Causal Behaviours and Nets

\Abandonment of causal ity as a matter of principl e shoul d be permitted onl y in the most extreme emergency" Abstract. Speciication formalisms in which causality and independence of actions can be explicitlyexpressed are beneecialfrom a design point of view. The explicit presence (or absence) of a causal dependency between actions can be used eeectivelyduring the design. We considera speciicationformal-ism in which causal relations between actions play a central role and provide a semantics in terms of (an extension of) labelled place/transition nets. The behaviour of nets is deened by labelled partially ordered sets. A number of formal descri pti on techniques are known that assist the development ofcompl ex di stri buted systems.Although suchtechniques are asigni cant contribution tothe treatment ofcompl exity in,for instance, protocol design and veriication, an engi neer may wonder whether the abstractions made by these approaches are appropri ate. From an engi neer' s view, the preferred scenario is to rst investigate whi ch desi gn concepts are convenient and what their intended meaning should be 33]. Once thi s i s i nvesti gated, an appropriate and intuitively appealing representation of these concepts can be chosen, eventually resulting in a \design" formalism,a formal i sm that can be used at di erent stages of the design trajectory. Such consid-erati ons have l ed to the i ntroduction of a design model which comprehends design concepts, an overal l desi gn methodology, and a design formalism 32, 33]. A full treatment of thi s model i s gi ven in 8]. Needl esstosay,a(desi gn)formalismshouldhaveaformalsemantics.Thisgivesa preci se meani ng tothe i ntroduced concepts, formsabasisfor thedeenition ofequiv-alence noti ons and i mpl ementation relations that are suitable to eeectively support the desi gn trajectory, and i s i ndispensable for the development of tools. A formal treatment of the formal i sm i n 8, 32, 33] is currently lacking. This paper presents a formal semanti cs of the kernel of the proposed formalism | causal relations and causal behavi ours | i n terms of place/transition nets 27]. The formal i sm i s adherent to the true concurrency (or partial-order) approach. Inanutshel lthemai nnovel ti esoftheformalismaretheinclusionoflabelledinternal acti ons on whi ch no synchroni sations may take place but which are visible by the