Search Results - Theory of computation- Algebraic complexity theory

On Solving Sparse Polynomial Factorization Related Problems by Bisht, Pranav, Volkovich, Ilya

“…In a recent result of Bhargava, Saraf and Volkovich [FOCS’18; JACM’20], the first factor sparsity bound for constant individual degree polynomials was shown…”
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Characterizing Valiant's algebraic complexity classes by Malod, Guillaume, Portier, Natacha

“…Valiant introduced 20 years ago an algebraic complexity theory to study the complexity of polynomial families…”
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Zero-one laws for provability logic: Axiomatizing validity in almost all models and almost all frames by Verbrugge, Rineke

“…It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of…”
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Minimal Taylor Algebras as a Common Framework for the Three Algebraic Approaches to the CSP by Barto, Libor, Brady, Zarathustra, Bulatov, Andrei, Kozik, Marcin, Zhuk, Dmitriy

“…This paper focuses on the algebraic theory underlying the study of the complexity and the algorithms for the Constraint Satisfaction Problem (CSP…”
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Efficient Computation of a Semi-Algebraic Basis of the First Homology Group of a Semi-Algebraic Set by Basu, Saugata, Percival, Sarah

“… ) . This algorithm generalizes well known algorithms having singly exponential complexity for computing a semi-algebraic basis of the zeroth homology group of semi-algebraic sets, which is equivalent…”
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CoqPilot, a plugin for LLM-based generation of proofs by Kozyrev, Andrei, Solovev, Gleb, Khramov, Nikita, Podkopaev, Anton

“…We present CoqPilot, a VS Code extension designed to help automate writing of Coq proofs. The plugin collects the parts of proofs marked with the admit tactic…”
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On the logical structure of choice and bar induction principles by Brede, Nuria, Herbelin, Hugo

“…We develop an approach to choice principles and their contrapositive bar-induction principles as extensionality schemes connecting an "intensional" or…”
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Categorical models of Linear Logic with fixed points of formulas by Ehrhard, Thomas, Jafarrahmani, Farzad

“…We develop a categorical semantics of µLL, a version of propositional Linear Logic with least and greatest fixed points extending David Baelde's propositional…”
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Accelerating All-SAT Computation with Short Blocking Clauses by Zhang, Yueling, Pu, Geguang, Sun, Jun

“…The All-SAT (All-SATisfiable) problem focuses on finding all satisfiable assignments of a given propositional formula, whose applications include model…”
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Constraint Satisfaction Problems over Finite Structures by Barto, Libor, DeMeo, William, Mottet, Antoine

“…We initiate a systematic study of the computational complexity of the Constraint Satisfaction Problem (CSP…”
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Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits by Limaye, Nutan, Srinivasan, Srikanth, Tavenas, Sebastien

“…An Algebraic Circuit for a polynomial P\ \ \in \mathbb{F}[x_{1}, \ldots, x_{N}] is a computational model for constructing the polynomial P using only additions and multiplications…”
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Decidability and Complexity in Weakening and Contraction Hypersequent Substructural Logics by Balasubramanian, A. R., Lang, Timo, Ramanayake, Revantha

“… . Decidability for the corresponding extensions of its contraction counterpart FL ec was established recently but their computational complexity was left unanswered…”
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Combinatorial Proofs and Decomposition Theorems for First-order Logic by Hughes, Dominic J. D., Strasburger, Lutz, Wu, Jui-Hsuan

“…We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in…”
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Parameterized Complexity of Elimination Distance to First-Order Logic Properties by Fomin, Fedor V., Golovach, Petr A., Thilikos, Dimitrios M.

“…The elimination distance to some target graph property {\mathcal{P}} is a general graph modification parameter introduced by Bulian and Dawar. We initiate the…”
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Counting Induced Subgraphs: An Algebraic Approach to #W[1]-Hardness by Dörfler, Julian, Roth, Marc, Schmitt, Johannes, Wellnitz, Philip

“…We study the problem # I N D S U B ( Φ ) of counting all induced subgraphs of size k in a graph G that satisfy the property Φ . It is shown that, given any…”
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Living without Beth and Craig: Definitions and Interpolants in the Guarded and Two-Variable Fragments by Jung, Jean Christoph, Wolter, Frank

“…In logics with the Craig interpolation property (CIP) the existence of an interpolant for an implication follows from the validity of the implication. In…”
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Higher Lenses by Capriotti, Paolo, Danielsson, Nils Anders, Vezzosi, Andrea

“…We show that total, very well-behaved lenses are not very well-behaved when treated proof-relevantly in the setting of homotopy type theory/univalent foundations…”
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First-Order Reasoning and Efficient Semi-Algebraic Proofs by Part, Fedor, Thapen, Neil, Tzameret, Iddo

“… Specifically, we develop first-order theories that capture in a precise manner constant degree algebraic and semi-algebraic proof systems…”
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An Algebraic Theory of Complexity for Discrete Optimization by Cohen, David A., Cooper, Martin C., Creed, Páidí, Jeavons, Peter G., Živný, Stanislav

“… Here we present a unifying theory of complexity for problems of this kind. We show that the complexity of a finite-domain discrete optimization problem…”
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Some Complete and Intermediate Polynomials in Algebraic Complexity Theory by Mahajan, Meena, Saurabh, Nitin

“…We provide a list of new natural VNP-intermediate polynomial families, based on basic (combinatorial) NP-complete problems that are complete under parsimonious…”
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