DROPS

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DOI: 10.4230/LIPIcs.ITCS.2026.44

Higher-Order Delsarte Dual LPs: Lifting, Constructions and Completeness

Authors: Leonardo Nagami Coregliano, Fernando Granha Jeronimo, Chris Jones, Nati Linial, and Elyassaf Loyfer

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract

A central and longstanding open problem in coding theory is the rate-versus-distance trade-off for binary error-correcting codes. In a seminal work, Delsarte introduced a family of linear programs establishing relaxations on the size of optimum codes. To date, the state-of-the-art upper bounds for binary codes come from dual feasible solutions to these LPs. Still, these bounds are exponentially far from the best-known existential constructions. Recently, hierarchies of linear programs extending and strengthening Delsarte’s original LPs were introduced for linear codes, which we refer to as higher-order Delsarte LPs. These new hierarchies were shown to provably converge to the actual value of optimum codes, namely, they are complete hierarchies. Therefore, understanding them and their dual formulations becomes a valuable line of investigation. Nonetheless, their higher-order structure poses challenges. In fact, analysis of all known convex programming hierarchies strengthening Delsarte’s original LPs has turned out to be exceedingly difficult and essentially nothing is known, stalling progress in the area since the 1970s. Our main result is an analysis of the higher-order Delsarte LPs via their dual formulation. Although quantitatively, our current analysis only matches the best-known upper bounds, it shows, for the first time, how to tame the complexity of analyzing a hierarchy strengthening Delsarte’s original LPs. In doing so, we reach a better understanding of the structure of the hierarchy, which may serve as the foundation for further quantitative improvements. We provide two additional structural results for this hierarchy. First, we show how to explicitly lift any feasible dual solution from level k to a (suitable) larger level 𝓁 while retaining the objective value. Second, we give a novel proof of completeness using the dual formulation.

Cite as

Leonardo Nagami Coregliano, Fernando Granha Jeronimo, Chris Jones, Nati Linial, and Elyassaf Loyfer. Higher-Order Delsarte Dual LPs: Lifting, Constructions and Completeness. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 44:1-44:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{coregliano_et_al:LIPIcs.ITCS.2026.44,
  author =	{Coregliano, Leonardo Nagami and Jeronimo, Fernando Granha and Jones, Chris and Linial, Nati and Loyfer, Elyassaf},
  title =	{{Higher-Order Delsarte Dual LPs: Lifting, Constructions and Completeness}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{44:1--44:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  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.ITCS.2026.44},
  URN =		{urn:nbn:de:0030-drops-253315},
  doi =		{10.4230/LIPIcs.ITCS.2026.44},
  annote =	{Keywords: Coding theory, code bounds, convex optimization, linear progamming hierarchy}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.70

Unconditional Pseudorandomness Against Shallow Quantum Circuits

Authors: Soumik Ghosh, Sathyawageeswar Subramanian, and Wei Zhan

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract

Quantum computational pseudorandomness has emerged as a fundamental notion that spans connections to complexity theory, cryptography and fundamental physics. However, all known constructions of efficient quantum-secure pseudorandom objects rely on complexity theoretic assumptions. In this work, we establish the first unconditionally secure efficient pseudorandom constructions against shallow-depth quantum circuit classes. We prove that: - Any quantum state 2-design yields unconditional pseudorandomness against both QNC⁰ circuits with arbitrarily many ancillae and AC⁰∘QNC⁰ circuits with nearly linear ancillae. - Random phased subspace states, where the phases are picked using a 4-wise independent function, are unconditionally pseudoentangled against the above circuit classes. - Any unitary 2-design yields unconditionally secure parallel-query pseudorandom unitaries against geometrically local QNC⁰ adversaries, even with limited AC⁰ postprocessing. Our results stand in stark contrast to the standard guarantee of the 2-design property, which only ensures that they cannot be distinguished from Haar random ensembles using two copies or queries. Our work demonstrates that quantum computational pseudorandomness can be achieved unconditionally for natural classes of restricted adversaries, opening new directions in quantum complexity theory.

Cite as

Soumik Ghosh, Sathyawageeswar Subramanian, and Wei Zhan. Unconditional Pseudorandomness Against Shallow Quantum Circuits. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 70:1-70:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ghosh_et_al:LIPIcs.ITCS.2026.70,
  author =	{Ghosh, Soumik and Subramanian, Sathyawageeswar and Zhan, Wei},
  title =	{{Unconditional Pseudorandomness Against Shallow Quantum Circuits}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{70:1--70:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  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.ITCS.2026.70},
  URN =		{urn:nbn:de:0030-drops-253578},
  doi =		{10.4230/LIPIcs.ITCS.2026.70},
  annote =	{Keywords: quantum pseudorandomness, shallow quantum circuits, pseudorandomness, t-designs}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.34

Testing Classical Properties from Quantum Data

Authors: Matthias C. Caro, Preksha Naik, and Joseph Slote

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract

Many properties of Boolean functions can be tested far more efficiently than the function itself can be learned. However, this dramatic advantage often disappears when testers are limited to random samples of f instead of adaptively chosen queries to f. In this work we investigate the quantum version of this restriction: quantum algorithms that test properties of a Boolean function f solely from copies of either the function state |f⟩∝ ∑_x|x,f(x)⟩ or the phase state |(-1)^f⟩∝ ∑_x (-1)^{f(x)}|x⟩. Quantum advantage in testing from data. For monotonicity, symmetry, and triangle-freeness, we show passive quantum testers are unboundedly or super-polynomially better than their classical passive testing counterparts. They are competitive with classic query-based testers in each case. Inadequacy of Fourier sampling. Our new testers use techniques beyond quantum Fourier sampling, and it turns out this is necessary: we show a certain class of bent functions can be tested from 𝒪(1) function states but has a sample complexity lower bound of 2^{Ω(n)} for any tester relying exclusively on Fourier and classical samples. Classical queries vs. quantum data. Our passive quantum testers are competitive with classical query-based testers, but this isn't universal: we exhibit a testing problem that can be solved from 𝒪(1) classical queries but requires Ω(2^{n/2}) function state copies. The Forrelation problem provides a separation of the same magnitude in the opposite direction, so we conclude that quantum data and classical queries are "maximally incomparable" resources for testing. Towards lower bounds. We also begin the study of lower bounds for testing from quantum data. For quantum monotonicity testing, we prove that the ensembles of [Goldreich et al., 2000; Black, 2024], which give exponential lower bounds for classical sample-based testing, do not yield any nontrivial lower bounds for testing from quantum data. New insights specific to quantum data will be required for proving copy complexity lower bounds for testing in this model.

Cite as

Matthias C. Caro, Preksha Naik, and Joseph Slote. Testing Classical Properties from Quantum Data. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 34:1-34:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{caro_et_al:LIPIcs.ITCS.2026.34,
  author =	{Caro, Matthias C. and Naik, Preksha and Slote, Joseph},
  title =	{{Testing Classical Properties from Quantum Data}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{34:1--34:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  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.ITCS.2026.34},
  URN =		{urn:nbn:de:0030-drops-253213},
  doi =		{10.4230/LIPIcs.ITCS.2026.34},
  annote =	{Keywords: Quantum Property Testing, Quantum Data, Boolean Functions}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.83

The Pure-State Consistency of Local Density Matrices Problem: In PSPACE and Complete for a Class Between QMA and QMA(2)

Authors: Jonas Kamminga and Dorian Rudolph

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract

In this work we investigate the computational complexity of the pure consistency of local density matrices (PureCLDM) and pure N-representability (Pure-N-Representability; analog of PureCLDM for bosonic or fermionic systems) problems. In these problems the input is a set of reduced density matrices and the task is to determine whether there exists a global pure state consistent with these reduced density matrices. While mixed CLDM, i.e. where the global state can be mixed, was proven to be QMA-complete by Broadbent and Grilo [JoC 2022], almost nothing was known about the complexity of the pure version. Before our work the best upper and lower bounds were QMA(2) and QMA. Our contribution to the understanding of these problems is twofold. Firstly, we define a pure state analogue of the complexity class QMA^+ of Aharanov and Regev [FOCS 2003], which we call PureSuperQMA. We prove that both pure-N-Representability and PureCLDM are complete for this new class. Along the way we supplement Broadbent and Grilo by proving hardness for 2-qubit reduced density matrices and showing that mixed N-Representability is QMA-complete. Secondly, we improve the upper bound on PureCLDM. Using methods from algebraic geometry, we prove that PureSuperQMA ⊆ PSPACE. Our methods, and the PSPACE upper bound, are also valid for PureCLDM with exponential or even perfect precision, hence precisePureCLDM is not preciseQMA(2) = NEXP-complete, unless PSPACE = NEXP. We view this as evidence for a negative answer to the longstanding open question whether PureCLDM is QMA(2)-complete. The techniques we develop for our PSPACE upper bound are quite general. We are able to use them for various applications: from proving PSPACE upper bounds on other quantum problems to giving an efficient parallel (NC) algorithm for (non-convex) quadratically constrained quadratic programs with few constraints.

Cite as

Jonas Kamminga and Dorian Rudolph. The Pure-State Consistency of Local Density Matrices Problem: In PSPACE and Complete for a Class Between QMA and QMA(2). In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 83:1-83:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kamminga_et_al:LIPIcs.ITCS.2026.83,
  author =	{Kamminga, Jonas and Rudolph, Dorian},
  title =	{{The Pure-State Consistency of Local Density Matrices Problem: In PSPACE and Complete for a Class Between QMA and QMA(2)}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{83:1--83:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  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.ITCS.2026.83},
  URN =		{urn:nbn:de:0030-drops-253701},
  doi =		{10.4230/LIPIcs.ITCS.2026.83},
  annote =	{Keywords: Quantum Complexity Theory, PSPACE, QMA(2), Consistency of Local Density Matrices, Polynomial Optimization}
}

Document

RANDOM

DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.29

A Simplified Reduction for Error Correcting Matrix Multiplication Algorithms

Authors: Igor Shinkar and Harsimran Singh

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract

We study the problem of transforming an algorithm for matrix multiplication, whose output has a small fraction of the entries correct into a matrix multiplication algorithm, whose output is fully correct for all inputs. In this work, we provide a new and simple way to transform an average-case algorithm that takes two matrices A,B ∈ 𝔽_p^{n×n} for a prime p, and outputs a matrix that agrees with the matrix product AB on a 1/p + ε fraction of entries on average for a small ε > 0, into a worst-case algorithm that correctly computes the matrix product for all possible inputs. Our reduction employs list-decodable codes to transform an average-case algorithm into an algorithm with one-sided error, which are known to admit efficient reductions from the work of Gola, Shinkar, and Singh [Gola et al., 2024]. Our reduction is more concise and straightforward compared to the recent work of Hirahara and Shimizu [Hirahara and Shimizu, 2025], and improves the overhead in the running time incurred during the reduction.

Cite as

Igor Shinkar and Harsimran Singh. A Simplified Reduction for Error Correcting Matrix Multiplication Algorithms. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{shinkar_et_al:LIPIcs.APPROX/RANDOM.2025.29,
  author =	{Shinkar, Igor and Singh, Harsimran},
  title =	{{A Simplified Reduction for Error Correcting Matrix Multiplication Algorithms}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{29:1--29:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.29},
  URN =		{urn:nbn:de:0030-drops-243953},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.29},
  annote =	{Keywords: Matrix Multiplication, Reductions, Worst case to average case reductions}
}

Document

RANDOM

DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.49

Pseudorandomness of Expander Walks via Fourier Analysis on Groups

Authors: Fernando Granha Jeronimo, Tushant Mittal, and Sourya Roy

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract

A long line of work has studied the pseudorandomness properties of walks on expander graphs. A central goal is to measure how closely the distribution over n-length walks on an expander approximates the uniform distribution of n-independent elements. One approach to do so is to label the vertices of an expander with elements from an alphabet Σ, and study closeness of the mean of functions over Σⁿ, under these two distributions. We say expander walks ε-fool a function if the expander walk mean is ε-close to the true mean. There has been a sequence of works studying this question for various functions, such as the XOR function, the AND function, etc. We show that: - The class of symmetric functions is O(|Σ|λ)-fooled by expander walks over any generic λ-expander, and any alphabet Σ . This generalizes the result of Cohen, Peri, Ta-Shma [STOC'21] which analyzes it for |Σ| = 2, and exponentially improves the previous bound of O(|Σ|^O(|Σ|) λ), by Golowich and Vadhan [CCC'22]. Moreover, if the expander is a Cayley graph over ℤ_|Σ|, we get a further improved bound of O(√{|Σ|} λ). Morever, when Σ is a finite group G, we show the following for functions over Gⁿ: - The class of symmetric class functions is O({√|G|}/D λ}-fooled by expander walks over "structured" λ-expanders, if G is D-quasirandom. - We show a lower bound of Ω(λ) for symmetric functions for any finite group G (even for "structured" λ-expanders). - We study the Fourier spectrum of a class of non-symmetric functions arising from word maps, and show that they are exponentially fooled by expander walks. Our proof employs Fourier analysis over general groups, which contrasts with earlier works that have studied either the case of ℤ₂ or ℤ. This enables us to get quantitatively better bounds even for unstructured sets.

Cite as

Fernando Granha Jeronimo, Tushant Mittal, and Sourya Roy. Pseudorandomness of Expander Walks via Fourier Analysis on Groups. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 49:1-49:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jeronimo_et_al:LIPIcs.APPROX/RANDOM.2025.49,
  author =	{Jeronimo, Fernando Granha and Mittal, Tushant and Roy, Sourya},
  title =	{{Pseudorandomness of Expander Walks via Fourier Analysis on Groups}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{49:1--49:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.49},
  URN =		{urn:nbn:de:0030-drops-244157},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.49},
  annote =	{Keywords: Expander graphs, pseudorandomness}
}

Document

APPROX

DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.5

Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT

Authors: Aditya Anand, Euiwoong Lee, Davide Mazzali, and Amatya Sharma

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract

This paper studies complete k-Constraint Satisfaction Problems (CSPs), where an n-variable instance has exactly one nontrivial constraint for each subset of k variables, i.e., it has binom(n,k) constraints. A recent work started a systematic study of complete k-CSPs [Anand, Lee, Sharma, SODA'25], and showed a quasi-polynomial time algorithm that decides if there is an assignment satisfying all the constraints of any complete Boolean-alphabet k-CSP, algorithmically separating complete instances from dense instances. The tractability of this decision problem is necessary for any nontrivial (multiplicative) approximation for the minimization version, whose goal is to minimize the number of violated constraints. The same paper raised the question of whether it is possible to obtain nontrivial approximation algorithms for complete Min-k-CSPs with k ≥ 3. In this work, we make progress in this direction and show a quasi-polynomial time polylog(n)-approximation to Min-NAE-3-SAT on complete instances, which asks to minimize the number of 3-clauses where all the three literals equal the same bit. To the best of our knowledge, this is the first known example of a CSP whose decision version is NP-Hard in general (and dense) instances while admitting a polylog(n)-approximation in complete instances. Our algorithm presents a new iterative framework for rounding a solution from the Sherali-Adams hierarchy, where each iteration interleaves the two well-known rounding tools: the conditioning procedure, in order to "almost fix" many variables, and the thresholding procedure, in order to "completely fix" them. Finally, we improve the running time of the decision algorithms of Anand, Lee, and Sharma and show a simple algorithm that decides any complete Boolean-alphabet k-CSP in polynomial time.

Cite as

Aditya Anand, Euiwoong Lee, Davide Mazzali, and Amatya Sharma. Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anand_et_al:LIPIcs.APPROX/RANDOM.2025.5,
  author =	{Anand, Aditya and Lee, Euiwoong and Mazzali, Davide and Sharma, Amatya},
  title =	{{Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{5:1--5:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.5},
  URN =		{urn:nbn:de:0030-drops-243712},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.5},
  annote =	{Keywords: Constraint Satisfiability Problems, Approximation Algorithms, Sherali Adams}
}

Document

DOI: 10.4230/LIPIcs.ITC.2025.9

Revocable Encryption, Programs, and More: The Case of Multi-Copy Security

Authors: Prabhanjan Ananth, Saachi Mutreja, and Alexander Poremba

Published in: LIPIcs, Volume 343, 6th Conference on Information-Theoretic Cryptography (ITC 2025)

Abstract

Fundamental principles of quantum mechanics have inspired many new research directions, particularly in quantum cryptography. One such principle is quantum no-cloning which has led to the emerging field of revocable cryptography. Roughly speaking, in a revocable cryptographic primitive, a cryptographic object (such as a ciphertext or program) is represented as a quantum state in such a way that surrendering it effectively translates into losing the capability to use this cryptographic object. All of the revocable cryptographic systems studied so far have a major drawback: the recipient only receives one copy of the quantum state. Worse yet, the schemes become completely insecure if the recipient receives many identical copies of the same quantum state - a property that is clearly much more desirable in practice. While multi-copy security has been extensively studied for a number of other quantum cryptographic primitives, it has so far received only little treatment in context of unclonable primitives. Our work, for the first time, shows the feasibility of revocable primitives, such as revocable encryption and revocable programs, which satisfy multi-copy security in oracle models. This suggest that the stronger notion of multi-copy security is within reach in unclonable cryptography more generally, and therefore could lead to a new research direction in the field.

Cite as

Prabhanjan Ananth, Saachi Mutreja, and Alexander Poremba. Revocable Encryption, Programs, and More: The Case of Multi-Copy Security. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ananth_et_al:LIPIcs.ITC.2025.9,
  author =	{Ananth, Prabhanjan and Mutreja, Saachi and Poremba, Alexander},
  title =	{{Revocable Encryption, Programs, and More: The Case of Multi-Copy Security}},
  booktitle =	{6th Conference on Information-Theoretic Cryptography (ITC 2025)},
  pages =	{9:1--9:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-385-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{343},
  editor =	{Gilboa, Niv},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2025.9},
  URN =		{urn:nbn:de:0030-drops-243592},
  doi =		{10.4230/LIPIcs.ITC.2025.9},
  annote =	{Keywords: quantum cryptography, unclonable primitives}
}

Document

DOI: 10.4230/LIPIcs.CCC.2025.7

Sparser Abelian High Dimensional Expanders

Authors: Yotam Dikstein, Siqi Liu, and Avi Wigderson

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract

The focus of this paper is the development of new elementary techniques for the construction and analysis of high dimensional expanders. Specifically, we present two new explicit constructions of Cayley high dimensional expanders (HDXs) over the abelian group 𝔽₂ⁿ. Our expansion proofs use only linear algebra and combinatorial arguments. The first construction gives local spectral HDXs of any constant dimension and subpolynomial degree exp(n^ε) for every ε > 0, improving on a construction by Golowich [Golowich, 2023] which achieves ε = 1/2. [Golowich, 2023] derives these HDXs by sparsifying the complete Grassmann poset of subspaces. The novelty in our construction is the ability to sparsify any expanding Grassmann posets, leading to iterated sparsification and much smaller degrees. The sparse Grassmannian (which is of independent interest in the theory of HDXs) serves as the generating set of the Cayley graph. Our second construction gives a 2-dimensional HDX of any polynomial degree exp(ε n) for any constant ε > 0, which is simultaneously a spectral expander and a coboundary expander. To the best of our knowledge, this is the first such non-trivial construction. We name it the Johnson complex, as it is derived from the classical Johnson scheme, whose vertices serve as the generating set of this Cayley graph. This construction may be viewed as a derandomization of the recent random geometric complexes of [Liu et al., 2023]. Establishing coboundary expansion through Gromov’s "cone method" and the associated isoperimetric inequalities is the most intricate aspect of this construction. While these two constructions are quite different, we show that they both share a common structure, resembling the intersection patterns of vectors in the Hadamard code. We propose a general framework of such "Hadamard-like" constructions in the hope that it will yield new HDXs.

Cite as

Yotam Dikstein, Siqi Liu, and Avi Wigderson. Sparser Abelian High Dimensional Expanders. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 7:1-7:98, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dikstein_et_al:LIPIcs.CCC.2025.7,
  author =	{Dikstein, Yotam and Liu, Siqi and Wigderson, Avi},
  title =	{{Sparser Abelian High Dimensional Expanders}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{7:1--7:98},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.7},
  URN =		{urn:nbn:de:0030-drops-237013},
  doi =		{10.4230/LIPIcs.CCC.2025.7},
  annote =	{Keywords: Local spectral expander, coboundary expander, Grassmannian expander}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2025.102

Fourier Analysis of Iterative Algorithms

Authors: Chris Jones and Lucas Pesenti

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract

We study a general class of nonlinear iterative algorithms which includes power iteration, belief propagation and approximate message passing, and many forms of gradient descent. When the input is a random matrix with i.i.d. entries, we use Boolean Fourier analysis to analyze these algorithms as low-degree polynomials in the entries of the input matrix. Each symmetrized Fourier character represents all monomials with a certain shape as specified by a small graph, which we call a Fourier diagram. We prove fundamental asymptotic properties of the Fourier diagrams: over the randomness of the input, all diagrams with cycles are negligible; the tree-shaped diagrams form a basis of asymptotically independent Gaussian vectors; and, when restricted to the trees, iterative algorithms exactly follow an idealized Gaussian dynamic. We use this to prove a state evolution formula, giving a "complete" asymptotic description of the algorithm’s trajectory. The restriction to tree-shaped monomials mirrors the assumption of the cavity method, a 40-year-old non-rigorous technique in statistical physics which has served as one of the most important techniques in the field. We demonstrate how to implement cavity method derivations by 1) restricting the iteration to its tree approximation, and 2) observing that heuristic cavity method-type arguments hold rigorously on the simplified iteration. Our proofs use combinatorial arguments similar to the trace method from random matrix theory. Finally, we push the diagram analysis to a number of iterations that scales with the dimension n of the input matrix, proving that the tree approximation still holds for a simple variant of power iteration all the way up to n^{Ω(1)} iterations.

Cite as

Chris Jones and Lucas Pesenti. Fourier Analysis of Iterative Algorithms. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 102:1-102:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jones_et_al:LIPIcs.ICALP.2025.102,
  author =	{Jones, Chris and Pesenti, Lucas},
  title =	{{Fourier Analysis of Iterative Algorithms}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{102:1--102:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.102},
  URN =		{urn:nbn:de:0030-drops-234791},
  doi =		{10.4230/LIPIcs.ICALP.2025.102},
  annote =	{Keywords: Iterative Algorithms, Message-passing Algorithms, Random Matrix Theory}
}

Document

RANDOM

DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.58

Expanderizing Higher Order Random Walks

Authors: Vedat Levi Alev and Shravas Rao

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract

We study a variant of the down-up (also known as the Glauber dynamics) and up-down walks over an n-partite simplicial complex, which we call expanderized higher order random walks - where the sequence of updated coordinates correspond to the sequence of vertices visited by a random walk over an auxiliary expander graph H. When H is the clique with self loops on [n], this random walk reduces to the usual down-up walk and when H is the directed cycle on [n], this random walk reduces to the well-known systematic scan Glauber dynamics. We show that whenever the usual higher order random walks satisfy a log-Sobolev inequality or a Poincaré inequality, the expanderized walks satisfy the same inequalities with a loss of quality related to the two-sided expansion of the auxillary graph H. Our construction can be thought as a higher order random walk generalization of the derandomized squaring algorithm of Rozenman and Vadhan (RANDOM 2005). We study the mixing times of our expanderized walks in two example cases: We show that when initiated with an expander graph our expanderized random walks have mixing time (i) O(n log n) for sampling a uniformly random list colorings of a graph G of maximum degree Δ = O(1) where each vertex has at least (11/6 - ε) Δ and at most O(Δ) colors, (ii) O_h((n log n)/(1 - ‖J‖_op)²) for sampling the Ising model with a PSD interaction matrix J ∈ ℝ^{n×n} satisfying ‖J‖_op ≤ 1 and the external field h ∈ ℝⁿ- here the O(•) notation hides a constant that depends linearly on the largest entry of h. As expander graphs can be very sparse, this decreases the amount of randomness required to simulate the down-up walks by a logarithmic factor. We also prove some simple results which enable us to argue about log-Sobolev constants of higher order random walks and provide a simple and self-contained analysis of local-to-global Φ-entropy contraction in simplicial complexes - giving simpler proofs for many pre-existing results.

Cite as

Vedat Levi Alev and Shravas Rao. Expanderizing Higher Order Random Walks. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 58:1-58:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{alev_et_al:LIPIcs.APPROX/RANDOM.2024.58,
  author =	{Alev, Vedat Levi and Rao, Shravas},
  title =	{{Expanderizing Higher Order Random Walks}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{58:1--58:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.58},
  URN =		{urn:nbn:de:0030-drops-210510},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.58},
  annote =	{Keywords: Higher Order Random Walks, Expander Graphs, Glauber Dynamics, Derandomized Squaring, High Dimensional Expansion, Spectral Independence, Entropic Independence}
}

Document

DOI: 10.4230/LIPIcs.CCC.2024.26

Dimension Independent Disentanglers from Unentanglement and Applications

Authors: Fernando Granha Jeronimo and Pei Wu

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

Quantum entanglement, a distinctive form of quantum correlation, has become a key enabling ingredient in diverse applications in quantum computation, complexity, cryptography, etc. However, the presence of unwanted adversarial entanglement also poses challenges and even prevents the correct behaviour of many protocols and applications. In this paper, we explore methods to "break" the quantum correlations. Specifically, we construct a dimension-independent k-partite disentangler (like) channel from bipartite unentangled input. In particular, we show: For every d,𝓁 ≥ k ∈ ℕ^+, there is an efficient channel Λ : ℂ^{d𝓁} ⊗ ℂ^{d𝓁} → ℂ^{dk} such that for every bipartite separable density operator ρ₁⊗ ρ₂, the output Λ(ρ₁⊗ρ₂) is close to a k-partite separable state. Concretely, for some distribution μ on states from C^d, ║ Λ(ρ₁⊗ρ₂) - ∫ |ψ⟩⟨ψ|^{⊗k} dμ(ψ) ║₁ ≤ Õ((k³/𝓁)^{1/4}). Moreover, Λ(|ψ⟩⟨ψ|^{⊗𝓁} ⊗ |ψ⟩⟨ψ|^{⊗𝓁}) = |ψ⟩⟨ψ|^{⊗k}. Without the bipartite unentanglement assumption, the above bound is conjectured to be impossible and would imply QMA(2) = QMA. Leveraging multipartite unentanglement ensured by our disentanglers, we achieve the following: (i) a new proof that QMA(2) admits arbitrary gap amplification; (ii) a variant of the swap test and product test with improved soundness, addressing a major limitation of their original versions. More importantly, we demonstrate that unentangled quantum proofs of almost general real amplitudes capture NEXP, thereby greatly relaxing the non-negative amplitudes assumption in the recent work of QMA^+(2) = NEXP [Jeronimo and Wu, STOC 2023]. Specifically, our findings show that to capture NEXP, it suffices to have unentangled proofs of the form |ψ⟩ = √a |ψ_{+}⟩ + √{1-a} |ψ_{-}⟩ where |ψ_{+}⟩ has non-negative amplitudes, |ψ_{-}⟩ only has negative amplitudes and |a-(1-a)| ≥ 1/poly(n) with a ∈ [0,1]. Additionally, we present a protocol achieving an almost largest possible completeness-soundness gap before obtaining QMA^ℝ(k) = NEXP, namely, a 1/poly(n) additive improvement to the gap results in this equality.

Cite as

Fernando Granha Jeronimo and Pei Wu. Dimension Independent Disentanglers from Unentanglement and Applications. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 26:1-26:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{jeronimo_et_al:LIPIcs.CCC.2024.26,
  author =	{Jeronimo, Fernando Granha and Wu, Pei},
  title =	{{Dimension Independent Disentanglers from Unentanglement and Applications}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{26:1--26:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.26},
  URN =		{urn:nbn:de:0030-drops-204228},
  doi =		{10.4230/LIPIcs.CCC.2024.26},
  annote =	{Keywords: QMA(2), disentangler, quantum proofs}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2024.9

Quantum Merlin-Arthur and Proofs Without Relative Phase

Authors: Roozbeh Bassirian, Bill Fefferman, and Kunal Marwaha

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract

We study a variant of QMA where quantum proofs have no relative phase (i.e. non-negative amplitudes, up to a global phase). If only completeness is modified, this class is equal to QMA [Grilo et al., 2014]; but if both completeness and soundness are modified, the class (named QMA+ by Jeronimo and Wu [Jeronimo and Wu, 2023]) can be much more powerful. We show that QMA+ with some constant gap is equal to NEXP, yet QMA+ with some other constant gap is equal to QMA. One interpretation is that Merlin’s ability to "deceive" originates from relative phase at least as much as from entanglement, since QMA(2) ⊆ NEXP.

Cite as

Roozbeh Bassirian, Bill Fefferman, and Kunal Marwaha. Quantum Merlin-Arthur and Proofs Without Relative Phase. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bassirian_et_al:LIPIcs.ITCS.2024.9,
  author =	{Bassirian, Roozbeh and Fefferman, Bill and Marwaha, Kunal},
  title =	{{Quantum Merlin-Arthur and Proofs Without Relative Phase}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.9},
  URN =		{urn:nbn:de:0030-drops-195370},
  doi =		{10.4230/LIPIcs.ITCS.2024.9},
  annote =	{Keywords: quantum complexity, QMA(2), PCPs}
}

Document

RANDOM

DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.60

Fast Decoding of Explicit Almost Optimal ε-Balanced q-Ary Codes And Fast Approximation of Expanding k-CSPs

Authors: Fernando Granha Jeronimo

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract

Good codes over an alphabet of constant size q can approach but not surpass distance 1-1/q. This makes the use of q-ary codes a necessity in some applications, and much work has been devoted to the case of constant alphabet q. In the large distance regime, namely, distance 1-1/q-ε for small ε > 0, the Gilbert-Varshamov (GV) bound asserts that rate Ω_q(ε²) is achievable whereas the q-ary MRRW bound gives a rate upper bound of O_q(ε²log(1/ε)). In this sense, the GV bound is almost optimal in this regime. Prior to this work there was no known explicit and efficiently decodable q-ary codes near the GV bound, in this large distance regime, for any constant q ≥ 3. We design an Õ_{ε,q}(N) time decoder for explicit (expander based) families of linear codes C_{N,q,ε} ⊆ F_q^N of distance (1-1/q)(1-ε) and rate Ω_q(ε^{2+o(1)}), for any desired ε > 0 and any constant prime q, namely, almost optimal in this regime. These codes are ε-balanced,i.e., for every non-zero codeword, the frequency of each symbol lies in the interval [1/q - ε, 1/q + ε]. A key ingredient of the q-ary decoder is a new near-linear time approximation algorithm for linear equations (k-LIN) over ℤ_q on expanding hypergraphs, in particular, those naturally arising in the decoding of these codes. We also investigate k-CSPs on expanding hypergraphs in more generality. We show that special trade-offs available for k-LIN over ℤ_q hold for linear equations over a finite group. To handle general finite groups, we design a new matrix version of weak regularity for expanding hypergraphs. We also obtain a near-linear time approximation algorithm for general expanding k-CSPs over q-ary alphabet. This later algorithm runs in time Õ_{k,q}(m + n), where m is the number of constraints and n is the number of variables. This improves the previous best running time of O(n^{Θ_{k,q}(1)}) by a Sum-of-Squares based algorithm of [AJT, 2019] (in the expanding regular case). We obtain our results by generalizing the framework of [JST, 2021] based on weak regularity decomposition for expanding hypergraphs. This framework was originally designed for binary k-XOR with the goal of providing near-linear time decoder for explicit binary codes, near the GV bound, from the breakthrough work of Ta-Shma [STOC, 2017]. The explicit families of codes over prime F_q are based on suitable instatiations of the Jalan-Moshkovitz (Abelian) generalization of Ta-Shma’s distance amplification procedure.

Cite as

Fernando Granha Jeronimo. Fast Decoding of Explicit Almost Optimal ε-Balanced q-Ary Codes And Fast Approximation of Expanding k-CSPs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 60:1-60:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jeronimo:LIPIcs.APPROX/RANDOM.2023.60,
  author =	{Jeronimo, Fernando Granha},
  title =	{{Fast Decoding of Explicit Almost Optimal \epsilon-Balanced q-Ary Codes And Fast Approximation of Expanding k-CSPs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{60:1--60:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.60},
  URN =		{urn:nbn:de:0030-drops-188858},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.60},
  annote =	{Keywords: Decoding, Approximation, GV bound, CSPs, HDXs, Regularity}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2023.40

Exact Completeness of LP Hierarchies for Linear Codes

Authors: Leonardo Nagami Coregliano, Fernando Granha Jeronimo, and Chris Jones

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract

Determining the maximum size A₂(n,d) of a binary code of blocklength n and distance d remains an elusive open question even when restricted to the important class of linear codes. Recently, two linear programming hierarchies extending Delsarte’s LP were independently proposed to upper bound A₂^{Lin}(n,d) (the analogue of A₂(n,d) for linear codes). One of these hierarchies, by the authors, was shown to be approximately complete in the sense that the hierarchy converges to A₂^{Lin}(n,d) as the level grows beyond n². Despite some structural similarities, not even approximate completeness was known for the other hierarchy by Loyfer and Linial. In this work, we prove that both hierarchies recover the exact value of A₂^{Lin}(n,d) at level n. We also prove that at this level the polytope of Loyfer and Linial is integral. Even though these hierarchies seem less powerful than general hierarchies such as Sum-of-Squares, we show that they have enough structure to yield exact completeness via pseudoprobabilities.

Cite as

Leonardo Nagami Coregliano, Fernando Granha Jeronimo, and Chris Jones. Exact Completeness of LP Hierarchies for Linear Codes. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 40:1-40:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{coregliano_et_al:LIPIcs.ITCS.2023.40,
  author =	{Coregliano, Leonardo Nagami and Jeronimo, Fernando Granha and Jones, Chris},
  title =	{{Exact Completeness of LP Hierarchies for Linear Codes}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{40:1--40:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.40},
  URN =		{urn:nbn:de:0030-drops-175433},
  doi =		{10.4230/LIPIcs.ITCS.2023.40},
  annote =	{Keywords: LP bound, linear codes, Delsarte’s LP, combinatorial polytopes, pseudoexpectation}
}

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