Automated and Formal Synthesis of Neural Barrier Certificates for Dynamical Models

Peruffo, Andrea; Ahmed, Daniele; Abate, Alessandro

doi:10.48550/arxiv.2007.03251

Cited by 3 publications

(4 citation statements)

References 27 publications

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“…CEGIS has been used to verify stability for such systems by synthesising Lyapunov functions with polynomial and neural templates [1,2,5]. Further, safety has been verified with barrier certificates [31,52].…”

Section: Dynamical Systemsmentioning

confidence: 99%

Quantitative Verification With Neural Networks For Probabilistic Programs and Stochastic Systems

Abate¹,

Edwards²,

Giacobbe³

et al. 2023

Preprint

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We present a machine learning approach to quantitative verification. We investigate the quantitative reachability analysis of probabilistic programs and stochastic systems, which is the problem of computing the probability of hitting in finite time a given target set of states. This general problem subsumes a wide variety of other quantitative verification problems, from the invariant and the safety analysis of discrete-time stochastic systems to the assertion-violation and the termination analysis of single-loop probabilistic programs. We exploit the expressive power of neural networks as novel templates for indicating supermartingale functions, which provide general certificates of reachability that are both tight and sound. Our method uses machine learning to train a neural certificate that minimises an upper bound for the probability of reachability over sampled observations of the state space. Then, it uses satisfiability modulo theories to verify that the obtained neural certificate is valid over every possible state of the program and conversely, upon receiving a counterexample, it refines neural training in a counterexample-guided inductive synthesis loop, until the solver confirms the certificate. We experimentally demonstrate on a diverse set of benchmark probabilistic programs and stochastic dynamical models that neural indicating supermartingales yield smaller or comparable probability bounds than existing state-of-the-art methods in all cases, and further that the approach succeeds on models that are entirely beyond the reach of such alternative techniques.

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Section: Dynamical Systemsmentioning

confidence: 99%

Quantitative Verification With Neural Networks For Probabilistic Programs and Stochastic Systems

Abate¹,

Edwards²,

Giacobbe³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Note that by formulating the barrier conditions as a satisfiability problem, one can alternatively search for parametric control barrier certificates using an iterative program synthesis framework, called Counter-Example-Guided Inductive Synthesis (CEGIS), with the help of Satisfiability Modulo Theories (SMT) solvers such as Z3 [45] and dReal [52]; see, e.g., [78] for more details. We also refer interested readers to the recent work [142], where machine learning techniques were exploited for the construction of barrier certificates.…”

Section: Xiang Yin Cdc 2021 December 11mentioning

confidence: 99%

Secure-by-Construction Synthesis of Cyber-Physical Systems

Liu¹,

Trivedi²,

Yin³

2022

Preprint

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Correct-by-construction synthesis is a cornerstone of the confluence of formal methods and control theory towards designing safety-critical systems. Instead of following the time-tested, albeit laborious (re)design-verify-validate loop, correct-by-construction methodology advocates the use of continual refinements of formal requirements-connected by chains of formal proofs-to build a system that assures the correctness by design. A remarkable progress has been made in scaling the scope of applicability of correct-byconstruction synthesis-with a focus on cyber-physical systems that tie discrete-event control with continuous environment-to enlarge control systems by combining symbolic approaches with principled state-space reduction techniques. Unfortunately, in the security-critical control systems, the security properties are verified ex post facto the design process in a way that undermines the correct-by-construction paradigm. We posit that, to truly realize the dream of correct-by-construction synthesis for security-critical systems, security considerations must take center-stage with the safety considerations. Moreover, catalyzed by the recent progress on the opacity sub-classes of security properties and the notion of hyperproperties capable of combining security with safety properties, we believe that the time is ripe for the research community to holistically target the challenge of secure-by-construction synthesis. This paper details our vision by highlighting the recent progress and open challenges that may serve as bricks for providing a solid foundation for secure-by-construction synthesis of cyber-physical systems.The revolution in miniaturized communication devices in the beginning of this millennium contributed towards a revolution in the internet-of-things (IoT) and the networked systems woven around them: the cyber-physical systems (CPS). CPS are marked by a close-knit interaction of discrete computation and continuous control over a network and are playing critical roles in virtually every aspect of our modern experience ranging from consumer electronics to implantable medical devices, from smart cars to smart hospitals, and from controlling our power systems to safeguarding our nuclear rectors. These systems are clearly safety-critical as a bug in their design could be life threatening, but given their societal implications, they are also security-critical where a bug in their design may have the potential to jeopardize the privacy, trust, and economic interests of society built around them." We believe that the security considerations should be elevated as primary design drivers along with safety ones to tackle the design challenge of modern CPS and call for a need to expand the correct-byconstruction paradigm of designing safety-critical systems to encompass security: we call this paradigm secure-by-construction. This paper synthesizes ideas from three research communities: discrete event systems (DES), control systems (CS), and formal methods (FM) to pose and study central problems supporting...

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“…( 8)-( 10)) as a satisfiability problem, one can alternatively search for parametric control barrier certificates using an iterative program synthesis framework, called Counter-Example-Guided Inductive Synthesis (CEGIS), with the help of Satisfiability Modulo Theories (SMT) solvers such as Z3 [20] and dReal [21]; see, e.g., [12] for more details. We also refer interested readers to the recent work [22], where machine learning techniques were exploited for the construction of barrier certificates.…”

Section: Computation Of Barrier Certificates Using Sum-of-squares Tec...mentioning

confidence: 99%

“…Then, we compute a function V (x, x) as in Lemma 11 to see if the system is lacking the approximate initial-state opacity. In this case, the regions considered in Lemma 11 are R 0 = {T ∈[21.5,22]×[21,22], T ∈ [21,21.5]×[21,22]},…”

mentioning

confidence: 99%

Verification of Approximate Opacity via Barrier Certificates

Liu,

Zamani

2021

Preprint

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This paper is motivated by the increasing security concerns of cyber-physical systems. Here, we develop a discretization-free verification scheme targeting an informationflow security property, called approximate initial-state opacity, for the class of discrete-time control systems. We propose notions of so-called augmented control barrier certificates in conjunction with specified regions of interest capturing the initial and secret sets of the system. Sufficient conditions for (the lack of) approximate initial-state opacity of discretetime control systems are proposed based on the existence of the proposed barrier certificates. We further present an efficient computation method by casting the conditions for barrier certificates as sum-of-squares programming problems. The effectiveness of the proposed results is illustrated through two numerical examples.

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Automated and Formal Synthesis of Neural Barrier Certificates for Dynamical Models

Cited by 3 publications

References 27 publications

Quantitative Verification With Neural Networks For Probabilistic Programs and Stochastic Systems

Quantitative Verification With Neural Networks For Probabilistic Programs and Stochastic Systems

Secure-by-Construction Synthesis of Cyber-Physical Systems

Verification of Approximate Opacity via Barrier Certificates

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