Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)
Prahladh Harsha, Tulasimohan Molli, and Ashutosh Shankar. Criticality of AC⁰-Formulae. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 19:1-19:24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
@InProceedings{harsha_et_al:LIPIcs.CCC.2023.19, author = {Harsha, Prahladh and Molli, Tulasimohan and Shankar, Ashutosh}, title = {{Criticality of AC⁰-Formulae}}, booktitle = {38th Computational Complexity Conference (CCC 2023)}, pages = {19:1--19:24}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-282-2}, ISSN = {1868-8969}, year = {2023}, volume = {264}, editor = {Ta-Shma, Amnon}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.19}, URN = {urn:nbn:de:0030-drops-182898}, doi = {10.4230/LIPIcs.CCC.2023.19}, annote = {Keywords: AC⁰ circuits, AC⁰ formulae, criticality, switching lemma, correlation bounds} }
Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)
Deepanshu Kush and Shubhangi Saraf. Improved Low-Depth Set-Multilinear Circuit Lower Bounds. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 38:1-38:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
@InProceedings{kush_et_al:LIPIcs.CCC.2022.38, author = {Kush, Deepanshu and Saraf, Shubhangi}, title = {{Improved Low-Depth Set-Multilinear Circuit Lower Bounds}}, booktitle = {37th Computational Complexity Conference (CCC 2022)}, pages = {38:1--38:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-241-9}, ISSN = {1868-8969}, year = {2022}, volume = {234}, editor = {Lovett, Shachar}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.38}, URN = {urn:nbn:de:0030-drops-166003}, doi = {10.4230/LIPIcs.CCC.2022.38}, annote = {Keywords: algebraic circuit complexity, complexity measure, set-multilinear formulas} }
Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)
Mrinal Kumar, C. Ramya, Ramprasad Saptharishi, and Anamay Tengse. If VNP Is Hard, Then so Are Equations for It. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 44:1-44:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
@InProceedings{kumar_et_al:LIPIcs.STACS.2022.44, author = {Kumar, Mrinal and Ramya, C. and Saptharishi, Ramprasad and Tengse, Anamay}, title = {{If VNP Is Hard, Then so Are Equations for It}}, booktitle = {39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)}, pages = {44:1--44:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-222-8}, ISSN = {1868-8969}, year = {2022}, volume = {219}, editor = {Berenbrink, Petra and Monmege, Benjamin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.44}, URN = {urn:nbn:de:0030-drops-158547}, doi = {10.4230/LIPIcs.STACS.2022.44}, annote = {Keywords: Computational Complexity, Algebraic Circuits, Algebraic Natural Proofs} }
Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)
C. Ramya and Anamay Tengse. On Finer Separations Between Subclasses of Read-Once Oblivious ABPs. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 53:1-53:23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
@InProceedings{ramya_et_al:LIPIcs.STACS.2022.53, author = {Ramya, C. and Tengse, Anamay}, title = {{On Finer Separations Between Subclasses of Read-Once Oblivious ABPs}}, booktitle = {39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)}, pages = {53:1--53:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-222-8}, ISSN = {1868-8969}, year = {2022}, volume = {219}, editor = {Berenbrink, Petra and Monmege, Benjamin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.53}, URN = {urn:nbn:de:0030-drops-158636}, doi = {10.4230/LIPIcs.STACS.2022.53}, annote = {Keywords: Algebraic Complexity Theory, Algebraic Branching Programs, Commutative Matrices} }
Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)
Suryajith Chillara. Functional Lower Bounds for Restricted Arithmetic Circuits of Depth Four. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 14:1-14:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
@InProceedings{chillara:LIPIcs.FSTTCS.2021.14, author = {Chillara, Suryajith}, title = {{Functional Lower Bounds for Restricted Arithmetic Circuits of Depth Four}}, booktitle = {41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)}, pages = {14:1--14:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-215-0}, ISSN = {1868-8969}, year = {2021}, volume = {213}, editor = {Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.14}, URN = {urn:nbn:de:0030-drops-155251}, doi = {10.4230/LIPIcs.FSTTCS.2021.14}, annote = {Keywords: Functional Lower Bounds, Boolean Circuit Lower Bounds, Depth Four, Connections to Boolean Complexity, Iterated Matrix Multiplication} }
Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)
Siddharth Bhandari, Prahladh Harsha, Mrinal Kumar, and Madhu Sudan. Ideal-Theoretic Explanation of Capacity-Achieving Decoding. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 56:1-56:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
@InProceedings{bhandari_et_al:LIPIcs.APPROX/RANDOM.2021.56, author = {Bhandari, Siddharth and Harsha, Prahladh and Kumar, Mrinal and Sudan, Madhu}, title = {{Ideal-Theoretic Explanation of Capacity-Achieving Decoding}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)}, pages = {56:1--56:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-207-5}, ISSN = {1868-8969}, year = {2021}, volume = {207}, editor = {Wootters, Mary and Sanit\`{a}, Laura}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.56}, URN = {urn:nbn:de:0030-drops-147499}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2021.56}, annote = {Keywords: List Decodability, List Decoding Capacity, Polynomial Ideal Codes, Multiplicity Codes, Folded Reed-Solomon Codes} }
Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)
Mrinal Kumar and Ben Lee Volk. A Lower Bound on Determinantal Complexity. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 4:1-4:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
@InProceedings{kumar_et_al:LIPIcs.CCC.2021.4, author = {Kumar, Mrinal and Volk, Ben Lee}, title = {{A Lower Bound on Determinantal Complexity}}, booktitle = {36th Computational Complexity Conference (CCC 2021)}, pages = {4:1--4:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-193-1}, ISSN = {1868-8969}, year = {2021}, volume = {200}, editor = {Kabanets, Valentine}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.4}, URN = {urn:nbn:de:0030-drops-142781}, doi = {10.4230/LIPIcs.CCC.2021.4}, annote = {Keywords: Determinantal Complexity, Algebraic Circuits, Lower Bounds, Singular Variety} }
Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)
Prerona Chatterjee. Separating ABPs and Some Structured Formulas in the Non-Commutative Setting. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 7:1-7:24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
@InProceedings{chatterjee:LIPIcs.CCC.2021.7, author = {Chatterjee, Prerona}, title = {{Separating ABPs and Some Structured Formulas in the Non-Commutative Setting}}, booktitle = {36th Computational Complexity Conference (CCC 2021)}, pages = {7:1--7:24}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-193-1}, ISSN = {1868-8969}, year = {2021}, volume = {200}, editor = {Kabanets, Valentine}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.7}, URN = {urn:nbn:de:0030-drops-142812}, doi = {10.4230/LIPIcs.CCC.2021.7}, annote = {Keywords: Non-Commutative Formulas, Lower Bound, Separating ABPs and Formulas} }
Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)
Mrinal Kumar and Ben Lee Volk. A Polynomial Degree Bound on Equations for Non-Rigid Matrices and Small Linear Circuits. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 9:1-9:9, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
@InProceedings{kumar_et_al:LIPIcs.ITCS.2021.9, author = {Kumar, Mrinal and Volk, Ben Lee}, title = {{A Polynomial Degree Bound on Equations for Non-Rigid Matrices and Small Linear Circuits}}, booktitle = {12th Innovations in Theoretical Computer Science Conference (ITCS 2021)}, pages = {9:1--9:9}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-177-1}, ISSN = {1868-8969}, year = {2021}, volume = {185}, editor = {Lee, James R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.9}, URN = {urn:nbn:de:0030-drops-135486}, doi = {10.4230/LIPIcs.ITCS.2021.9}, annote = {Keywords: Rigid Matrices, Linear Circuits, Degree Bounds, Circuit Lower Bounds} }
Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
Markus Bläser and Anurag Pandey. Polynomial Identity Testing for Low Degree Polynomials with Optimal Randomness. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 8:1-8:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
@InProceedings{blaser_et_al:LIPIcs.APPROX/RANDOM.2020.8, author = {Bl\"{a}ser, Markus and Pandey, Anurag}, title = {{Polynomial Identity Testing for Low Degree Polynomials with Optimal Randomness}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)}, pages = {8:1--8:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-164-1}, ISSN = {1868-8969}, year = {2020}, volume = {176}, editor = {Byrka, Jaros{\l}aw and Meka, Raghu}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.8}, URN = {urn:nbn:de:0030-drops-126112}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2020.8}, annote = {Keywords: Algebraic Complexity theory, Polynomial Identity Testing, Hitting Set, Pseudorandomness} }
Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
Abhishek Bhrushundi, Prahladh Harsha, Pooya Hatami, Swastik Kopparty, and Mrinal Kumar. On Multilinear Forms: Bias, Correlation, and Tensor Rank. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 29:1-29:23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
@InProceedings{bhrushundi_et_al:LIPIcs.APPROX/RANDOM.2020.29, author = {Bhrushundi, Abhishek and Harsha, Prahladh and Hatami, Pooya and Kopparty, Swastik and Kumar, Mrinal}, title = {{On Multilinear Forms: Bias, Correlation, and Tensor Rank}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)}, pages = {29:1--29:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-164-1}, ISSN = {1868-8969}, year = {2020}, volume = {176}, editor = {Byrka, Jaros{\l}aw and Meka, Raghu}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.29}, URN = {urn:nbn:de:0030-drops-126325}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2020.29}, annote = {Keywords: polynomials, Boolean functions, tensor rank, bias, correlation} }
Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)
Prerona Chatterjee, Mrinal Kumar, Adrian She, and Ben Lee Volk. A Quadratic Lower Bound for Algebraic Branching Programs. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 2:1-2:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
@InProceedings{chatterjee_et_al:LIPIcs.CCC.2020.2, author = {Chatterjee, Prerona and Kumar, Mrinal and She, Adrian and Volk, Ben Lee}, title = {{A Quadratic Lower Bound for Algebraic Branching Programs}}, booktitle = {35th Computational Complexity Conference (CCC 2020)}, pages = {2:1--2:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-156-6}, ISSN = {1868-8969}, year = {2020}, volume = {169}, editor = {Saraf, Shubhangi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.2}, URN = {urn:nbn:de:0030-drops-125546}, doi = {10.4230/LIPIcs.CCC.2020.2}, annote = {Keywords: Algebraic Branching Programs, Lower Bound} }
Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)
Mrinal Kumar and Ben Lee Volk. Lower Bounds for Matrix Factorization. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 5:1-5:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
@InProceedings{kumar_et_al:LIPIcs.CCC.2020.5, author = {Kumar, Mrinal and Volk, Ben Lee}, title = {{Lower Bounds for Matrix Factorization}}, booktitle = {35th Computational Complexity Conference (CCC 2020)}, pages = {5:1--5:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-156-6}, ISSN = {1868-8969}, year = {2020}, volume = {169}, editor = {Saraf, Shubhangi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.5}, URN = {urn:nbn:de:0030-drops-125578}, doi = {10.4230/LIPIcs.CCC.2020.5}, annote = {Keywords: Algebraic Complexity, Linear Circuits, Matrix Factorization, Lower Bounds} }
Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)
Prasad Chaugule, Mrinal Kumar, Nutan Limaye, Chandra Kanta Mohapatra, Adrian She, and Srikanth Srinivasan. Schur Polynomials Do Not Have Small Formulas If the Determinant Doesn't. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 14:1-14:27, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
@InProceedings{chaugule_et_al:LIPIcs.CCC.2020.14, author = {Chaugule, Prasad and Kumar, Mrinal and Limaye, Nutan and Mohapatra, Chandra Kanta and She, Adrian and Srinivasan, Srikanth}, title = {{Schur Polynomials Do Not Have Small Formulas If the Determinant Doesn't}}, booktitle = {35th Computational Complexity Conference (CCC 2020)}, pages = {14:1--14:27}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-156-6}, ISSN = {1868-8969}, year = {2020}, volume = {169}, editor = {Saraf, Shubhangi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.14}, URN = {urn:nbn:de:0030-drops-125660}, doi = {10.4230/LIPIcs.CCC.2020.14}, annote = {Keywords: Schur polynomial, Jacobian, Algebraic independence, Generalized Vandermonde determinant, Taylor expansion, Formula complexity, Lower bound} }
Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)
Amit Sinhababu and Thomas Thierauf. Factorization of Polynomials Given By Arithmetic Branching Programs. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 33:1-33:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
@InProceedings{sinhababu_et_al:LIPIcs.CCC.2020.33, author = {Sinhababu, Amit and Thierauf, Thomas}, title = {{Factorization of Polynomials Given By Arithmetic Branching Programs}}, booktitle = {35th Computational Complexity Conference (CCC 2020)}, pages = {33:1--33:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-156-6}, ISSN = {1868-8969}, year = {2020}, volume = {169}, editor = {Saraf, Shubhangi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.33}, URN = {urn:nbn:de:0030-drops-125854}, doi = {10.4230/LIPIcs.CCC.2020.33}, annote = {Keywords: Arithmetic Branching Program, Multivariate Polynomial Factorization, Hensel Lifting, Newton Iteration, Hardness vs Randomness} }
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