AbstractAlgorithms and protocols with time dependent behavior are often specified formally using timed automata. For practical real-time systems, besides real-valued clock variables, these specifications typically contain discrete data variables with nontrivial data flow. In this paper, we propose a configurable lazy abstraction framework for the location reachability problem of timed automata that potentially contain discrete variables. Moreover, based on our previous work, we uniformly formalize in our framework several abstraction refinement strategies for both clock and discrete variables that can be freely combined, resulting in many distinct algorithm configurations. Besides the proposed refinement strategies, the configurability of the framework allows the integration of existing efficient lazy abstraction algorithms for clock variables based on $${\textit{LU}}$$
LU
-bounds. We demonstrate the applicability of the framework and the proposed refinement strategies by an empirical evaluation on a wide range of timed automata models, including ones that contain discrete variables or diagonal constraints.
PolyAR: A Highly Parallelizable Solver For Polynomial Inequality Constraints Using Convex Abstraction Refinement
