Suchergebnisse - Circuit complexity Algebraic Formulas

Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits.

Autoren: Limaye, Nutan Srinivasan, Srikanth Tavenas, Sébastien

Quelle: Journal of the ACM; Aug2025, Vol. 72 Issue 4, p1-35, 35p

Schlagwörter: COMPUTATIONAL complexity, CIRCUIT complexity, POLYNOMIALS, COMPUTER circuits, MATHEMATICAL bounds

On the Power of Homogeneous Algebraic Formulas

Autoren: Fournier, Hervé Limaye, Nutan Srinivasan, Srikanth et al.

Weitere Verfasser: Fournier, Hervé Limaye, Nutan Srinivasan, Srikanth et al.

Quelle: Fournier, H, Limaye, N, Srinivasan, S & Tavenas, S 2024, On the Power of Homogeneous Algebraic Formulas . in B Mohar, I Shinkar & R O�Donnell (eds), STOC 2024-Proceedings of the 56th Annual ACM Symposium on Theory of Computing . Association for Computing Machinery, pp. 141-151, 56th Annual ACM Symposium on Theory of Computing, STOC 2024, Vancouver, Canada, 24/06/2024 . https://doi.org/10.1145/3618260.3649760

Schlagwörter: Formula Homogenization ACM Reference, Algebraic Formulas, Formula Homogenization, [INFO.INFO-CC] Computer Science [cs]/Computational Complexity [cs.CC], Theory of computation → Algebraic complexity theory, Circuit complexity Algebraic Formulas

Dateibeschreibung: application/pdf

Zugangs-URL: https://curis.ku.dk/ws/files/431873603/On_the_Power_of_Homogeneous_Algebraic_Formula.pdf
https://hal.science/hal-04683830v1/document
https://doi.org/10.1145/3618260.3649760
https://hal.science/hal-04683830v1

Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits.

Autoren: Limaye, Nutan Srinivasan, Srikanth Tavenas, Sébastien

Quelle: Communications of the ACM; Feb2024, Vol. 67 Issue 2, p101-108, 8p

Schlagwörter: ALGEBRA, POLYNOMIALS, CIRCUIT complexity, ALGORITHMS, DIRECTED acyclic graphs, LOGIC circuits

Monotone Arithmetic Complexity of Graph Homomorphism Polynomials

Autoren: Komarath, Balagopal Pandey, Anurag Rahul, Chengot Sankaramenon et al.

Weitere Verfasser: Komarath, Balagopal Pandey, Anurag Rahul, Chengot Sankaramenon et al.

Quelle: Algorithmica. 85:2554-2579

Schlagwörter: Algebraic complexity, Fixed-parameter algorithms and complexity, Treewidth, Graph homomorphisms, Fine-grained complexity, Algebraic circuits, Homomorphism polynomials, Pathwidth, Monotone complexity, Treedepth, Algebraic branching programs, Algebraic formulas, ddc:004, Graph algorithms

Dateibeschreibung: application/pdf

Zugangs-URL: https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.83

Riffle Rank.

Autoren: Rossman, Benjamin¹ (AUTHOR) benjamin.rossman@duke.edu

Quelle: Procedia Computer Science. 2025, Vol. 273, p215-222. 8p.

Schlagwörter: Circuit complexity, Tensor algebra, Computational complexity

Improved Low-Depth Set-Multilinear Circuit Lower Bounds

Autoren: Kush, Deepanshu Saraf, Shubhangi Deepanshu Kush and Shubhangi Saraf

Weitere Verfasser: Kush, Deepanshu Saraf, Shubhangi Deepanshu Kush and Shubhangi Saraf

Schlagwörter: set-multilinear formulas, FOS: Computer and information sciences, Computer Science - Computational Complexity, 0102 computer and information sciences, ddc:004, complexity measure, Computational Complexity (cs.CC), 01 natural sciences, algebraic circuit complexity

Dateibeschreibung: application/pdf

Zugangs-URL: http://arxiv.org/abs/2205.00611
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.38

Homogeneous Algebraic Complexity Theory and Algebraic Formulas

Autoren: Dutta, Pranjal Gesmundo, Fulvio Ikenmeyer, Christian et al.

Weitere Verfasser: Dutta, Pranjal Gesmundo, Fulvio Ikenmeyer, Christian et al.

Quelle: 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Schlagwörter: FOS: Computer and information sciences, Symmetric polynomials, 68Qxx, Waring rank, Computational Complexity (cs.CC), Computer Science - Computational Complexity, Mathematics - Algebraic Geometry, Geometric Complexity theory, Homogeneous polynomials, Arithmetic formulas, FOS: Mathematics, ddc:004, F.1.3, Border complexity, Algebraic Geometry (math.AG)

Dateibeschreibung: application/pdf

Zugangs-URL: http://arxiv.org/abs/2311.17019
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.43

Logical characterizations of algebraic circuit classes over integral domains.

Autoren: Barlag, Timon Chudigiewitsch, Florian Gaube, Sabrina A.

Quelle: Mathematical Structures in Computer Science; May2024, Vol. 34 Issue 5, p346-374, 29p

Schlagwörter: INTEGRAL domains, FIRST-order logic, CIRCUIT complexity, GENERALIZED integrals, GENERALIZATION

Small-Depth Multilinear Formula Lower Bounds for Iterated Matrix Multiplication with Applications

Autoren: Chillara, Suryajith Limaye, Nutan Srinivasan, Srikanth et al.

Weitere Verfasser: Chillara, Suryajith Limaye, Nutan Srinivasan, Srikanth et al.

Quelle: SIAM Journal on Computing. 48:70-92

Schlagwörter: FOS: Computer and information sciences, Lower Bounds, Computer Science - Computational Complexity, Multilinear formulas, 0102 computer and information sciences, ddc:004, Computational Complexity (cs.CC), 01 natural sciences, Algebraic circuit complexity

Dateibeschreibung: application/pdf

Zugangs-URL: https://drops.dagstuhl.de/opus/volltexte/2018/8523/pdf/LIPIcs-STACS-2018-21.pdf
http://arxiv.org/abs/1710.05481
https://drops.dagstuhl.de/opus/volltexte/2018/8523/
https://dblp.uni-trier.de/db/conf/stacs/stacs2018.html#ChillaraL018
https://doi.org/10.4230/LIPIcs.STACS.2018.21
https://epubs.siam.org/doi/10.1137/18M1191567
https://arxiv.org/abs/1710.05481
https://dblp.uni-trier.de/db/journals/corr/corr1710.html#abs-1710-05481
https://locus.siam.org/doi/abs/10.1137/18M1191567
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.21

THE DEVELOPMENT OF AN ELECTRONIC CIRCUIT SIMULATION SYSTEM USING VARIABLE TABULAR BASES.

Alternate Title: РОЗРОБКА СИСТЕМИ МОДЕЛЮВАННЯ ЕЛЕКТРОННИХ СХЕМ З ВИКОРИСТАННЯМ ЗМІННИХ ТАБЛИЧНИХ БАЗИСІВ. (Ukrainian)

Autoren: Kharchenko, Kostyantyn Beznosyk, Oleksandr Kornachevskyy, Yaroslav et al.

Quelle: Eastern-European Journal of Enterprise Technologies; 2025, Vol. 133 Issue 4, p30-40, 11p

Schlagwörter: ELECTRONIC circuit design, ELECTRONIC circuits, CIRCUIT complexity, ALGEBRAIC equations, ELECTRONIC systems

Monotone Arithmetic Complexity of Graph Homomorphism Polynomials

Autoren: Komarath, Balagopal Pandey, Anurag Rahul, Chengot Sankaramenon et al.

Weitere Verfasser: Komarath, Balagopal Pandey, Anurag Rahul, Chengot Sankaramenon et al.

Schlagwörter: Homomorphism polynomials, Monotone complexity, Algebraic complexity, Graph algorithms, Fine-grained complexity, Fixed-parameter algorithms and complexity, Treewidth, Pathwidth, Treedepth, Graph homomorphisms, Algebraic circuits, Algebraic branching programs, Algebraic formulas

Dateibeschreibung: application/pdf

Relation: Is Part Of LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.83

Verfügbarkeit: https://doi.org/10.4230/LIPIcs.ICALP.2022.83
https://nbn-resolving.org/urn:nbn:de:0030-drops-164245
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.83

Regular Representations of Uniform TC⁰.

Autoren: Hella, Lauri Kontinen, Juha Luosto, Kerkko

Quelle: ACM Transactions on Computational Logic; Oct2025, Vol. 26 Issue 4, p1-46, 46p

Schlagwörter: CIRCUIT complexity, FIRST-order logic, MATHEMATICAL logic, QUANTIFIERS (Linguistics)

Proof Complexity Lower Bounds from Algebraic Circuit Complexity

Autoren: Forbes, Michael A. Shpilka, Amir Tzameret, Iddo et al.

Weitere Verfasser: Forbes, Michael A. Shpilka, Amir Tzameret, Iddo et al.

Quelle: arXiv: Computational Complexity.

Schlagwörter: FOS: Computer and information sciences, Technology, HARDNESS, Computer Science - Logic in Computer Science, Theory & Methods, 1702 Cognitive Sciences, IPS, 0102 computer and information sciences, Computational Complexity (cs.CC), 01 natural sciences, hardness versus randomness, Nullstellensatz, lower bounds, POLYNOMIAL CALCULUS, Computer Science, Theory & Methods, NULLSTELLENSATZ, FOS: Mathematics, 0101 mathematics, Algebraic Complexity, algebraic circuit complexity, 0802 Computation Theory and Mathematics, Science & Technology, SUM, Proof Complexity, Subset-Sum, Mathematics - Logic, functional lower bounds, Logic in Computer Science (cs.LO), Computer Science - Computational Complexity, RESOLUTION, HITTING-SETS, Computer Science, Proof complexity, polynomial calculus, ddc:004, Logic (math.LO), ABPs, algebraic proof systems, ARITHMETIC CIRCUITS

Dateibeschreibung: application/pdf

Zugangs-URL: http://arxiv.org/abs/1606.05050
http://export.arxiv.org/pdf/1606.05050
https://arxiv.org/pdf/1606.05050
https://arxiv.org/pdf/1606.05050.pdf
https://arxiv.org/abs/1606.05050
https://128.84.21.199/abs/1606.05050
https://arxiv.org/pdf/1606.05050
http://drops.dagstuhl.de/opus/volltexte/2016/5832/pdf/11.pdf/
https://experts.illinois.edu/en/publications/proof-complexity-lower-bounds-from-algebraic-circuit-complexity
https://drops.dagstuhl.de/opus/volltexte/2016/5832/pdf/11.pdf/
http://ui.adsabs.harvard.edu/abs/2016arXiv160605050F/abstract
https://arxiv.org/abs/1606.05050
https://toc.cs.uchicago.edu/articles/v017a010/
https://tocmirror.cs.uchicago.edu/articles/v017a010/
https://tocbeta.cs.uchicago.edu/articles/v017a010/
https://logspace.org/articles/v017a010/
http://hdl.handle.net/10044/1/93217
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.32

Polynomial Formulations as a Barrier for Reduction-Based Hardness Proofs.

Autoren: Belova, Tatiana Golovnev, Alexander S. Kulikov, Alexander et al.

Quelle: ACM Transactions on Algorithms; Oct2025, Vol. 21 Issue 4, p1-44, 44p

Schlagwörter: LOGIC circuits, CIRCUIT complexity, ORTHOGONAL functions, INDEPENDENT sets, ARITHMETIC

CONSTANT DEPTH FORMULA AND PARTIAL FUNCTION VERSIONS OF MCSP ARE HARD.

Autoren: ILANGO, RAHUL

Quelle: SIAM Journal on Computing; 2024, Vol. 53 Issue 6, p317-367, 51p

Schlagwörter: CIRCUIT complexity, BOOLEAN functions, CRYPTOGRAPHY, HYPOTHESIS, MOTIVATION (Psychology)

SEMIALGEBRAIC PROOFS, IPS LOWER BOUNDS, AND THE τ-CONJECTURE: CAN A NATURAL NUMBER BE NEGATIVE?

Autoren: ALEKSEEV, YAROSLAV GRIGORIEV, DIMA HIRSCH, EDWARD A. et al.

Quelle: SIAM Journal on Computing; 2024, Vol. 53 Issue 3, p648-700, 53p

Schlagwörter: VALUE capture, LINEAR equations, NATURAL numbers, SUM of squares, CIRCUIT complexity, BOOLEAN functions

Algebraic Pseudorandomness in VNC⁰

Autoren: Andrews, Robert Robert Andrews

Weitere Verfasser: Andrews, Robert Robert Andrews

Schlagwörter: Polynomial identity testing, Algebraic circuits, ddc:004, Ideal Proof System

Dateibeschreibung: application/pdf

Zugangs-URL: https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.15

a quadratic size hierarchy theorem for small depth multilinear formulas

Autoren: Chillara, Suryajith Limaye, Nutan Srinivasan, Srikanth et al.

Weitere Verfasser: Chillara, Suryajith Limaye, Nutan Srinivasan, Srikanth et al.

Schlagwörter: Lower Bounds, Multilinear formulas, ddc:004, Algebraic circuit complexity

Dateibeschreibung: application/pdf

Zugangs-URL: https://drops.dagstuhl.de/opus/volltexte/2018/9040/
https://drops.dagstuhl.de/opus/volltexte/2018/9040/pdf/LIPIcs-ICALP-2018-36.pdf/
https://dblp.uni-trier.de/db/conf/icalp/icalp2018.html#ChillaraL018
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.36

Algebraic Pseudorandomness in $VNC^0$

Autoren: Andrews, Robert

Schlagwörter: FOS: Computer and information sciences, Computational Complexity, Computational Complexity (cs.CC)

Zugangs-URL: http://arxiv.org/abs/2505.10675

Discovering the Roots: Uniform Closure Results for Algebraic Classes Under Factoring: Discovering the roots: uniform closure results for algebraic classes under factoring

Autoren: Pranjal Dutta Nitin Saxena Amit Sinhababu

Quelle: Journal of the ACM. 69:1-39

Schlagwörter: FOS: Computer and information sciences, Computational methods for problems pertaining to field theory, Computer Science - Computational Complexity, F.1.1, I.1.2, F.1.3, G.1.5, Networks and circuits as models of computation, circuit complexity, Analysis of algorithms and problem complexity, Polynomials in real and complex fields: location of zeros (algebraic theorems), Computational Complexity (cs.CC), Symbolic computation and algebraic computation

Dateibeschreibung: application/xml

Zugangs-URL: https://dl.acm.org/doi/pdf/10.1145/3510359
http://arxiv.org/pdf/1710.03214
http://arxiv.org/abs/1710.03214
https://arxiv.org/abs/1710.03214
https://dl.acm.org/doi/pdf/10.1145/3188745.3188760
https://dblp.uni-trier.de/db/journals/corr/corr1710.html#abs-1710-03214