A Counterexample-Guided Approach to Parameter Synthesis for Linear Hybrid Automata
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Our goal is to find the set of parameters for which a given linear hybrid automaton does not reach a given set of bad states. The problem is known to be semi-solvable (if the algorithm terminates the result is correct) by introducing the parameters as state variables and computing the set of reachable states. This is usually too expensive, however, and in our experiments only possible for very simple systems with few parameters. We propose an adaptation of counterexample-guided abstraction refinement (CEGAR) with which one can obtain an underapproximation of the set of good parameters using linear programming. The adaptation is generic and can be applied on top of any CEGAR method where the counterexamples correspond to paths in the concrete system. For each counterexample, the cost incurred by underapproximating the parameters is polynomial in the number of variables, parameters, and the length of counterexample. We identify a syntactic condition for which the approach is complete in the sense that the underapproximation is empty only if the problem has no solution. Experimental results are provided for two CEGAR methods, a simple discrete version and iterative relaxation abstraction (IRA), both of which show a drastic improvement in performance compared to standard reachability.
KeywordsLinear Constraint Good Parameter Reachable State Parameter Synthesis Feasible Path
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