Quantitative Verification and Design Space Exploration under Uncertainty with Parametric Stochastic Contracts

This paper proposes an automated framework for quantitative verification and design space exploration of cyber-physical systems in the presence of uncertainty, leveraging assume-guarantee contracts expressed in Stochastic Signal Temporal Logic (StSTL). We introduce quantitative semantics for StSTL and formulations of the quantitative verification and design space exploration problems as bi-level optimization problems. We show that these optimization problems can be effectively solved for a class of stochastic systems and a fragment of bounded-time StSTL formulas. Our algorithm searches for partitions of the upper-level design space such that the solutions of the lower-level problems satisfy the upper-level constraints. A set of optimal parameter values are then selected within these partitions. We illustrate the effectiveness of our framework on the design of a multi-sensor perception system and an automatic cruise control system.