GSOS for non-deterministic processes with quantitative aspects

Abstract

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

Bisimulation of Labelled State-to-Function Transition Systems Coalgebraically

“…Stochastic GSOS (SGSOS) and Weighted GSOS appear to be a special case of Miculan and Peressotti's weight function GSOS. In [35,41] a treatment is given for PEPA, in line with Section 5 of the present paper. The formats mentioned above arise from the abstract theory of SOS.…”

“…In the treatment below the bi-algebraic perspective of SOS and bisimulation [55] is left implicit. In [41] an approach similar to ours has been applied to the ULTraS model, a model which shares some features with simple FuTS. In ULTraS posets are used instead of semirings, although a monoidal structure is then implicitly assumed when process equivalences are taken into consideration [7].…”

Endofunctors modelling higher-order behaviours

“…We stress the fact that behavioural functors are "syntax agnostic": they define the semantic behaviours, abstracting from any specific concrete representation of systems. In the wake of these important results, many functors have been defined for modelling a wide range of behaviours: deterministic and nondeterministic systems [30]; systems with I/O, with names, with resources [12,13]; systems with quantitative aspects such as probabilities [10,22,27,28,37]; systems with continuous states [3], etc. Despite these results, a general coalgebraic treatment of higher-order systems is still missing.…”

Rooted branching bisimulation as a congruence for probabilistic transition systems

“…The format ntyft/ntyxt is translated to the probabilistic setting in [11], while generation of axiomatizations [1,4] for probabilistic GSOS is reported in [10]. In [26] socalled weight-function SOS is proposed for ULTraS, a generalization of probabilistic transition systems.…”