Transition system specifications with negative premises

Abstract

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.

A congruence theorem for structured operational semantics with predicates and negative premises

“…We show t.his in the following two examples. Groote [14] gives similar examples with relations instead of predicates.…”

“…Also in this section we do our very best not to loose the reader by interspersing a running example among the abstract definitions. Following Groote [14] we show that stratifiability is a sufficient condition on a term deduction system to guarantee that there exist.s a transition relation that agrees with it. In section 4, we define the pantk forma.t and t.he HOt.iOH of st.rong bisimulation in the presence of predicates on states.…”

“…This notion is based on Groote [14]. Strong bisimulation is based on Park [21] but we require also that bisimilar processes satisfy the same predicates; cf.…”

“…Baeten and Verhoef [S] already conjectured that this result could be proved in the same way as their congruence theorem for the path format. Indeed, this turns out to be the case: we code each predicate as a binary relation and we apply the congruence theorem of Groote [14] to the coded system. Consequently, all the operators that can be defined in the panth format can also be defined in Groote's ntyfi/ntyxt format.…”

Bisimulation and Language Equivalence

“…Bisimulation equivalence is a congruence for all the operators of these calculi. By permitting more general operators, whose rules for transitions belong to a general format, bisimulation equivalence turns out to be the least congruence induced by language equivalence [9]. Models for richer process calculi capturing value passing, mobility, causality, time, probability and locations have been developed.…”