A timed rewriting logic semantics for SDL: A case study of alternating bit protocol

Abstract SDL is an industrial standard formal description technique for telecommunication systems. Despite its wide spread use and industrial importance it lacks at present an adequate formal semantics integrating its static, dynamic, and real-time aspects. Timed Rewriting Logic (TRL) is a new variant of Rewriting Logic, an algebraic formalism which allows the dynamic behaviour of systems to be axiomatised using rewrite rules. In TRL rewrite rules can be labelled with time constraints and this provides a means of reasoning about time elapse in real-time systems. TRL has been used to develop an object-oriented specification language Timed Maude for distributed real-time systems. In this paper we demonstrate the expressive power and versatility of Timed Maude by applying it to the definition of a formal semantics for SDL. The semantics we develop captures in an intuitive way the hierarchical structure of SDL specifications and integrates within one formalism the static and dynamic aspects of an SDL system. We demonstrate and motivate the semantics we develop by considering in detail a case study of the bench mark alternating bit protocol. It is a pleasure to thank U. Hinkel, K. Meinke and M. Wirsing for their helpful comments and advice during the preparation of this paper. We also gratefully acknowledge the financial support of the British Council and DAAD which has made this collaborative work possible.