New refinement relations of Z specifications for multiple viewpoints oriented requirements method

TP311.5; In this paper we develop several new refinement relations of Zfor mul tiple viewpoints oriented requirements method (MVORM). The original motivation i s that we found the standard Z refinement relation is not adequate or correct wh en considering specifications that have temporal relationships of operations. Th e concept of temporal state variables is introduced into Z. Then new implementat ion relations are defined and new refinement relations are deduced, mainly for t emporal state variables to process temporal relationships of operations. We use state transition systems to abstract the temporal state transitions. A simple ex ample is used to show the procedures of MVORM. Finally some directions of furthe r work are forwarded.