Joint Optimization and Reachability Analysis in Graph Transformation Systems with Time

  • Authors:

  • Szilvia Gyapay;Akos Schmidt;Dániel Varró

  • Affiliations:

  • Department of Measurement and Information Systems, Budapest University of Technology and Economics, H-1521 Budapest, Magyar tudósok körútja 2., Hungary;Department of Measurement and Information Systems, Budapest University of Technology and Economics, H-1521 Budapest, Magyar tudósok körútja 2., Hungary;Department of Measurement and Information Systems, Budapest University of Technology and Economics, H-1521 Budapest, Magyar tudósok körútja 2., Hungary

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2004

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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. Varro, 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, A. and D. Varro, 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.