Lean and Full Congruence Formats for Recursion

In this paper I distinguish two (pre)congruence requirements for semantic equivalences and preorders on processes given as closed terms in a system description language with a recursion construct. A lean congruence preserves equivalence when replacing closed subexpressions of a process by equivalent alternatives. A full congruence moreover allows replacement within a recursive specification of subexpressions that may contain recursion variables bound outside of these subexpressions. I establish that bisimilarity is a lean (pre)congruence for recursion for all languages with a structural operational semantics in the ntyft/ntyxt format. Additionally, it is a full congruence for the tyft/tyxt format.Comment: To appear in: Proc. LICS'17, Reykjavik, Iceland, IEE

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

Structural operational semantics for continuous state stochastic transition systems

2siIn this paper we show how to model syntax and semantics of stochastic processes with continuous states, respectively as algebras and coalgebras of suitable endofunctors over the category of measurable spaces Meas. Moreover, we present an SOS-like rule format, called MGSOS, representing abstract GSOS over Meas, and yielding fully abstract universal semantics, for which behavioral equivalence is a congruence. An MGSOS specification defines how semantics of processes are composed by means of measure terms, which are expressions specifically designed for describing finite measures. The syntax of these measure terms, and their interpretation as measures, are part of the MGSOS specification. We give two example applications, with a simple and neat MGSOS specification: a "quantitative CCS", and a calculus of processes living in the plane R2 whose communication rate depends on their distance. The approach we follow in these cases can be readily adapted to deal with other quantitative aspects. © 2014 Elsevier Inc. All rights reserved.reservedmixedBacci, G.; Miculan, M.Bacci, G.; Miculan, Marin