Search Results - Circuit complexity Algebraic Formulas

Monotone Arithmetic Complexity of Graph Homomorphism Polynomials by Komarath, Balagopal, Pandey, Anurag, Rahul, C. S.

“… families which are complete for algebraic complexity classes VBP , V P , and VNP . We discover that, in the monotone setting, the formula complexity, the ABP complexity…”
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Quadratic Lower Bounds for Algebraic Branching Programs and Formulas by Chatterjee, Prerona, Kumar, Mrinal, She, Adrian, Lee Volk, Ben

“…We show that any Algebraic Branching Program (ABP) computing the polynomial ∑ i = 1 n x i n has at least Ω ( n 2 ) vertices…”
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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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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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Demystifying the border of depth-3 algebraic circuits by Dutta, Pranjal, Dwivedi, Prateek, Saxena, Nitin

“… We show that the border of bounded top-fanin-k depth-3 circuits, for constant k, is relatively easy- it can be computed by a polynomial size algebraic branching program (ABP…”
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An Iterative FEM Solver for IC Electromagnetic Analysis via Hybrid Geometric-Algebraic Partitioning and Neural Network Optimization by Li, Mingtao, Yan, Changhao, Cui, Tao, Jiang, Liguo, Dai, Wenliang, Bi, Zhaori, Zhu, Keren, Zeng, Xuan

“…In electromagnetic finite element analysis of integrated circuits (ICs), direct solvers face high time and space complexity in large-scale problems…”
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Lower Bounds and PIT for Non-commutative Arithmetic Circuits with Restricted Parse Trees by Lagarde, Guillaume, Limaye, Nutan, Srinivasan, Srikanth

“…We investigate the power of Non-commutative Arithmetic Circuits , which compute polynomials over the free non-commutative polynomial ring F ⟨ x 1 , … , x N…”
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Multilinear formulas, maximal-partition discrepancy and mixed-sources extractors by Raz, Ran, Yehudayoff, Amir

“… We prove lower bounds for several old and new subclasses of circuits: monotone circuits, orthogonal formulas, non-canceling formulas, and noise-resistant formulas…”
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Homogeneous Algebraic Complexity Theory and Algebraic Formulas by Dutta, Pranjal, Gesmundo, Fulvio, Ikenmeyer, Christian, Jindal, Gorav, Lysikov, Vladimir

“…We study algebraic complexity classes and their complete polynomials under \emph{homogeneous linear} projections, not just under the usual affine linear projections that were originally introduced by Valiant in 1979…”
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Algebraic proofs over noncommutative formulas by Tzameret, Iddo

“…We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas…”
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Schur Polynomials Do Not Have Small Formulas If the Determinant does not by Chaugule, Prasad, Kumar, Mrinal, Limaye, Nutan, Mohapatra, Chandra Kanta, She, Adrian, Srinivasan, Srikanth

“…) and geometric complexity theory Ikenmeyer & Panova (2017). However, unlike some other families of symmetric polynomials like the elementary symmetric polynomials, the power…”
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Slightly improved lower bounds for homogeneous formulas of bounded depth and bounded individual degree by Chillara, Suryajith

“…•A finer product decomposition for Homogeneous Formulas of small depth.•A finer product decomposition for small-depth homogeneous multi-r-ic formulas…”
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Small Space Analogues of Valiant’s Classes and the Limitations of Skew Formulas by Mahajan, Meena, Raghavendra Rao, B. V.

“…” complexity of the computed function. Looking for a similar relationship in Valiant’s algebraic model of computation, we propose width of an arithmetic circuit as a possible measure of space…”
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Formulas are Exponentially Stronger than Monotone Circuits in Non-commutative Setting by Hrube, Pavel, Yehudayoff, Amir

“…We give an example of a non-commutative monotone polynomial f which can be computed by a polynomial-size non-commutative formula, but every monotone non-commutative circuit computing f must have an exponential size…”
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Average-case linear matrix factorization and reconstruction of low width algebraic branching programs by Kayal, Neeraj, Nair, Vineet, Saha, Chandan

“…? Finding such a minimal representation is closely related to finding an optimal way to compute a given polynomial via an algebraic branching program…”
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The Complexity of Tensor Circuit Evaluation by Beaudry, Martin, Holzer, Markus

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z-Reliable SE-Coprognosability of Discrete Event Systems and an Algebraic State Space Approach to Verification by Yingrui, Zhou, Chen, Zengqiang, Ni, Yuanhua, Liu, Zhongxin

“…This brief investigates the problem of fault prognosis in decentralized structure, where given systems are monitored by <inline-formula> <tex-math notation="LaTeX">r </tex-math></inline-formula…”
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Reduced-Complexity LCC Reed-Solomon Decoder Based on Unified Syndrome Computation by Zhang, Wei, Wang, Hao, Pan, Boyang

“… Algebraic soft-decision decoding (ASD) of RS codes can obtain significant coding gain over the hard-decision decoding (HDD…”
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The Arithmetic Complexity of Tensor Contraction by Capelli, Florent, Durand, Arnaud, Mengel, Stefan

“…We investigate the algebraic complexity of tensor calculus. We consider a generalization of iterated matrix product to tensors and show that the resulting…”
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A Near-Optimal Depth-Hierarchy Theorem for Small-Depth Multilinear Circuits by Chillara, Suryajith, Engels, Christian, Limaye, Nutan, Srinivasan, Srikanth

“…We study the size blow-up that is necessary to convert an algebraic circuit of product-depth δ…”
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