Related papers: Closure Certificates
Browsers can detect malicious websites that are provisioned with forged or fake TLS/SSL certificates. However, they are not so good at detecting malicious websites if they are provisioned with mistakenly issued certificates or certificates…
Control barrier functions provide a powerful means for synthesizing safety filters that ensure safety framed as forward set invariance. Key to CBFs' effectiveness is the simple inequality on the system dynamics: $\dot{h} \geq - \alpha(h)$.…
We deal with the problem of designing one-sided error property testers for cycle-freeness in bounded degree graphs. Such a property tester always accepts forests. Furthermore, when it rejects an input, it provides a short cycle as a…
Bounded self-certification in Turing machines fails because self-simulation necessarily incurs a strictly positive temporal overhead. We translate this operational constraint into a domain-theoretic framework, defining an operator that…
Timed automata are a common formalism for the verification of concurrent systems subject to timing constraints. They extend finite-state automata with clocks, that constrain the system behavior in locations, and to take transitions. While…
Verifying the safety of controllers is critical for many applications, but is especially challenging for systems with bounded inputs. Backup control barrier functions (bCBFs) offer a structured approach to synthesizing safe controllers that…
In this letter, we detail our randomized approach to safety-critical system verification. Our method requires limited system data to make a strong verification statement. Specifically, our method first randomly samples initial conditions…
Control barrier functions are mathematical constructs used to guarantee safety for robotic systems. When integrated as constraints in a quadratic programming optimization problem, instantaneous control synthesis with real-time performance…
For a given computational problem, a certificate is a piece of data that one (the prover) attaches to the output with the aim of allowing efficient verification (by the verifier) that this output is correct. Here, we consider the minimal…
Differential-algebraic equations (DAEs) arise in power networks, chemical processes, and multibody systems, where algebraic constraints encode physical conservation laws. The safety of such systems is critical, yet safe control is…
The safety of infinite state systems can be checked by a backward reachability procedure. For certain classes of systems, it is possible to prove the termination of the procedure and hence conclude the decidability of the safety problem.…
This paper offers a direct data-driven approach for learning robust control barrier certificates (R-CBCs) and robust safety controllers (R-SCs) for discrete-time input-affine polynomial systems with unknown dynamics under…
High-order control barrier functions (HOCBFs) can be used to provide autonomous systems with safety, though computational methods to verify and synthesize these functions remain lacking. In this work, we address this need by formulating SOS…
This work presents a sum-of-squares (SOS) based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by L-infinity bounded input,…
The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more…
The existence of a Control Barrier Function (CBF) for a control-affine system provides a powerful design tool to ensure safety. Any controller that satisfies the CBF condition and ensures that the trajectories of the closed-loop system are…
This paper develops a smooth safety-filtering framework for nonlinear control-affine systems under limited perception. Classical Control Barrier Function (CBF) filters assume global availability of the safety function - its value and…
A classical approach to studying Markov decision processes (MDPs) is to view them as state transformers. However, MDPs can also be viewed as distribution transformers, where an MDP under a strategy generates a sequence of probability…
Certifying the Region of Attraction (ROA) for high-dimensional nonlinear dynamical systems remains a severe computational bottleneck. Traditional deterministic verification methods, such as Sum-of-Squares (SOS) programming and…
We develop a general and unconditional framework for certifying the global nonnegativity of multivariate integer polynomials; based on rewriting them as sum of squares modulo their gradient ideals. We remove the two structural assumptions…