Joint Optimization and Reachability Analysis in Graph Transformation Systems with Time

Abstract

The design of safety critical systems frequently necessitates to simultaneously fulfill several logical and numerical constraints as requirements in order to deliver a functionally correct and optimal target system. In the current paper, we present a combined optimization and reachability analysis approach using the Spin model checker [IEEE Transactions on Software Engineering 23 (1997), pp. 279–295] for problems modeled with graph transformation systems with time [Gyapay, S., R. Heckel and D. Varró, Graph transformation with time: Causality and logical clocks, in: A. Corradini, H. Ehrig, H.-J. Kreowski and G. Rozenberg, editors, Proc. ICGT 2002: 1st International Conference on Graph Transformation, LNCS 2505 (2002), pp. 120–134]. First, we encode graph transformation rules into transitions systems in Promela (the input language of Spin) following [Schmidt, Á. and D. Varró, CheckVML: A tool for model checking visual modeling languages, in: P. Stevens, J. Whittle and G. Booch, editors, Proc. UML 2003: 6th International Conference on the Unified Modeling Language, LNCS 2863 (2003), pp. 92–95, Journal of Software and Systems Modelling (2003)]. Then we restrict valid execution paths to time-ordered transformation sequences by additional logical conditions. The desired reachability property (as logical condition) is used to potentially decrease the global best cost variable whenever a new path satisfies the property. The optimal solution for the problem is found by a single exhaustive run of the model checker encoding the numerical constraints into a dynamic LTL formula to cut off suboptimal paths violating the Branch-and-Bound heuristics.