GSOS for non-deterministic processes with quantitative aspects

Recently, some general frameworks have been proposed as unifying theories for processes combining non-determinism with quantitative aspects (such as probabilistic or stochastically timed executions), aiming to provide general results and tools. This paper provides two contributions in this respect. First, we present a general GSOS specification format (and a corresponding notion of bisimulation) for non-deterministic processes with quantitative aspects. These specifications define labelled transition systems according to the ULTraS model, an extension of the usual LTSs where the transition relation associates any source state and transition label with state reachability weight functions (like, e.g., probability distributions). This format, hence called Weight Function SOS (WFSOS), covers many known systems and their bisimulations (e.g. PEPA, TIPP, PCSP) and GSOS formats (e.g. GSOS, Weighted GSOS, Segala-GSOS, among others). The second contribution is a characterization of these systems as coalgebras of a class of functors, parametric on the weight structure. This result allows us to prove soundness of the WFSOS specification format, and that bisimilarities induced by these specifications are always congruences.Comment: In Proceedings QAPL 2014, arXiv:1406.156

The Way We Were: Structural Operational Semantics Research in Perspective

This position paper on the (meta-)theory of Structural Operational Semantic (SOS) is motivated by the following two questions: (1) Is the (meta-)theory of SOS dying out as a research field? (2) If so, is it possible to rejuvenate this field with a redefined purpose? In this article, we will consider possible answers to those questions by first analysing the history of the EXPRESS/SOS workshops and the data concerning the authors and the presentations featured in the editions of those workshops as well as their subject matters. The results of our quantitative and qualitative analyses all indicate a diminishing interest in the theory of SOS as a field of research. Even though `all good things must come to an end', we strive to finish this position paper on an upbeat note by addressing our second motivating question with some optimism. To this end, we use our personal reflections and an analysis of recent trends in two of the flagship conferences in the field of Programming Languages (namely POPL and PDLI) to draw some conclusions on possible future directions that may rejuvenate research on the (meta-)theory of SOS. We hope that our musings will entice members of the research community to breathe new life into a field of research that has been kind to three of the authors of this article.Comment: In Proceedings EXPRESS/SOS2023, arXiv:2309.0578

Generic Trace Semantics via Coinduction

Trace semantics has been defined for various kinds of state-based systems, notably with different forms of branching such as non-determinism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these "trace semantics," namely coinduction in a Kleisli category. This claim is based on our technical result that, under a suitably order-enriched setting, a final coalgebra in a Kleisli category is given by an initial algebra in the category Sets. Formerly the theory of coalgebras has been employed mostly in Sets where coinduction yields a finer process semantics of bisimilarity. Therefore this paper extends the application field of coalgebras, providing a new instance of the principle "process semantics via coinduction."Comment: To appear in Logical Methods in Computer Science. 36 page