Towards Pareto-Optimal Parameter Synthesis for Monotonic Cost Functions

Designers are often required to explore alternative solutions, trading off along different dimensions (e.g., power consumption, weight, cost, reliability, response time). Such exploration can be encoded as a problem of parameter synthesis, i.e., finding a parameter valuation (representing a design solution) such that the corresponding system satisfies a desired property. In this paper, we tackle the problem of parameter synthesis with multi-dimensional cost functions by finding solutions that are in the Pareto front: in the space of best trade-offs possible. We propose several algorithms, based on IC3, that interleave in various ways the search for parameter valuations that satisfy the property, and the optimization with respect to costs. The most effective one relies on the reuse of inductive invariants and on the extraction of unsatisfiable cores to accelerate convergence. Our experimental evaluation shows the feasibility of the approach on practical benchmarks from diagnosability synthesis and productline engineering, and demonstrates the importance of a tight integration between model checking and cost optimization.