Related papers: Simulating reachability using first-order logic wi…
Learning-enabled planning and control algorithms are increasingly popular, but they often lack rigorous guarantees of performance or safety. We introduce an algorithm for computing underapproximate backward reachable sets of nonlinear…
Recent literature has proposed approaches that learn control policies with high performance while maintaining safety guarantees. Synthesizing Hamilton-Jacobi (HJ) reachable sets has become an effective tool for verifying safety and…
This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…
Like other engineering disciplines, software engineering should also have principles to guide the construction of sustainable computer applications. Tangible properties include a) unlimited scalability, b) maximal reproducibility, and c)…
A first-order conditional logic is considered, with semantics given by a variant of epsilon-semantics, where p -> q means that Pr(q | p) approaches 1 super-polynomially --faster than any inverse polynomial. This type of convergence is…
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in…
Reachability analysis is important for studying optimal control problems and differential games, which are powerful theoretical tools for analyzing and modeling many practical problems in robotics, aircraft control, among other application…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
It is well known that we can use structural proof theory to refine, or generalize, existing paradigmatic computational primitives, or to discover new ones. Under such a point of view we keep developing a programme whose goal is establishing…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
Ensuring safety is important for the practical deployment of reinforcement learning (RL). Various challenges must be addressed, such as handling stochasticity in the environments, providing rigorous guarantees of persistent state-wise…
We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for…
Sharpness is an almost generic assumption in continuous optimization that bounds the distance from minima by objective function suboptimality. It facilitates the acceleration of first-order methods through restarts. However, sharpness…
We study fundamental reachability problems on pseudo-orbits of linear dynamical systems. Pseudo-orbits can be viewed as a model of computation with limited precision and pseudo-reachability can be thought of as a robust version of classical…
We present a general framework for applying machine-learning algorithms to the verification of Markov decision processes (MDPs). The primary goal of these techniques is to improve performance by avoiding an exhaustive exploration of the…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
The model of asynchronous programming arises in many contexts, from low-level systems software to high-level web programming. We take a language-theoretic perspective and show general decidability and undecidability results for asynchronous…
Local reasoning about programs that combine aliasing and mutable state is a longstanding challenge. Existing approaches -- ownership systems, linear and affine types, uniqueness types, and lexical effect tracking -- impose global…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…