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The minimization problem for propositional formulas is an important optimization problem in the second level of the polynomial hierarchy. In general, the problem is Sigma-2-complete under Turing reductions, but restricted versions are…

Computational Complexity · Computer Science 2011-04-13 Edith Hemaspaandra , Henning Schnoor

A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify the quantum advantage of an untrusted prover. That is, a quantum prover can correctly answer the verifier's challenges and…

Quantum Physics · Physics 2022-09-21 Zhenning Liu , Alexandru Gheorghiu

In this article we present two ways of structuring bodies of evidence, which allow us to reduce the complexity of the operations usually performed in the framework of evidence theory. The first structure just partitions the focal elements…

Artificial Intelligence · Computer Science 2013-03-26 Sandra Sandri

We introduce a low-memory framework for certifying numerical solutions to polynomial systems which uses solution iterators and spatial partitioning trees to reduce memory requirements. We provide a prototypical algorithm, analyze its…

Numerical Analysis · Mathematics 2026-04-21 Paul Breiding , Taylor Brysiewicz , David K. Johnson

In previous work, summarized in this paper, we proposed an operation of parallel composition for rewriting-logic theories, allowing compositional specification of systems and reusability of components. The present paper focuses on…

Logic in Computer Science · Computer Science 2023-08-01 Óscar Martín , Alberto Verdejo , Narciso Martí-Oliet

Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of…

Numerical Analysis · Mathematics 2018-11-28 Xiu Yang , Xiaoliang Wan , Lin Lin , Huan Lei

The continuous growth of quantum computing and the increasingly complex quantum programs resulting from it lead to unprecedented obstacles in ensuring program correctness. Runtime assertions are, therefore, becoming a crucial tool in the…

Quantum Physics · Physics 2025-05-08 Damian Rovara , Lukas Burgholzer , Robert Wille

We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-09-08 Fabian Reiter

A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the…

Quantum Physics · Physics 2020-05-12 Zvika Brakerski , Venkata Koppula , Umesh Vazirani , Thomas Vidick

Quantitative Bipolar Argumentation Frameworks (QBAFs) provide an alternative approach to computing argument acceptability in Bipolar Argumentation Frameworks (BAFs). Each argument is assigned an initial strength, which is then updated to a…

Artificial Intelligence · Computer Science 2026-05-05 Gianvincenzo Alfano , Sergio Greco , Lucio La Cava , Francesco Parisi , Irina Trubitsyna

We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique…

Quantum Physics · Physics 2007-05-23 Sophie Laplante , Frederic Magniez

We study sign structures of the ground states of spin-$1/2$ magnetic systems using the methods of Boolean Fourier analysis. Previously it was shown that the sign structures of frustrated systems are of complex nature: specifically, neural…

Disordered Systems and Neural Networks · Physics 2025-08-14 Ilya Schurov , Anna Kravchenko , Mikhail I. Katsnelson , Andrey A. Bagrov , Tom Westerhout

We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal)…

Logic · Mathematics 2019-05-21 Taus Brock-Nannestad , Danko Ilik

We propose a system that finds the strongest supporting evidence for a given answer to a question, using passage-based question-answering (QA) as a testbed. We train evidence agents to select the passage sentences that most convince a…

Computation and Language · Computer Science 2019-09-16 Ethan Perez , Siddharth Karamcheti , Rob Fergus , Jason Weston , Douwe Kiela , Kyunghyun Cho

We present a new variant of the quantum adversary method. All adversary methods give lower bounds on the quantum query complexity of a function by bounding the change of a progress function caused by one query. All previous variants…

Quantum Physics · Physics 2007-05-23 Robert Spalek

Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…

Computational Complexity · Computer Science 2017-10-25 Nadia Creignou , Markus Kröll , Reinhard Pichler , Sebastian Skritek , Heribert Vollmer

This paper is concerned with the computational complexity of equivalence and minimisation for automata with transition weights in the field Q of rational numbers. We use polynomial identity testing and the Isolation Lemma to obtain…

Formal Languages and Automata Theory · Computer Science 2015-07-01 Stefan Kiefer , Andrzej Murawski , Joel Ouaknine , Bjoern Wachter , James Worrell

We study the computational complexity of multi-stage robust optimization problems. Such problems are formulated with alternating min/max quantifiers and therefore naturally fall into a higher stage of the polynomial hierarchy. Despite this,…

Optimization and Control · Mathematics 2023-03-23 Marc Goerigk , Stefan Lendl , Lasse Wulf

We initiate the systematic study of QMA algorithms in the setting of property testing, to which we refer as QMA proofs of proximity (QMAPs). These are quantum query algorithms that receive explicit access to a sublinear-size untrusted proof…

Quantum Physics · Physics 2022-10-17 Marcel Dall'Agnol , Tom Gur , Subhayan Roy Moulik , Justin Thaler

Verifiable learning advocates for training machine learning models amenable to efficient security verification. Prior research demonstrated that specific classes of decision tree ensembles -- called large-spread ensembles -- allow for…

Machine Learning · Computer Science 2024-02-26 Stefano Calzavara , Lorenzo Cazzaro , Claudio Lucchese , Giulio Ermanno Pibiri