Related papers: Solving QBF by Abstraction
This paper presents a method to certify the computational complexity of a standard Branch and Bound method for solving Mixed-Integer Quadratic Programming (MIQP) problems defined as instances of a multi-parametric MIQP. Beyond previous…
Convex (specifically semidefinite) relaxation provides a powerful approach to constructing robust machine perception systems, enabling the recovery of certifiably globally optimal solutions of challenging estimation problems in many…
The recently developed massively parallel satisfiability (SAT) solver HordeSAT was designed in a modular way to allow the integration of any sequential CDCL-based SAT solver in its core. We integrated the QCDCL-based quantified Boolean…
Automatically verifying safety properties of programs is hard, and it is even harder if the program acts upon arrays or other forms of maps. Many approaches exist for verifying programs operating upon Boolean and integer values (e.g.…
In abstract interpretation-based static analysis, approximation is encoded by abstract domains. They provide systematic guidelines for designing abstract semantic functions that approximate some concrete system behaviors under analysis. It…
This paper develops certificates that propagate compatibility of multiple control barrier function (CBF) constraints from sampled vertices to their convex hull. Under mild concavity and affinity assumptions, we present three sufficient…
In this paper, we create a systematic and automatic procedure for transforming the integer factorization problem into the problem of solving a system of Boolean equations. Surprisingly, the resulting system of Boolean equations takes on a…
Recent advances in large language models have demonstrated impressive capabilities in mathematical formalization. However, existing benchmarks focus on logical verification of declarative propositions, often neglecting the task of…
Case-Based Reasoning (CBR) is an artificial intelligence approach to problem-solving with a good record of success. This article proposes using Quantum Computing to improve some of the key processes of CBR, such that a Quantum Case-Based…
Quantified Boolean Formulas (QBF) extend propositional logic with quantification $\forall, \exists$. In QBF, an existentially quantified variable is allowed to depend on all universally quantified variables in its scope. Dependency…
In this paper, we present several new linearizations of a quadratic binary optimization problem (QBOP), primarily using the method of aggregations. Although aggregations were studied in the past in the context of solving system of…
A common technique to verify complex logic specifications for dynamical systems is the construction of symbolic abstractions: simpler, finite-state models whose behaviour mimics the one of the systems of interest. Typically, abstractions…
We study quantified propositional logics from the complexity theoretic point of view. First we introduce alternating dependency quantified boolean formulae (ADQBF) which generalize both quantified and dependency quantified boolean formulae.…
This paper studies the efficient implementation of safety filters that are designed using control barrier functions (CBFs), which minimally modify a nominal controller to render it safe with respect to a prescribed set of states. Although…
ASP(Q) extends Answer Set Programming (ASP) with Quantifiers over answer sets. In this paper we focus on the class of ASP(Q) programs with two quantifiers and weak constraints, denoted as 2-ASP(Q)^w. 2-ASP(Q)^w is a practically relevant…
Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause…
We describe QGLAB, a new MATLAB package for analyzing partial differential equations on quantum graphs. The software is built on the existing, object-oriented MATLAB directed-graph class, inheriting its structure and adding additional…
Formal program verification is a longstanding goal in the field. We present the first quantitative comparison of the two primary compiler verification approaches, credible compilation/translation validation and full verification. Working…
Curved Boolean Logic (CBL) generalizes propositional logic by allowing local truth assignments that do not extend to a single global valuation, analogous to curvature in geometry. We give equivalent sheaf and exclusivity-graph semantics and…
Recently, we have developed an efficient generic partition refinement algorithm, which computes behavioural equivalence on a state-based system given as an encoded coalgebra, and implemented it in the tool CoPaR. Here we extend this to a…