Direct Sums for Parity Decision Trees | Paper Citation Record

Observation 320d42ce-e69b-46f0-ae95-c5c4fe8a0135 · outbound

This paper cites Lifting Dichotomies.

Direct Sums for Parity Decision Trees Lifting Dichotomies

Reference 1

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Observation 5bd20e8f-2d7f-4f4c-97cb-793c563c83e1 · outbound

This paper cites Lifting to bounded-depth and regular resolutions over parities via games.

Direct Sums for Parity Decision Trees Lifting to bounded-depth and regular resolutions over parities via games

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:42:18.351168Z

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Observation d31240e7-8967-42bc-8037-88f33851f4d8 · outbound

This paper cites Optimal separation and strong direct sum for randomized query complexity.

Direct Sums for Parity Decision Trees Optimal separation and strong direct sum for randomized query complexity

Reference 3

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Observation 56a03121-48cd-4e40-9e18-66d55754be48 · outbound

This paper cites A tight composition theorem for the randomized query complexity of partial functions: Extended abstract.

Direct Sums for Parity Decision Trees A tight composition theorem for the randomized query complexity of partial functions: Extended abstract

Reference 4

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Observation c5a4c44c-4f55-405c-a5ae-09d581b60f42 · outbound

This paper cites A new minimax theorem for randomized algorithms.

Direct Sums for Parity Decision Trees A new minimax theorem for randomized algorithms

Reference 5

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.475388Z

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Observation 9903dc78-53c4-4e46-9ead-03d816414bd9 · outbound

This paper cites How to compress interactive communication.

Direct Sums for Parity Decision Trees How to compress interactive communication

Reference 6

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.467639Z

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Observation c2ceb8ff-4392-42d2-ab78-9a57e0272f2a · outbound

This paper cites Randomised Composition and Small-Bias Minimax.

Direct Sums for Parity Decision Trees Randomised Composition and Small-Bias Minimax

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.114328Z

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Observation 88c782e9-cb41-4047-895c-4b38f93275fc · outbound

This paper cites Exponential Separation Between Powers of Regular and General Resolution over Parities.

Direct Sums for Parity Decision Trees Exponential Separation Between Powers of Regular and General Resolution over Parities

Reference 8

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.460042Z

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Observation 2e839084-6bbf-40c8-b15c-c070aa1164d4 · outbound

This paper cites Complexity classes in communication complexity theory.

Direct Sums for Parity Decision Trees Complexity classes in communication complexity theory

Reference 9

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.452230Z

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Observation f12a4f14-d56d-4145-aa41-6156953ea9f8 · outbound

This paper cites When Is Amplification Necessary for Composition in Randomized Query Complexity? In Approximation, Randomization, and Combinatorial Optimization.

Direct Sums for Parity Decision Trees When Is Amplification Necessary for Composition in Randomized Query Complexity? In Approximation, Randomization, and Combinatorial Optimization

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.121759Z

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Observation 0f93e58c-f2eb-4c5f-81a0-dfbe1fec6b89 · outbound

This paper cites Information lower bounds via self-reducibility.

Direct Sums for Parity Decision Trees Information lower bounds via self-reducibility

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.124199Z

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Observation f6d59860-d9c1-4a3e-b024-0cd0a7cf5b41 · outbound

This paper cites Lifting to randomized parity decision trees.

Direct Sums for Parity Decision Trees Lifting to randomized parity decision trees

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:42:18.342196Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2a6c414c-04e5-42e4-aaab-b091574c8080 · outbound

This paper cites Randomized query complexity of sabotaged and composed functions.

Direct Sums for Parity Decision Trees Randomized query complexity of sabotaged and composed functions

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.130443Z

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Observation 14f459d4-e812-4747-a758-8f087412ce9c · outbound

This paper cites On Disperser/Lifting Properties of the Index and Inner-Product Functions.

Direct Sums for Parity Decision Trees On Disperser/Lifting Properties of the Index and Inner-Product Functions

Reference 14

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.432470Z

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Observation 0694ac2d-0cd6-41b1-811e-53fbdaefea50 · outbound

This paper cites A strong XOR lemma for randomized query complexity.

Direct Sums for Parity Decision Trees A strong XOR lemma for randomized query complexity

Reference 15

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.425404Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 5f6b2a82-c846-4126-b71c-868cfb6d0fd2 · outbound

This paper cites A Strong Direct Sum Theorem for Distributional Query Complexity.

Direct Sums for Parity Decision Trees A Strong Direct Sum Theorem for Distributional Query Complexity

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.137754Z

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Observation 4018af53-1d88-49e5-8de6-df52099443ac · outbound

This paper cites Information equals amortized communication.

Direct Sums for Parity Decision Trees Information equals amortized communication

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.140353Z

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Observation a8b77061-6d76-4591-b840-dd5abddef750 · outbound

This paper cites Super-critical trade-offs in resolution over parities via lifting.

Direct Sums for Parity Decision Trees Super-critical trade-offs in resolution over parities via lifting

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:42:18.333861Z

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Observation 3f7126c0-30a1-4637-bae8-cc7da9d0f78c · outbound

This paper cites Boolean functions with small approximate spectral norm.

Direct Sums for Parity Decision Trees Boolean functions with small approximate spectral norm

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.145191Z

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Observation bca5d453-6c82-4dba-9c18-b07bfc39bbda · outbound

This paper cites Lifting to Parity Decision Trees via Stifling.

Direct Sums for Parity Decision Trees Lifting to Parity Decision Trees via Stifling

Reference 20

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.411472Z

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Observation f9f3752e-3b8e-42d0-bd09-758e87b14000 · outbound

This paper cites Improved direct product theorems for randomized query complexity.

Direct Sums for Parity Decision Trees Improved direct product theorems for randomized query complexity

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.150590Z

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Observation 3d7acdb0-9999-4bb5-981f-614a80cbffc4 · outbound

This paper cites Lower bounds for regular resolution over parities.

Direct Sums for Parity Decision Trees Lower bounds for regular resolution over parities

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.153092Z

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Observation ddec8462-9456-4c61-87fb-b603c64bb4fd · outbound

This paper cites Proving Unsatisfiability with Hitting Formulas.

Direct Sums for Parity Decision Trees Proving Unsatisfiability with Hitting Formulas

Reference 23

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.401127Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b80ef179-d100-4afd-9a35-c460c8330e3c · outbound

This paper cites Amortized communication complexity.

Direct Sums for Parity Decision Trees Amortized communication complexity

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.158064Z

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Observation 61a472d1-cedf-4e60-acd0-aa7d3908e763 · outbound

This paper cites Feige, D.

Direct Sums for Parity Decision Trees Feige, D

Reference 25

Resolution: metadata mismatch; raw_fallback, observed 2026-08-11T19:42:17.945646Z

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Observation bf23d46d-381d-4792-8e9f-daceded0fa00 · outbound

This paper cites Exponential separation of information and communication for boolean functions.

Direct Sums for Parity Decision Trees Exponential separation of information and communication for boolean functions

Reference 26

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.390378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d9425d37-35b1-445a-8a66-f599f6639e61 · outbound

This paper cites A majority lemma for randomised query complexity.

Direct Sums for Parity Decision Trees A majority lemma for randomised query complexity

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.164642Z

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Observation 58d1de17-b87f-4c8b-8ef8-62be82ad1515 · outbound

This paper cites Fourier growth of communication protocols for XOR functions.

Direct Sums for Parity Decision Trees Fourier growth of communication protocols for XOR functions

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.166995Z

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Observation 3cf27816-c6e5-457e-aaf2-bfb4a7b7f4e5 · outbound

This paper cites Fourier growth of parity decision trees.

Direct Sums for Parity Decision Trees Fourier growth of parity decision trees

Reference 29

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.379799Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1acdb09b-47b7-4555-af3f-da5d481b272b · outbound

This paper cites Structure of protocols for XOR functions.

Direct Sums for Parity Decision Trees Structure of protocols for XOR functions

Reference 30

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.373136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ac28cd7c-cdc5-4d14-9fd8-9af68734008e · outbound

This paper cites Refuting Approaches to the Log-Rank Conjecture for XOR Functions.

Direct Sums for Parity Decision Trees Refuting Approaches to the Log-Rank Conjecture for XOR Functions

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.173898Z

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Observation 2eea80f6-3d88-41f7-b14b-3fd5eb02181c · outbound

This paper cites Better Boosting of Communication Oracles, or Not.

Direct Sums for Parity Decision Trees Better Boosting of Communication Oracles, or Not

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.175972Z

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Observation f60409b6-3fb3-443e-8aa6-85bfc641fb8b · outbound

This paper cites An XOR Lemma for Deterministic Communication Complexity.

Direct Sums for Parity Decision Trees An XOR Lemma for Deterministic Communication Complexity

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-11T19:42:17.780450Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2e69834a-250e-4f21-a345-42a7d30b7cee · outbound

This paper cites XOR lemmas for communication via marginal information.

Direct Sums for Parity Decision Trees XOR lemmas for communication via marginal information

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.180350Z

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Observation de4ef6d4-c235-4057-bbac-f5a48d7f06ef · outbound

This paper cites Resolution over linear equations modulo two.

Direct Sums for Parity Decision Trees Resolution over linear equations modulo two

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.182295Z

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Observation eafc94a3-6f32-47af-b1c5-abf9062693f0 · outbound

This paper cites Optimal direct sum results for deterministic and randomized decision tree complexity.

Direct Sums for Parity Decision Trees Optimal direct sum results for deterministic and randomized decision tree complexity

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.184357Z

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Observation e3b48e77-49cc-4039-a0be-d37b5d44b62b · outbound

This paper cites A direct sum theorem in communication complexity via message compression.

Direct Sums for Parity Decision Trees A direct sum theorem in communication complexity via message compression

Reference 37

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.354993Z

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Observation 4cc16ff9-f459-4d59-814a-49d8f713469c · outbound

This paper cites an unresolved cited work.

Direct Sums for Parity Decision Trees Unresolved cited work

Reference 38

Resolution: metadata mismatch; raw_fallback, observed 2026-08-11T19:42:17.575020Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 26ea9ac4-cc36-4d7e-8322-e391d37ffb51 · outbound

This paper cites Learning decision trees using the fourier spectrum.

Direct Sums for Parity Decision Trees Learning decision trees using the fourier spectrum

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.191330Z

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Observation 502d2731-7d7c-4fbf-9911-23f564086c4b · outbound

This paper cites Quantum and classical strong direct product theorems and optimal time‐space tradeoffs.

Direct Sums for Parity Decision Trees Quantum and classical strong direct product theorems and optimal time‐space tradeoffs

Reference 40

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.343656Z

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Observation e47950ff-131d-4f69-8baf-177619823812 · outbound

This paper cites Learning complexity vs.

Direct Sums for Parity Decision Trees Learning complexity vs

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.196458Z

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Observation 59765191-2672-48e5-b8dd-041c3b8c6ead · outbound

This paper cites A direct product theorem for discrepancy.

Direct Sums for Parity Decision Trees A direct product theorem for discrepancy

Reference 42

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.332416Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 4390cf34-cd54-4ada-b993-d270f163ddc5 · outbound

This paper cites On parity decision trees for fourier-sparse boolean functions.

Direct Sums for Parity Decision Trees On parity decision trees for fourier-sparse boolean functions

Reference 43

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.324728Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 972a41db-18c1-4743-95ed-12b3c5008932 · outbound

This paper cites The communication complexity of threshold gates.

Direct Sums for Parity Decision Trees The communication complexity of threshold gates

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:42:18.325712Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3358f3b5-1571-4ede-849d-c473b3d9c667 · outbound

This paper cites Analysis of Boolean Functions.

Direct Sums for Parity Decision Trees Analysis of Boolean Functions

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.206538Z

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Observation 63589535-ff0d-4ded-9401-60ee9b9436f4 · outbound

This paper cites A Composition Theorem for Parity Kill Number.

Direct Sums for Parity Decision Trees A Composition Theorem for Parity Kill Number

Reference 46

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.312660Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 5288ef28-c185-47f1-80ea-5950a2c2c6bc · outbound

This paper cites Simplified separation of information and communication.

Direct Sums for Parity Decision Trees Simplified separation of information and communication

Reference 47

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.304319Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 635036fe-bb8c-4163-9b45-868b218c25db · outbound

This paper cites Fourier sparsity and dimension.

Direct Sums for Parity Decision Trees Fourier sparsity and dimension

Reference 48

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.296916Z

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Observation fee40975-e57f-4793-8da1-ee17630b3245 · outbound

This paper cites Randomized query composition and product distributions.

Direct Sums for Parity Decision Trees Randomized query composition and product distributions

Reference 49

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.289325Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 735156b1-c32b-4a29-9f73-8f5ba282480c · outbound

This paper cites On determinism versus unambiquous nondeterminism for decision trees.

Direct Sums for Parity Decision Trees On determinism versus unambiquous nondeterminism for decision trees

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:42:18.317270Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 60b4cb7c-3da2-4195-85fd-865ffce85243 · outbound

This paper cites Towards proving strong direct product theorems.

Direct Sums for Parity Decision Trees Towards proving strong direct product theorems

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.222422Z

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Observation 139f5db5-cd2c-4bfe-b375-0de58e81d324 · outbound

This paper cites Randomized lifting to semi-structured communication complexity via linear diversity.

Direct Sums for Parity Decision Trees Randomized lifting to semi-structured communication complexity via linear diversity

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T19:42:18.307779Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ba9bc693-dffb-4ea6-bca8-74816b4eec0c · outbound

This paper cites On the structure of boolean functions with small spectral norm.

Direct Sums for Parity Decision Trees On the structure of boolean functions with small spectral norm

Reference 53

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.278449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 65871924-d3d1-4dfa-92de-08cd14f254d3 · outbound

This paper cites Fourier sparsity, spectral norm, and the log-rank conjecture.

Direct Sums for Parity Decision Trees Fourier sparsity, spectral norm, and the log-rank conjecture

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.230008Z

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Observation cbbc2224-9c6d-4460-92d0-15d40dfee07b · outbound

This paper cites Probabilistic computations: Toward a unified measure of complexity.

Direct Sums for Parity Decision Trees Probabilistic computations: Toward a unified measure of complexity

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.232453Z

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Observation 84553a73-5657-42a3-a617-6be80072b348 · outbound

This paper cites Lower bounds by probabilistic arguments.

Direct Sums for Parity Decision Trees Lower bounds by probabilistic arguments

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-11T19:42:17.234496Z

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Observation b659c430-e008-478e-b760-8853cb57fb5a · outbound

This paper cites On the parity complexity measures of boolean functions.

Direct Sums for Parity Decision Trees On the parity complexity measures of boolean functions

Reference 57

Resolution: verified exact; doi, observed 2026-08-11T19:42:17.258757Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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