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For a given computational problem, a certificate is a piece of data that one (the prover) attaches to the output with the aim of allowing efficient verification (by the verifier) that this output is correct. Here, we consider the minimal…

Symbolic Computation · Computer Science 2018-05-21 Pascal Giorgi , Vincent Neiger

We present an approach to unsolvability certification of temporal planning. Our approach is based on encoding the planning problem into a network of timed automata, and then using an efficient model checker on the network followed by a…

Logic in Computer Science · Computer Science 2025-10-21 David Wang , Mohammad Abdulaziz

We propose a maturity-based framework for certifying embodied AI systems through explicit measurement mechanisms. We argue that certifiable embodied AI requires structured assessment frameworks, quantitative scoring mechanisms, and methods…

Artificial Intelligence · Computer Science 2026-01-09 Michael C. Darling , Alan H. Hesu , Michael A. Mardikes , Brian C. McGuigan , Reed M. Milewicz

We explain how to encode an algebraic series by finite data and how to do effective arithmetic on the level of these encodings. The reasoning is based on the Newton-Puiseux algorithm and an effective equality test for algebraic series.…

Combinatorics · Mathematics 2025-09-18 Manfred Buchacher

We introduce a framework for the formal specification and verification of quantum circuits based on the Feynman path integral. Our formalism, built around exponential sums of polynomial functions, provides a structured and natural way of…

Quantum Physics · Physics 2019-01-30 Matthew Amy

The PC algorithm infers causal relations using conditional independence tests that require a pre-specified Type I $\alpha$ level. PC is however unsupervised, so we cannot tune $\alpha$ using traditional cross-validation. We therefore…

Machine Learning · Statistics 2020-12-23 Eric V. Strobl

Validation is often defined as the process of determining the degree to which a model is an accurate representation of the real world from the perspective of its intended uses. Validation is crucial as industries and governments depend…

Data Analysis, Statistics and Probability · Physics 2015-06-26 D. Sornette , A. B. Davis , K. Ide , K. R. Vixie , V. Pisarenko , J. R. Kamm

We offer a digital signature scheme using Boolean automorphisms of a multivariate polynomial algebra over integers. Verification part of this scheme is based on the approximation of the number of zeros of a multivariate Boolean function.

Cryptography and Security · Computer Science 2023-09-08 Dima Grigoriev , Ilia Ilmer , Alexey Ovchinnikov , Vladimir Shpilrain

Model counting, or counting the satisfying assignments of a Boolean formula, is a fundamental problem with diverse applications. Given #P-hardness of the problem, developing algorithms for approximate counting is an important research area.…

Logic in Computer Science · Computer Science 2023-12-20 Kuldeep S. Meel , Supratik Chakraborty , S. Akshay

We consider the parameterized verification problem for distributed algorithms where the goal is to develop techniques to prove the correctness of a given algorithm regardless of the number of participating processes. Motivated by an…

Formal Languages and Automata Theory · Computer Science 2022-04-26 Nathalie Bertrand , Nicolas Markey , Ocan Sankur , Nicolas Waldburger

Checking two probabilistic automata for equivalence has been shown to be a key problem for efficiently establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test…

Formal Languages and Automata Theory · Computer Science 2012-01-09 Stefan Kiefer , Andrzej S. Murawski , Joël Ouaknine , Björn Wachter , James Worrell

As machine learning is increasingly used in essential systems, it is important to reduce or eliminate the incidence of serious bugs. A growing body of research has developed machine learning algorithms with formal guarantees about…

Machine Learning · Computer Science 2020-07-15 Jean-Baptiste Tristan , Joseph Tassarotti , Koundinya Vajjha , Michael L. Wick , Anindya Banerjee

We build a class of polynomial problems with not polynomial certificates. The parameter concerning which are defined efficiency of corresponding algorithms is the number $n$ of elements of the set has used at construction of combinatory…

General Mathematics · Mathematics 2013-02-22 B. S. Kochkarev

In this paper, we extend an available neural network verification technique to support a wider class of piece-wise linear activation functions. Furthermore, we extend the algorithms, which provide in their original form exact respectively…

Machine Learning · Computer Science 2023-11-21 László Antal , Hana Masara , Erika Ábrahám

In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…

Functional Analysis · Mathematics 2008-12-09 Geraldo Botelho , Daniel Pellegrino , Pilar Rueda

Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…

Computer Vision and Pattern Recognition · Computer Science 2016-09-20 Reza Borhani , Jeremy Watt , Aggelos Katsaggelos

In this article, we study a calibrated version of Reifenberg theorem "with holes". In particular we study sets that are suitably approximable at all points and scales by calibrated planes and show that, without any additional hypotheses on…

Analysis of PDEs · Mathematics 2025-09-10 Susanna Bertolini , Alessandro Preti , Daniele Valtorta

In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…

Symbolic Computation · Computer Science 2016-10-06 Moulay A. Barkatou , Maximilian Jaroschek , Suzy S. Maddah

Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs…

Logic in Computer Science · Computer Science 2024-02-27 Sam Buss , Emre Yolcu

We build a SAT solver implementing the DPLL algorithm in the verification-enabled programming language Dafny. The resulting solver is fully verified (soundness, completeness and termination are computer checked). We benchmark our Dafny…

Logic in Computer Science · Computer Science 2020-07-22 Cezar-Constantin Andrici , Ştefan Ciobâcă