Cycle encoding-based parameter synthesis for timed automata safety

Parametric timed automata (PTA) extend timed automata (TA) with parameters instead of fixed timing constraints, providing the flexibility to accommodate uncertainties during the design phase. Once a parametric model is obtained, the next step is finding the optimal parameters such that the resulting TA satisfies the specifications. This paper introduces a new algorithm for determining parameters from safety specifications for PTA with bounded integer parameters and no nested cycles. The algorithm searches for unsafe paths through a depth-first search and generates parameter constraints. In particular, the realizability of simple and cyclic paths are encoded via mixed integer linear programming and non-linear programming problems. Then, the parameter constraints rendering the path unrealizable are derived via quantifier elimination. The accumulated constraints through the depth-first search guarantee that a parameter valuation satisfying these constraints solves the synthesis problem. The results are illustrated over benchmarks.