AbstractWe 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 [Bloom et al. 1995; Groote 1993]. Finally, we provide a sound and complete axiomatization for this example.
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Categories and Subject Descriptors: D.3.1 [Programming Languages]: Formal Definitions and Theory; F.3.1 [Logics and Meanings of Programs]: Specifying and Verifying and Reasoning about Programs; F.3.2 [Logics and Meanings of Programs]: Semantics of Programming Languages; I.2.3 [Artificial Intelligence]: Deduction and Theorem Proving
General Terms: Algebra, Semantics
Additional Key Words and Phrases: Bisimulation, congruence, conservative extension of TSSs, logic programming, negative premises, \emph{ntyft/ntyxt}-format, priorities and abstraction, process algebra
Selected papers that cite this one
- Luca Aceto and Anna Ingólfsdóttir. CPO models for compact GSOS languages. Information and Computation, 129(2):107-141, 15 September 1996.
- Pedro R. D'Argenio and Chris Verhoef. A general conservative extension theorem in process algebras with inequalities. Theoretical Computer Science, 177(2):351-380, 15 May 1997.
- Wan Fokkink and Chris Verhoef. A conservative look at operational semantics with variable binding. Information and Computation, 146(1):24-54, 10 October 1998.
- Roberto Giacobazzi and Francesco Ranzato. Uniform closures: Order-theoretically reconstructing logic program semantics and abstract domain refinements. Information and Computation, 145(2):153-190, 15 September 1998.
- Jaco van de Pol. Operational semantics of rewriting with priorities. Theoretical Computer Science, 200(1-2):289-312, 28 June 1998.
Selected references
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- Bard Bloom, Sorin Istrail, and Albert R. Meyer. Bisimulation can't be traced. Journal of the ACM, 42(1):232-268, January 1995.
- Rance Cleaveland and Matthew Hennessy. Priorities in process algebras. In Proceedings, Third Annual Symposium on Logic in Computer Science, pages 193-202, Edinburgh, Scotland, 5-8 July 1988. IEEE Computer Society.
- Jan Friso Groote. Transition system specifications with negative premises. Theoretical Computer Science, 118(2):263-299, 27 September 1993.
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