5 research outputs found
Distributive Laws and Decidable Properties of SOS Specifications
Some formats of well-behaved operational specifications, correspond to
natural transformations of certain types (for example, GSOS and coGSOS laws).
These transformations have a common generalization: distributive laws of monads
over comonads. We prove that this elegant theoretical generalization has
limited practical benefits: it does not translate to any concrete rule format
that would be complete for specifications that contain both GSOS and coGSOS
rules. This is shown for the case of labeled transition systems and
deterministic stream systems.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127
Distributive Laws for Monotone Specifications
Turi and Plotkin introduced an elegant approach to structural operational
semantics based on universal coalgebra, parametric in the type of syntax and
the type of behaviour. Their framework includes abstract GSOS, a categorical
generalisation of the classical GSOS rule format, as well as its categorical
dual, coGSOS. Both formats are well behaved, in the sense that each
specification has a unique model on which behavioural equivalence is a
congruence. Unfortunately, the combination of the two formats does not feature
these desirable properties. We show that monotone specifications - that
disallow negative premises - do induce a canonical distributive law of a monad
over a comonad, and therefore a unique, compositional interpretation.Comment: In Proceedings EXPRESS/SOS 2017, arXiv:1709.0004
Structural operational semantics for non-deterministic processes with quantitative aspects
General frameworks have been recently 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 GSOS (WF-GSOS), 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 and completeness of the WF-GSOS specification format, and
that bisimilarities induced by these specifications are always congruences.Comment: Extended version of arXiv:1406.206