Related papers: Recycling Algebraic Proof Certificates
We consider efficient route planning for robots in applications such as infrastructure inspection and automated surgical imaging. These tasks can be modeled via the combinatorial problem Graph Inspection. The best known algorithms for this…
CeTA was originally developed as a tool for certifying termination proofs which have to be provided as certificates in the CPF-format. Its soundness is proven as part of IsaFoR, the Isabelle Formalization of Rewriting. By now, CeTA can also…
Fact-checking the truthfulness of claims usually requires reasoning over multiple evidence sentences. Oftentimes, evidence sentences may not be always self-contained, and may require additional contexts and references from elsewhere to…
Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…
Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the…
In program verification, constraint-based random testing is a powerful technique which aims at generating random test cases that satisfy functional properties of a program. However, on recursive constrained data-structures (e.g., sorted…
Continuous testing during development is a well-established technique for software-quality assurance. Continuous model checking from revision to revision is not yet established as a standard practice, because the enormous resource…
A low-degree test is a collection of simple, local rules for checking the proximity of an arbitrary function to a low-degree polynomial. Each rule depends on the function's values at a small number of places. If a function satisfies many…
Automatic and efficient verification of multiplier designs, especially through a provably correct method, is a difficult problem. We show how to utilize a theorem prover, ACL2, to implement an efficient rewriting algorithm for multiplier…
Compilers are a prime target for formal verification, since compiler bugs invalidate higher-level correctness guarantees, but compiler changes may become more labor-intensive to implement, if they must come with proof patches. One appealing…
ML4PG is an extension of the Proof General interface, allowing the user to invoke machine-learning algorithms and find proof similarities in Coq/SSReect libraries. In this paper, we present three new improvements to ML4PG. First, a new…
In this work we study the cost of local and global proofs on distributed verification. In this setting the nodes of a distributed system are provided with a nondeterministic proof for the correctness of the state of the system, and the…
This paper presents differential-algebraic refinement logic (dARL) with which one can deductively verify both properties and relations of differential-algebraic programs (DAPs) that extend hybrid dynamical systems with…
The study of distributed interactive proofs was initiated by Kol, Oshman, and Saxena [PODC 2018] as a generalization of distributed decision mechanisms (proof-labeling schemes, etc.), and has received a lot of attention in recent years. In…
Numerical and symbolic methods for optimization are used extensively in engineering, industry, and finance. Various methods are used to reduce problems of interest to ones that are amenable to solution by such software. We develop a…
In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each…
Development of formal proofs of correctness of programs can increase actual and perceived reliability and facilitate better understanding of program specifications and their underlying assumptions. Tools supporting such development have…
Certifying verification algorithms not only return whether a given property holds or not, but also provide an accompanying independently checkable certificate and a corresponding witness. The certificate can be used to easily validate the…
The trace test in numerical algebraic geometry verifies the completeness of a witness set of an irreducible variety in affine or projective space. We give a brief derivation of the trace test and then consider it for subvarieties of…
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…