Related papers: Certified Symmetry and Dominance Breaking for Comb…
There is a growing need for computational tools to automatically design and verify autonomous systems, especially complex robotic systems involving perception, planning, control, and hardware in the autonomy stack. Differentiable…
The Circuit Satisfiability (CSAT) problem, a variant of the Boolean Satisfiability (SAT) problem, plays a critical role in integrated circuit design and verification. However, existing SAT solvers, optimized for Conjunctive Normal Form…
Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution…
In Verification and in (optimal) AI Planning, a successful method is to formulate the application as boolean satisfiability (SAT), and solve it with state-of-the-art DPLL-based procedures. There is a lack of understanding of why this works…
The queen domination problem asks for the minimum number of queens needed to attack all squares on an $n\times n$ chessboard. Once this optimal number is known, determining the number of distinct solutions up to isomorphism has also…
Using polynomial equations to model combinatorial problems has been a popular tool both in computational combinatorics as well as an approach to proving new theorems. In this paper, we look at several combinatorics problems modeled by…
We present a proof system for establishing the correctness of results produced by optimization algorithms, with a focus on mixed-integer programming (MIP). Our system generalizes the seminal work of Bogaerts, Gocht, McCreesh, and…
Accuracy certificates for convex minimization problems allow for online verification of the accuracy of approximate solutions and provide a theoretically valid online stopping criterion. When solving the Lagrange dual problem, accuracy…
In their nature configuration problems are combinatorial (optimization) problems. In order to find a configuration a solver has to instantiate a number of components of a some type and each of these components can be used in a relation…
Nonnegativity certificates can be used to obtain tight dual bounds for polynomial optimization problems. Hierarchies of certificate-based relaxations ensure convergence to the global optimum, but higher levels of such hierarchies can become…
Many industrial applications require finding solutions to challenging combinatorial problems. Efficient elimination of symmetric solution candidates is one of the key enablers for high-performance solving. However, existing model-based…
Constrained-random simulation is the predominant approach used in the industry for functional verification of complex digital designs. The effectiveness of this approach depends on two key factors: the quality of constraints used to…
Established techniques that enable robots to learn from demonstrations are based on learning a stable dynamical system (DS). To increase the robots' resilience to perturbations during tasks that involve static obstacle avoidance, we propose…
Symmetry reduction is crucial for solving many interesting SAT instances in practice. Numerous approaches have been proposed, which try to strike a balance between symmetry reduction and computational overhead. Arguably the most readily…
Global polynomial optimization methods typically rely on compactness of the feasible region in order to find solutions. These methods can incur considerable computational expense and most commercially available solvers do not verify the…
When Model Predictive Control (MPC) is used in real-time to control linear systems, quadratic programs (QPs) need to be solved within a limited time frame. Recently, several parametric methods have been proposed that certify the number of…
The measure and conquer approach has proven to be a powerful tool to analyse exact algorithms for combinatorial problems, like Dominating Set and Independent Set. In this paper, we propose to use measure and conquer also as a tool in the…
Boolean Satisfiability (SAT) solving underpins a wide range of applications in Electronic Design Automation (EDA), particularly formal verification. However, this paper observes that the mainstream clause reduction heuristic in modern SAT…
The complexity of software in embedded systems has increased significantly over the last years so that software verification now plays an important role in ensuring the overall product quality. In this context, SAT-based bounded model…
We present a Satisfiability (SAT)-based approach for building Mixed Covering Arrays with Constraints of minimum length, referred to as the Covering Array Number problem. This problem is central in Combinatorial Testing for the detection of…