise in (4) Negative premises are known to be potentially troublesome (see Groote [41] and Van Glabbeek [36] indeed, when treating recursion (see below) we will have to take precautions. The semantics of deadlock and action constants, as well as parallel composition, are as expected in the light of the discussion above. Let us use Lfy to denote the fiat, finite fragment of L ....

....term of the transition is syntactically simpler than the source term of the conclusion; since this is already true of all other operational rules, it follows that there can be no infinite proofs of a positive transition; hence negative transitions are unambiguously decidable. In terms of Groote [41], a stratification trivially exists. Naturally, however, this new rule potentially gives rise to a different transition relation; in order to avoid this, one simultaneously restricts recursion to guarded terms. In general, a term may be called guarded if all variables occur in so called sleeping ....

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J. F. Groote. Transition system specifications with negative premises. Theo- retical Cornput. Sci., 118:263-299, 1993. 56

....inference system is inconsistent, the semantic model cannot exist. Unfortunately, our inference system contains negative premises in some inference rules. So consistency is not self evident. However, our inference rules can be proved con sistent by using the stratification technique described in [17]. We omit the proof for lack of space. 2.4. Example of LTS construction By applying the inference rules shown in this section, we can construct the corresponding LTS as follows. Let us consider the process E in Figure 2. E = a[t = x] b; c[t k x 2] stop a b[ c[t 2] stop (by rule (4) b; ....

J. F. Groote, "Transition system specifications with negative premises," in Proc. of CONCUR '90, vol. 458 of Lecture Notes in Computer Science, pp. 332-341, Springer-Verlag, 1990.

....has been a natural handle to establish results that hold for all languages whose semantics is given by means of inference rules that fit a certain format. Examples of the kind of meta theoretic results that have been systematically derived from the form of the SOS rules may be found in, e.g. [78, 79, 23, 19, 36, 35, 24, 53, 88, 13, 7, 87, 16, 90, 91, 6]. So far, this line of research has produced a wealth of results which generalize and explain several of the most important theorems and constructions in process theory. For example, given a language with an SOS semantics, an examination of the SOS rules is often all that is needed to On leave ....

....coexist with unguarded recursive definitions. This contrasts with the standard GSOS semantics given in [23, 19] in which the interplay between negative premises and unguarded recursion may lead to the operational specification of languages without a well defined operational semantics. See, e.g. [19, 35] and Sect. 4 of this paper for an example. Our first main result is that, with our choice of operational semantics for GSOS languages, the bisimulation preorder is substitutive with respect to all language contexts. See Thm. 3.9 and Thm. 4.8. Moreover, as a consequence of general results ....

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J. Groote, Transition system specifications with negative premises, Report CSR8950, CWI, Amsterdam,

....an axiom, since the only capability a prefix process has is of performing an exponential activity. With negative premises present in the operational rules, it is by no means clear that the rules are consistent, and that a transition system may be derived. Such problems were described by Groote [31]. To illustrate, Groote presents the following operational rule (amongst several others) 113 F # # F F # F Of course, no such transition system is consistent with this rule. Given a set of rules, Groote constructs a literal dependency graph, where . a p labelled edge exists from # ....

J. F. Groote. Transition system specifications with negative premises. Theoretical Computer Science, 118(2):263--299, 27 September 1993.

....A transition system stratification is a technique whereby transition rules with negative premises can be meaningfully included. By evaluating the transition system in layers, or strata, it can be shown that no transition s validity depends on its own negation, as circularities can be removed [16]. In our system, the lowest stratum contains transitions between sequential expressions, the second contains all internal system communications, and the third (and highest) contains system time transitions and external communications. By organising the transition system in this way, the negative ....

J F Groote. Transition system specifications with negative premises. In J C M Baeten and J W Klop, editors, CONCUR '90, Amsterdam, Lecture Notes in Computer Science 458, pages 332--341. Springer-Verlag, 1990.

.... does not require us to give a semantics to open terms: P[x : x : P] p 0 x : P p 0 P[x : x : P] a 0 P 0 x : P a 0 P 0 These rules are more standard, but are not obviously well defined, since the semantics of the recursive term x : P may involve negative premises (in GROOTE s (GROOTE, 1989) terms, this provides a stratification of the operational semantics) For example, if we were to allow unguarded recursions such as x : q(0 r succ x) then there would be no transition system 0 . Fortunately, the above transition systems are equivalent, since we are only dealing with ....

GROOTE, J. F. (1989). Transition system specifications with negative premises. Report CS-R8950, CWI, Amsterdam.

....Plotkin has clearly formalized the technics of Structural Operational Semantics specification as a general method for defining semantics of programming languages [Plo81] Milner [Mil81] Mil89] introduced his calculus, CCS, by using this approach. Next, Groote and Vaandrager in [GV89] [Gro90] have considerably enriched the field by deriving transition systems [Kel76] modulo strong bisimulation [Par81] Mil81] from a wide family of Structural Operational Semantics specifications (see also [BIM88] At the same time, in the general interest for True Concurrency, Boudol and Castellani, ....

J. F. Groote. Transition system specifications with negative premisses. In Proc. CONCUR'90, Amsterdam, LNCS 458, pages 332--341. Springer-Verlag, August 1990.

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J.F. Groote. Transition systems specification with negative premises. In CONCUR'90, LNCS 458, pp. 332-341, 1990.

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J.F. Groote. Transition systems specification with negative premises. In CONCUR '90, LNCS 458, pp. 332-341, 1990.

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Groote, J. F.: Transition System Specification with Negative Premises, Theoretical Computer Science, Vol.118, No.2, pp.263-299 (1993).

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J.F. Groote. Transition systems specifications with negative premises. Theoretical Computer Science, 118, 263--299, 1993. (pp ix, 18, 29, 30)

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J. F. Groote, Transition system specifications with negative premises, Theoretical Comput. Sci., 118 (1993), pp. 263--299.

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J F Groote. Transition system specifications with negative premises. In J C M Baeten and J W Klop, editors, CONCUR '90, Amsterdam, Lecture Notes in Computer Science 458, pages 332--341. Springer-Verlag, 1990.

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J F Groote. Transition system specifications with negative premises. In J C M Baeten and J W Klop, editors, CONCUR '90, Lecture Notes in Computer Science 458, pages 332--341, 1990.

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J.F. Groote. Transition system specifications with negative premises. In J.C.M. Baeton and J.W.Klop, editors, CONCUR '90, Lecture Notes in Computer Science 458, pages 332--341. 1990.

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J.F. Groote. Transition system specifications with negative premises. Theoretical Computer Science, 118(2):263--299, 1993.

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Groote, J.: Transition system specifications with negative premises. Theoretical

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J. F. Groote (1993): Transition system specifications with negative premises. Theoretical Computer Science 118(2), pp. 263--299.

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J.F. Groote. Transition system specifications with negative premises. Report CS-R8950, CWI, 1989. An extended abstract appeared in J.C.M. Baeten and J.W. Klop, editors, Proceedings CONCUR 90, Amsterdam, LNCS 458, pages 332--341. SpringerVerlag,

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