Modeling and verification of real-time systems based on equations

We describe timed observational transition systems (TOTSs). TOTSs are written in terms of equations. By regarding equations as left-to-right rewrite rules, rewriting, together with induction and/or case analysis, can be used to verify that timing properties hold for TOTSs. Concretely, CafeOBJ, an algebraic specification language, is used to specify TOTSs and verify that TOTSs have timing properties by writing proofs, or proof scores. Two case studies are used to demonstrate how to model real-time systems based on TOTSs, specify TOTSs in CafeOBJ and verify that TOTSs have timing properties with the CafeOBJ system.