Formalizing Timing Diagram Requirements in Discrete Duration Calulus

Abstract: Several temporal logics have been proposed to formalise timing diagram requirements over hardware and embedded controllers. These include LTL, discrete time MTL and the recent industry standard PSL. However, succintness and visual structure of a timing diagram are not adequately captured by their formulae. Interval temporal logic QDDC is a highly succint and visual notation for specifying patterns of behaviours. In this paper, we propose a practically useful notation called SeCeCntnl which enhances negation free fragment of QDDC with features of nominals and limited liveness. We show that timing diagrams can be naturally (compositionally) and succintly formalized in SeCeCntnl as compared with PSL and MTL. We give a linear time translation from timing diagrams to SeCeCntnl. As our second main result, we propose a linear time translation of SeCeCntnl into QDDC. This allows QDDC tools such as DCVALID and DCSynth to be used for checking consistency of timing diagram requirements as well as for automatic synthesis of property monitors and controllers. We give examples of a minepump controller and a bus arbiter to illustrate our tools. Giving a theoretical analysis, we show that for the proposed SeCeCntnl, the satisfiability and model checking have elementary complexity as compared to the non-elementary complexity for the full logic QDDC.