Paper Citation Record · LEDGER

The Complexity of Order-Finding for ROABPs

As of 17 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 1 inbound Pith citation observation for arXiv:2411.18981.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2411.18981 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T10:55:42.684032Z

measured 50 of 50 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:14:05.143844Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-15T16:14:05.348647Z

Reference resolution

49 of 49 outbound references displayed

verified exact15
verified fuzzy12
unresolved19
parse uncertain0
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External citation measurements

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Outbound references

Observation e747d2d6-4551-41d7-b13e-e65fa2abdc0f · outbound

This paper cites write newline toupdate empty.

The Complexity of Order-Finding for ROABPs write newline toupdate empty

Reference 1

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Observation e0c559d7-75ad-45b3-8228-15be2336ae2e · outbound

This paper cites Hitting-sets for ROABP and Sum of Set-Multilinear circuits.

The Complexity of Order-Finding for ROABPs Hitting-sets for ROABP and Sum of Set-Multilinear circuits

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-12T10:55:43.673226Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6282cafe-f004-42eb-8eb9-a2cbe9e1b2f7 · outbound

This paper cites http://dx.doi.org/10.1137/080729256 Inapproximability Results for Maximum Edge Biclique, Minimum Linear Arrangement, and Sparsest Cut.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1137/080729256 Inapproximability Results for Maximum Edge Biclique, Minimum Linear Arrangement, and Sparsest Cut

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-12T10:55:42.502067Z

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Observation 917463bf-2904-43de-b859-db8aadd4e130 · outbound

This paper cites http://dx.doi.org/10.1007/978-3-642-32512-0\_2 Inapproximability of Treewidth, One-Shot Pebbling, and Related Layout Problems.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1007/978-3-642-32512-0\_2 Inapproximability of Treewidth, One-Shot Pebbling, and Related Layout Problems

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-12T10:55:42.506394Z

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Observation 744cf278-b213-44bb-b8ba-1289daf5022b · outbound

This paper cites Equivalence of-algebras and cubic forms.

The Complexity of Order-Finding for ROABPs Equivalence of-algebras and cubic forms

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:55:43.829300Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 15108231-e59a-47ef-9388-fbe3cdf560ea · outbound

This paper cites http://dx.doi.org/10.4230/LIPICS.ICALP.2024.16 NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.4230/LIPICS.ICALP.2024.16 NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials

Reference 6

Resolution: verified exact; doi, observed 2026-08-12T10:55:42.906204Z

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Observation 4bb193dc-2fe0-4665-bc09-f371098b5ae5 · outbound

This paper cites Kulikov, Ivan Mihajlin, and Denil Sharipov.

The Complexity of Order-Finding for ROABPs Kulikov, Ivan Mihajlin, and Denil Sharipov

Reference 7

Resolution: verified exact; doi, observed 2026-08-12T10:55:42.895281Z

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Observation 021d3388-74ce-4e47-8690-3f3d011ebcb0 · outbound

This paper cites http://dx.doi.org/10.4230/LIPICS.APPROX/RANDOM.2022.21 Learning Generalized Depth Three Arithmetic Circuits in the Non-Degenerate Case.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.4230/LIPICS.APPROX/RANDOM.2022.21 Learning Generalized Depth Three Arithmetic Circuits in the Non-Degenerate Case

Reference 8

Resolution: verified exact; doi, observed 2026-08-12T10:55:42.884857Z

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Observation 5b3be2c3-4b7e-4bc0-a342-418eb9d6681b · outbound

This paper cites an unresolved cited work.

The Complexity of Order-Finding for ROABPs Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-12T10:55:42.529259Z

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Observation 22eda03d-f09e-4669-b46c-bfcdd4dab03e · outbound

This paper cites http://dx.doi.org/10.1145/3406325.3451096 Reconstruction algorithms for low-rank tensors and depth-3 multilinear circuits.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1145/3406325.3451096 Reconstruction algorithms for low-rank tensors and depth-3 multilinear circuits

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-12T10:55:42.532673Z

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Observation a6ff7a34-b034-4bf4-ba65-5de311cc5625 · outbound

This paper cites Explicit Commutative ROABPs from Partial Derivatives.

The Complexity of Order-Finding for ROABPs Explicit Commutative ROABPs from Partial Derivatives

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-12T10:55:42.873644Z

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Observation 32c3fb16-72e3-4301-b536-00c9c8510746 · outbound

This paper cites The complexity of boolean formula minimization.

The Complexity of Order-Finding for ROABPs The complexity of boolean formula minimization

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:55:43.815773Z

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Observation 4ecc8db0-4dfb-4b7d-ac65-095a47c807d9 · outbound

This paper cites Improving the variable ordering of OBDDs is NP-complete.

The Complexity of Order-Finding for ROABPs Improving the variable ordering of OBDDs is NP-complete

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:55:43.804895Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f9552fa0-042e-4d0d-b12e-b94b2cc0252e · outbound

This paper cites http://dx.doi.org/10.4230/LIPICS.ITCS.2024.25 Learning Arithmetic Formulas in the Presence of Noise: A General Framework and Applications to Unsupervised Learning.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.4230/LIPICS.ITCS.2024.25 Learning Arithmetic Formulas in the Presence of Noise: A General Framework and Applications to Unsupervised Learning

Reference 14

Resolution: verified exact; doi, observed 2026-08-12T10:55:42.856955Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a3dc1c21-4728-4157-8c6c-3c403d5c96e8 · outbound

This paper cites http://dx.doi.org/10.4230/LIPIcs.STACS.2023.22 On Hardness of Testing Equivalence to Sparse Polynomials Under Shifts.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.4230/LIPIcs.STACS.2023.22 On Hardness of Testing Equivalence to Sparse Polynomials Under Shifts

Reference 15

Resolution: verified exact; doi, observed 2026-08-12T10:55:42.840812Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4d96fac0-20b8-4a36-a505-10c43d951b78 · outbound

This paper cites http://dx.doi.org/10.1007/978-0-387-35651-8 Ideals, Varieties and Algorithms.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1007/978-0-387-35651-8 Ideals, Varieties and Algorithms

Reference 16

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Observation 86d9061c-8bc4-4caf-81ba-5a781e071df5 · outbound

This paper cites https://www.cse.iitk.ac.in/users/nitin/papers/border-depth3.pdf Demystifying the border of depth-3 algebraic circuits.

The Complexity of Order-Finding for ROABPs https://www.cse.iitk.ac.in/users/nitin/papers/border-depth3.pdf Demystifying the border of depth-3 algebraic circuits

Reference 17

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Observation 8cf659ca-6eac-4e53-ac51-7e0e557e6bf4 · outbound

This paper cites http://dx.doi.org/10.4230/LIPICS.CCC.2021.11 Deterministic Identity Testing Paradigms for Bounded Top-Fanin Depth-4 Circuits.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.4230/LIPICS.CCC.2021.11 Deterministic Identity Testing Paradigms for Bounded Top-Fanin Depth-4 Circuits

Reference 18

Resolution: verified exact; doi, observed 2026-08-12T10:55:42.822638Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2f74d659-6be9-465e-96ea-8dbc93a95a76 · outbound

This paper cites DeMillo and Richard J.

The Complexity of Order-Finding for ROABPs DeMillo and Richard J

Reference 19

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Observation 449da946-7235-466b-8f4c-b0ef855d2ac6 · outbound

This paper cites http://dx.doi.org/10.1145/568522.568523 A survey of graph layout problems.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1145/568522.568523 A survey of graph layout problems

Reference 20

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Observation 22ed1d6c-d0ab-433c-933f-624b9889514c · outbound

This paper cites Quasipolynomial-time Identity Testing of Non-Commutative and Read-Once Oblivious Algebraic Branching Programs.

The Complexity of Order-Finding for ROABPs Quasipolynomial-time Identity Testing of Non-Commutative and Read-Once Oblivious Algebraic Branching Programs

Reference 21

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5f26e670-043d-46ca-b6cd-c3ade883251f · outbound

This paper cites Forbes, Ramprasad Saptharishi, and Amir Shpilka.

The Complexity of Order-Finding for ROABPs Forbes, Ramprasad Saptharishi, and Amir Shpilka

Reference 22

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Observation 2c8c3703-32a9-473c-8830-754fe89b2588 · outbound

This paper cites Garey and David S.

The Complexity of Order-Finding for ROABPs Garey and David S

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:55:43.781795Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 637ce018-e38b-4163-88c6-46d793185cba · outbound

This paper cites Identity Testing for Constant-Width, and Any-Order, Read-Once Oblivious Arithmetic Branching Programs.

The Complexity of Order-Finding for ROABPs Identity Testing for Constant-Width, and Any-Order, Read-Once Oblivious Arithmetic Branching Programs

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-12T10:55:43.348272Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5dc3f50c-d12c-46e5-9249-a535c1794f86 · outbound

This paper cites Learning sums of powers of low-degree polynomials in the non-degenerate case.

The Complexity of Order-Finding for ROABPs Learning sums of powers of low-degree polynomials in the non-degenerate case

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:55:43.770815Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5ddf9a1b-3863-45cb-9de9-5ddc78ca853c · outbound

This paper cites Deterministic Identity Testing for Sum of Read-Once Oblivious Arithmetic Branching Programs.

The Complexity of Order-Finding for ROABPs Deterministic Identity Testing for Sum of Read-Once Oblivious Arithmetic Branching Programs

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-08-12T10:55:43.331899Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 51ec4505-edc3-487f-a096-551ef779ddd8 · outbound

This paper cites http://dx.doi.org/10.1016/0196-6774(90)90014-6 Tensor Rank is NP-Complete.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1016/0196-6774(90)90014-6 Tensor Rank is NP-Complete

Reference 27

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Observation 93cd3dfb-7cd0-422c-9f3d-60ef387c63fb · outbound

This paper cites http://dx.doi.org/10.1109/FOCS54457.2022.00095 NP-Hardness of Learning Programs and Partial MCSP.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1109/FOCS54457.2022.00095 NP-Hardness of Learning Programs and Partial MCSP

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-12T10:55:42.604598Z

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Observation 516518af-e7f2-4188-87fe-c48ff25c36ae · outbound

This paper cites Oliveira, and Rahul Santhanam.

The Complexity of Order-Finding for ROABPs Oliveira, and Rahul Santhanam

Reference 29

Resolution: verified exact; doi, observed 2026-08-12T10:55:42.797008Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2473d8f6-1fd3-44f5-abf9-71ce4a0b78c3 · outbound

This paper cites http://dx.doi.org/10.1109/FOCS52979.2021.00050 The Minimum Formula Size Problem is (ETH) Hard.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1109/FOCS52979.2021.00050 The Minimum Formula Size Problem is (ETH) Hard

Reference 30

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Observation e7b25572-5c34-4920-aaaa-498114e5c9cc · outbound

This paper cites http://dx.doi.org/10.1137/1.9781611973082.108 Efficient algorithms for some special cases of the polynomial equivalence problem.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1137/1.9781611973082.108 Efficient algorithms for some special cases of the polynomial equivalence problem

Reference 31

Resolution: verified exact; doi, observed 2026-08-12T10:55:42.786588Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4779c1c7-4429-41b4-b7e3-72eb3f286ab6 · outbound

This paper cites http://eccc.hpi-web.de/report/2015/154/ Separation between Read-once Oblivious Algebraic Branching Programs (ROABPs) and Multilinear Depth Three Circuits.

The Complexity of Order-Finding for ROABPs http://eccc.hpi-web.de/report/2015/154/ Separation between Read-once Oblivious Algebraic Branching Programs (ROABPs) and Multilinear Depth Three Circuits

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:55:43.759074Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6e8a9ab8-5c5b-4bd9-836e-287c659f6c7e · outbound

This paper cites Klivans and Amir Shpilka.

The Complexity of Order-Finding for ROABPs Klivans and Amir Shpilka

Reference 33

Resolution: verified exact; doi, observed 2026-08-12T10:55:42.774834Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 24c820b2-f637-42bf-a083-bfdc8ba60965 · outbound

This paper cites Reconstruction of non-degenerate homogeneous depth three circuits.

The Complexity of Order-Finding for ROABPs Reconstruction of non-degenerate homogeneous depth three circuits

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:55:43.747498Z

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Observation 5a700e32-3d1e-422e-9ea7-84988cf5f01f · outbound

This paper cites http://dx.doi.org/10.1145/3611094 Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1145/3611094 Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits

Reference 35

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Observation 21c0522d-7266-4923-a257-c540f84217cb · outbound

This paper cites an unresolved cited work.

The Complexity of Order-Finding for ROABPs Unresolved cited work

Reference 36

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ae75465d-b93d-4286-8d37-d3492586cc68 · outbound

This paper cites http://dx.doi.org/https://doi.org/10.1016/j.jsc.2011.12.018 Dimension-dependent bounds for Gr \"o bner bases of polynomial ideals.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/https://doi.org/10.1016/j.jsc.2011.12.018 Dimension-dependent bounds for Gr \"o bner bases of polynomial ideals

Reference 37

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Observation 1ff3e759-8957-4fe0-9ae8-e08832d3d48c · outbound

This paper cites Monien and I.H.

The Complexity of Order-Finding for ROABPs Monien and I.H

Reference 38

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Source-reported events for the cited work

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Observation eabbcbd3-0315-4ce9-9bf5-1062f230eedc · outbound

This paper cites Algorithms and Data Structures in VLSI Design: OBDD-foundations and applications.

The Complexity of Order-Finding for ROABPs Algorithms and Data Structures in VLSI Design: OBDD-foundations and applications

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:55:43.721363Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 02712158-b06d-4132-8701-9ba1cf567a8b · outbound

This paper cites http://dx.doi.org/10.1145/100216.100242 Psuedorandom Generators for Space-Bounded Computation.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1145/100216.100242 Psuedorandom Generators for Space-Bounded Computation

Reference 40

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 22e42452-3420-4fc3-9b18-284aeedfb5ba · outbound

This paper cites http://dx.doi.org/10.1145/103418.103462 Lower bounds for non-commutative computation.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1145/103418.103462 Lower bounds for non-commutative computation

Reference 41

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Observation 823c42b3-f1cf-498d-a518-59d4e8dfa7f8 · outbound

This paper cites U ber h \.

The Complexity of Order-Finding for ROABPs U ber h \

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:55:43.708603Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 96627b6a-11be-46cb-9ec7-67fb933ce21c · outbound

This paper cites http://dx.doi.org/10.4086/toc.2006.v002a006 Separation of Multilinear Circuit and Formula Size.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.4086/toc.2006.v002a006 Separation of Multilinear Circuit and Formula Size

Reference 43

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Observation 2c7889ed-4318-40b1-a48a-bdadb2b1d22a · outbound

This paper cites http://dx.doi.org/10.1007/s00037-005-0188-8 Deterministic polynomial identity testing in non-commutative models.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1007/s00037-005-0188-8 Deterministic polynomial identity testing in non-commutative models

Reference 44

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Observation c4d22271-80e7-45ce-a292-120341491239 · outbound

This paper cites Schwartz.

The Complexity of Order-Finding for ROABPs Schwartz

Reference 45

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Observation e5f30b9b-94db-4b11-bc5a-c85acfcae045 · outbound

This paper cites How hard is the tensor rank?.

The Complexity of Order-Finding for ROABPs How hard is the tensor rank?

Reference 46

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Observation 040f0d94-07d6-4dcb-844f-55d10df8b4d2 · outbound

This paper cites The nonapproximability of OBDD minimization.

The Complexity of Order-Finding for ROABPs The nonapproximability of OBDD minimization

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:55:43.695883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1b8eaa3d-c1a8-48a9-bd6f-ddee57debc84 · outbound

This paper cites Branching programs and binary decision diagrams: theory and applications.

The Complexity of Order-Finding for ROABPs Branching programs and binary decision diagrams: theory and applications

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:55:43.683413Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ed6c20c9-577e-4fa2-84d7-04ebe69a4bbd · outbound

This paper cites http://dx.doi.org/10.1007/3-540-09519-5_73 Probabilistic algorithms for sparse polynomials.

The Complexity of Order-Finding for ROABPs http://dx.doi.org/10.1007/3-540-09519-5_73 Probabilistic algorithms for sparse polynomials

Reference 49

Resolution: verified exact; doi, observed 2026-08-12T10:55:42.719072Z

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Pith citing papers

Observation 59283401-3653-4278-89b3-105bc835dc21 · inbound

On Closure Properties of Read-Once Oblivious Algebraic Branching Programs cites this paper.

On Closure Properties of Read-Once Oblivious Algebraic Branching Programs The Complexity of Order-Finding for ROABPs

Reference 241

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:14:05.355223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.