171 research outputs found

    (b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!)

    Get PDF
    (b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!

    Constant-Depth Circuits vs. Monotone Circuits

    Get PDF

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Applications

    Get PDF
    Volume 3 describes how resource-aware machine learning methods and techniques are used to successfully solve real-world problems. The book provides numerous specific application examples: in health and medicine for risk modelling, diagnosis, and treatment selection for diseases in electronics, steel production and milling for quality control during manufacturing processes in traffic, logistics for smart cities and for mobile communications

    On when the union of two algebraic sets is algebraic

    Full text link
    In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize equational domains, with respect to polynomial equations, inside congruence permutable varieties, and with respect to term equations, among all algebras of size two and all algebras of size three with a cyclic automorphism. Furthermore, for each size at least three, we prove that, modulo term equivalence, there is a continuum of equational domains of that size.Comment: 50 pages, 1 figure, 1 tabl

    Quantum Darwinism and Friends

    Get PDF
    In honor of Wojciech Zurek’s 70th birthday, this Special Issue is dedicated to recent advances in our understanding the emergence of classical reality, and pays tribute to Zurek’s seminal contributions to our understanding of the Universe. To this end, “Quantum Darwinism and Friends” collects articles that make sense of the apparent chasm between quantum weirdness and classical perception, and provides a snapshot of this fundamental, exciting, and vivid field of theoretical physics

    Parameterized aspects of team-based formalisms and logical inference

    Get PDF
    Parameterized complexity is an interesting subfield of complexity theory that has received a lot of attention in recent years. Such an analysis characterizes the complexity of (classically) intractable problems by pinpointing the computational hardness to some structural aspects of the input. In this thesis, we study the parameterized complexity of various problems from the area of team-based formalisms as well as logical inference. In the context of team-based formalism, we consider propositional dependence logic (PDL). The problems of interest are model checking (MC) and satisfiability (SAT). Peter Lohmann studied the classical complexity of these problems as a part of his Ph.D. thesis proving that both MC and SAT are NP-complete for PDL. This thesis addresses the parameterized complexity of these problems with respect to a wealth of different parameterizations. Interestingly, SAT for PDL boils down to the satisfiability of propositional logic as implied by the downwards closure of PDL-formulas. We propose an interesting satisfiability variant (mSAT) asking for a satisfiable team of size m. The problem mSAT restores the ‘team semantic’ nature of satisfiability for PDL-formulas. We propose another problem (MaxSubTeam) asking for a maximal satisfiable team if a given team does not satisfy the input formula. From the area of logical inference, we consider (logic-based) abduction and argumentation. The problem of interest in abduction (ABD) is to determine whether there is an explanation for a manifestation in a knowledge base (KB). Following Pfandler et al., we also consider two of its variants by imposing additional restrictions over the size of an explanation (ABD and ABD=). In argumentation, our focus is on the argument existence (ARG), relevance (ARG-Rel) and verification (ARG-Check) problems. The complexity of these problems have been explored already in the classical setting, and each of them is known to be complete for the second level of the polynomial hierarchy (except for ARG-Check which is DP-complete) for propositional logic. Moreover, the work by Nord and Zanuttini (resp., Creignou et al.) explores the complexity of these problems with respect to various restrictions over allowed KBs for ABD (ARG). In this thesis, we explore a two-dimensional complexity analysis for these problems. The first dimension is the restrictions over KB in Schaefer’s framework (the same direction as Nord and Zanuttini and Creignou et al.). What differentiates the work in this thesis from an existing research on these problems is that we add another dimension, the parameterization. The results obtained in this thesis are interesting for two reasons. First (from a theoretical point of view), ideas used in our reductions can help in developing further reductions and prove (in)tractability results for related problems. Second (from a practical point of view), the obtained tractability results might help an agent designing an instance of a problem come up with the one for which the problem is tractable

    Flow-augmentation III: Complexity dichotomy for Boolean CSPs parameterized by the number of unsatisfied constraints

    Get PDF
    We study the parameterized problem of satisfying ``almost all'' constraints of a given formula FF over a fixed, finite Boolean constraint language Γ\Gamma, with or without weights. More precisely, for each finite Boolean constraint language Γ\Gamma, we consider the following two problems. In Min SAT(Γ)(\Gamma), the input is a formula FF over Γ\Gamma and an integer kk, and the task is to find an assignment α ⁣:V(F)→{0,1}\alpha \colon V(F) \to \{0,1\} that satisfies all but at most kk constraints of FF, or determine that no such assignment exists. In Weighted Min SAT(Γ(\Gamma), the input additionally contains a weight function w ⁣:F→Z+w \colon F \to \mathbb{Z}_+ and an integer WW, and the task is to find an assignment α\alpha such that (1) α\alpha satisfies all but at most kk constraints of FF, and (2) the total weight of the violated constraints is at most WW. We give a complete dichotomy for the fixed-parameter tractability of these problems: We show that for every Boolean constraint language Γ\Gamma, either Weighted Min SAT(Γ)(\Gamma) is FPT; or Weighted Min SAT(Γ)(\Gamma) is W[1]-hard but Min SAT(Γ)(\Gamma) is FPT; or Min SAT(Γ)(\Gamma) is W[1]-hard. This generalizes recent work of Kim et al. (SODA 2021) which did not consider weighted problems, and only considered languages Γ\Gamma that cannot express implications (u→v)(u \to v) (as is used to, e.g., model digraph cut problems). Our result generalizes and subsumes multiple previous results, including the FPT algorithms for Weighted Almost 2-SAT, weighted and unweighted ℓ\ell-Chain SAT, and Coupled Min-Cut, as well as weighted and directed versions of the latter. The main tool used in our algorithms is the recently developed method of directed flow-augmentation (Kim et al., STOC 2022)
    • 

    corecore