Counterexample guided inductive optimization based on satisfiability modulo theories

Abstract

This paper describes three variants of a counterexample guided inductive optimization (CEGIO) approach based on Satisfiability Modulo Theories (SMT) solvers. In particular, CEGIO relies on iterative executions to constrain a verification procedure, in order to perform inductive generalization, based on counterexamples extracted from SMT solvers. CEGIO is able to successfully optimize a wide range of functions, including non-linear and non-convex optimization problems based on SMT solvers, in which data provided by counterexamples are employed to guide the verification engine, thus reducing the optimization domain. The present algorithms are evaluated using a large set of benchmarks typically employed for evaluating optimization techniques. Experimental results show the efficiency and effectiveness of the proposed algorithms, which find the optimal solution in all evaluated benchmarks, while traditional techniques are usually trapped by local minima.

Survey on automated symbolic verification and its application for synthesising cyber‐physical systems

“…Cyber security is also a concern of Fiore et al [112], who aim to ensure secure-state estimation of UAV systems under sparse attacks. Indeed, many situations can be regarded as satisfiability problems and solved, for instance with approaches based on SMT [113][114][115], which indicate many links with other research areas and might lead to a unified approach regarding system verification, security enforcement, and interaction handling.…”

“…The ninth one is related to the widespread use of embedded systems in autonomous‐vehicle navigation systems [197], which demands optimisation solving during their execution for a wide range of functions, including non‐linear and non‐convex problems using fixed‐ and floating‐point arithmetic. One example is optimisation through CEGIO [113], which uses an iterative approach, based on formal verification, to perform inductive generalisation and then reduce optimisation domains. As a consequence, one may notice that formal methods may be regarded as a base framework, which can be applied to many problems related to ECPS design and verification.…”

“…In addition to that, another research direction for synthesisers is to generate code for UAV trajectory and mission planning, by taking into account system's dynamics and non‐holonomic constraints [113]. As a consequence, verifiers, and synthesisers need to handle a wide range of functions, including non‐linear and non‐convex optimisation problems based on both fixed‐ and floating‐point arithmetic.…”

“…As already mentioned in Section 2, even problems that are not directly related to code correctness may be tackled with formal methods, as long as they are conveniently modelled. Araújo et al [113] employed SMT for handling non-convex optimisation problems, with the goal of ensuring optimal solutions. Indeed, it is possible to recursively re-constrains a model checking procedure, by using the current counterexample as a seed for the next run, until a global minimum is achieved.…”

“…This way, by using an SMT-based verification method, one may map TS error indication and other performance figures as properties and then recursively perform realignment procedures, until no counterexample is output. It is worth noticing that associated timing requirements should be more relaxed, as mentioned in work developed by Araújo et al [113], which can be seen as an advantage for such an implementation.…”