Related papers: Recycling Algebraic Proof Certificates
In rule-based systems, goal-oriented computations correspond naturally to the possible ways that an observation may be explained. In some applications, we need to compute explanations for a series of observations with the same domain. The…
Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear…
Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
We consider statistical procedures for hypothesis testing of real valued functionals of matched pairs with missing values. In order to improve the accuracy of existing methods, we propose a novel multiplication combination procedure.…
Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…
Probably Approximately Correct (PAC) bounds are widely used to derive probabilistic guarantees for the generalisation of machine learning models. They highlight the components of the model which contribute to its generalisation capacity.…
Large language models are increasingly capable at closed-world mathematical reasoning, but research assistance also requires source-grounded use of the literature. When a proof reaches a non-trivial step, a useful assistant should determine…
Constrained Horn Clauses (CHCs) are often used in automated program verification. Thus, techniques for (dis-)proving satisfiability of CHCs are a very active field of research. On the other hand, acceleration techniques for computing…
This paper presents the integration of constraint propagation and dual proof analysis in an exact, roundoff-error-free MIP solver. The authors employ safe rounding methods to ensure that all results remain provably correct, while…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
Retrieval-augmented generation (RAG) is increasingly deployed in enterprise search and document-centric assistants, where responses must be grounded in long and complex source materials. In practice, verifying that generated answers…
Proof search in non-confluent tableau calculi, such as the connection tableau calculus, suffers from excess backtracking, but simple restrictions on backtracking are incomplete. We adopt constraint learning to reduce backtracking in the…
Evaluating the veracity of everyday claims is time consuming and in some cases requires domain expertise. We empirically demonstrate that the commonly used fact checking pipeline, known as the retriever-reader, suffers from performance…
We show that Connes' embedding conjecture on von Neumann algebras is equivalent to the existence of certain algebraic certificates for a polynomial in noncommuting variables to satisfy the following nonnegativity condition: The trace is…
The rule labeling heuristic aims to establish confluence of (left-)linear term rewrite systems via decreasing diagrams. We present a formalization of a confluence criterion based on the interplay of relative termination and the rule…
ACL2 has long supported user-defined simplifiers, so-called metafunctions and clause processors, which are installed when corresponding rules of class :meta or :clause-processor are proved. Historically, such simplifiers could access the…
Number fields and their rings of integers, which generalize the rational numbers and the integers, are foundational objects in number theory. There are several computer algebra systems and databases concerned with the computational aspects…
In mathematics, LaTeX is the de facto standard to prepare documents, e.g., scientific publications. While some formulae are still developed using pen and paper, more complicated mathematical expressions used more and more often with…
This paper aims to develop a verification method for procedural programs via a transformation into Logically Constrained Term Rewriting Systems (LCTRSs). To this end, we extend transformation methods based on integer TRSs to handle…