On Relating Some Models for Concurrency

Some models for concurrency are compared according to the way each run is observed (interleaving vs. true concurrency) and the way these observations are organised to form the behaviour of a concurrent system (linear-time vs. branching-time). Hoare trace languages, Synchronisation Trees, Mixed-ordering languages and Causal Trees have been chosen as representatives of each of the four classes, and are provided with a useful categorical presentation. We give formal evidence to the intuitive fact that Causal Trees are the minimal model which comprises both information on causality and branching. Moreover, we introduce an extension of Prime Event Structures suitable to represent prioritised events. We show that there is an intuitive relationship betweenCausal trees and Prioritised Event structures. This is a revised version of the paper appeared in Proc. Theory and Practice of Software Technology (TAPSOFT’93), Lecture Notes in Computer Science 668, 15-30, Springer-Verlag, 1993. 1. The first author was partially supported by C.N.R. project “Progetto finalizzato sistemi informatici e calcolo parallelo” and by project MASK Sc1-CT92-00776, funded by C.E.C. The second author was partially supported by C.E.C. Esprit Programme Basic Research Action number 6360 BROADCAST. The authors were also partially supported by MURST 40%. 2. Dipartimento di Informatica, Università di Pisa, Corso Italia 40, I-56125 Pisa PI, Italy, Fax: +39-50-510226; e mail: [email protected] 3. Dipartimento di Matematica, Università di Bologna, Piazza di Porta SanDonato 5, I-40127 Bologna BO, Italy, Fax: +39-51-354490; e mail: [email protected] 4. Dipartimento di Scienze dell’Informazione, Università di Milano, Via Comelico 39/41, I-20135 Milano MI, Italy, Fax: +39-2-55006276; e mail: [email protected]