In this paper we are interested in general properties of classes of transition system specifications in Plotkin style. The discussion takes place in a setting of labelled transition systems. The states of the transition systems are terms generated by a single sorted signature and the transitions between states are defined by conditional rules over tne syntax. It is argued that in this setting it is natural to require that strong bisimulation equivalence be a congruence on the states of the transition systems. A general format, called the 1xfi/1yxt format, is presented for the rules in a transition system specification, such that bisimulation is always a congruence when all the rules fit this format. With a series of examples it is demonstrated that the t.i:fi/1yxt format cannot be generalized in any obvious way. Another series of examples illustrates the usefulness of our congruence theorem. Briefly we touch upon the issue of modularity of transition system specifications. It is argued that certain pathological tyft/tyxt rules (the ones which are not pure) can be disqualified because they behave badly with respect to modularization. Next we address the issue of full abstraction. We characterize the completed trace congruence induced by the operators in pure tyft/tyxt format as 2-nested simulation equivalence. The pure tyft/tyxt format includes the format given by de Simone (Theoret. Comput. Sci. 37, 245-267 (1985)) but is incomparable to the GSOS format of Bloom,

Groote, J.F., Transition system specifications with negative premises, Theoretical Computer Science 118 (1993) 263-299.In this article the general approach to Plotkin-style operational semantics of Groote and Vaandrager ( 1989) is extended lo transition system specifications (TSSs) with rules that may contain negative premises. Two problems arise: firstly the rules may be inconsistent, and secondly it is not obvious how a TSS determines a transition relation. We present a general method, based on the stratification technique in logic programming, to prove consistency of a set of rules and we show how a specific transition relation can be associated with a TSS in a natural way. Then a special format for the rules, the ntyft/ntyxt format, is defined. It is shown that for this format three important theorems hold. The first theorem says that bisimulation is a congruence if all operators are defined using this format. The second theorem states that, under certain restrictions, a TSS in ntyft format can be added conservatively to a TSS in pure myfi/ntyxt format. Finally, it is shown that the trace congruence for image-finite processes induced by the pure ntyfi/nryxt format is precisely bisimulation equivalence.

Cr.intrumvoc..rWis''L~-...1~ CO lnfonnetiN Report CS-R9001 January The Centre for Mathematics and Computer Science is a research institute of the Stichting Mathematisch Centrum , which was founded on February 11 , 1946, as a nonprofit institution aiming at the promotion of mathematics, computer science, and their applications . It is sponsored by the Dutch Government through the Netherlands Organization for the Advancement of Research (N .W.O.).

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Abstract. We present a general theory for the use of negative premises in the rules of Transition System Specifications (TSSs). We formulate a criterion that should be satisfied by a TSS in order to be meaningful, that is, to unequivocally define a transition relation. We also provide powerful techniques for proving that a TSS satisfies this criterion, meanwhile constructing this transition relation. Both the criterion and the techniques originate from logic programming [van Gelder et al. 1988;Gelfond and Lifschitz 1988] to which TSSs are close. In an appendix we provide an extensive comparison between them.As in Groote [1993], we show that the bisimulation relation induced by a TSS is a congruence, provided that it is in ntyft/ntyxt-format and can be proved meaningful using our techniques. We also considerably extend the conservativity theorems of Groote [1993] and Groote and Vaandrager [1992]. As a running example, we study the combined addition of priorities and abstraction to Basic Process Algebra (BPA). Under some reasonable conditions we show that this TSS is indeed meaningful, which could not be shown by other methods Groote 1993]. Finally, we provide a sound and complete axiomatization for this example.