7 Search Results for "Charles, Valentine"

Document
DOI: 10.4230/LIPIcs.STACS.2026.23
Simple Circuit Extensions for XOR in PTIME

Authors: Marco Carmosino, Ngu Dang, and Tim Jackman

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
The Minimum Circuit Size Problem for Partial Functions (MCSP^*) is hard assuming the Exponential Time Hypothesis (ETH) (Ilango, 2020). This breakthrough result leveraged a characterization of the optimal {∧, ∨, ¬} circuits for n-bit OR (OR_n) and a reduction from the partial f-Simple Extension Problem where f = OR_n. It remains open to extend that reduction to show ETH-hardness of total MCSP. However, Ilango observed that the total f-Simple Extension Problem is easy whenever f is computed by read-once formulas (like OR_n). Therefore, extending Ilango’s proof to total MCSP would require replacing OR_n with a more complex but similarly well-understood Boolean function. This work shows that the f-Simple Extension problem remains easy when f is the next natural candidate: XOR_n. We first develop a fixed-parameter tractable algorithm for the f-Simple Extension Problem that is efficient whenever the optimal circuits for f are (1) linear in size, (2) polynomially "few" and efficiently enumerable in the truth-table size (up to isomorphism and permutation of inputs), and (3) all have constant bounded fan-out. XOR_n satisfies all three of these conditions. When ¬ gates count towards circuit size, optimal XOR_n circuits are binary trees of n-1 subcircuits computing (¬)XOR₂ (Kombarov, 2011). We extend this characterization when ¬ gates do not contribute the circuit size. Thus, the XOR-Simple Extension Problem is in polynomial time under both measures of circuit complexity. We conclude by discussing conjectures about the complexity of the f-Simple Extension problem for each explicit function f with known and unrestricted circuit lower bounds over the DeMorgan basis. Examining the conditions under which our Simple Extension Solver is efficient, we argue that multiplexer functions (MUX) are the most promising candidate for ETH-hardness of a Simple Extension Problem, towards proving ETH-hardness of total MCSP.
Cite as

Marco Carmosino, Ngu Dang, and Tim Jackman. Simple Circuit Extensions for XOR in PTIME. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{carmosino_et_al:LIPIcs.STACS.2026.23,
  author =	{Carmosino, Marco and Dang, Ngu and Jackman, Tim},
  title =	{{Simple Circuit Extensions for XOR in PTIME}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.23},
  URN =		{urn:nbn:de:0030-drops-255127},
  doi =		{10.4230/LIPIcs.STACS.2026.23},
  annote =	{Keywords: Minimum Circuit Size Problem, Circuit Lower Bounds, Exponential Time Hypothesis}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.25
Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing

Authors: Marek Černý and Tim Seppelt

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Two graphs G and H are homomorphism indistinguishable over a graph class ℱ if they admit the same number of homomorphisms from every graph F ∈ ℱ. Many graph isomorphism relaxations such as (quantum) isomorphism and cospectrality can be characterised as homomorphism indistinguishability over specific graph classes. Thereby, the problems HomInd(ℱ) of deciding homomorphism indistinguishability over ℱ subsume diverse graph isomorphism relaxations whose complexities range from logspace to undecidable. Establishing the first general result on the complexity of HomInd(ℱ), Seppelt (MFCS 2024) showed that HomInd(ℱ) is in randomised polynomial time for every graph class ℱ of bounded treewidth that can be defined in counting monadic second-order logic CMSO₂. We show that this algorithm is conditionally optimal, i.e. it cannot be derandomised unless polynomial identity testing is in P. For CMSO₂-definable graph classes ℱ of bounded pathwidth, we improve the previous complexity upper bound for HomInd(ℱ) from P to C_ = L and show that this is tight. Secondarily, we establish a connection between homomorphism indistinguishability and multiplicity automata equivalence which allows us to pinpoint the complexity of the latter problem as C_ = L-complete.
Cite as

Marek Černý and Tim Seppelt. Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cerny_et_al:LIPIcs.STACS.2026.25,
  author =	{\v{C}ern\'{y}, Marek and Seppelt, Tim},
  title =	{{Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.25},
  URN =		{urn:nbn:de:0030-drops-255144},
  doi =		{10.4230/LIPIcs.STACS.2026.25},
  annote =	{Keywords: treewidth, Courcelle’s theorem, logspace, multiplicity automata, polynomial identity testing}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.33
Bit-Fixing Extractors for Almost-Logarithmic Entropy

Authors: Dean Doron and Ori Fridman

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

Abstract
An oblivious bit-fixing source is a distribution over {0,1}ⁿ, where k bits are uniform and independent and the rest n-k are fixed a priori to some constant value. Extracting (close to) true randomness from an oblivious bit-fixing source has been studied since the 1980s, with applications in cryptography and complexity theory. We construct explicit extractors for oblivious bit-fixing source that support k = Õ(log n), outputting almost all the entropy with low error. The previous state-of-the-art construction that outputs many bits is due to Rao [Rao, CCC '09], and requires entropy k ≥ log^{c} n for some large constant c. The two key components in our constructions are new low-error affine condensers for poly-logarithmic entropies (that we achieve using techniques from the nonmalleable extractors literature), and a dual use of linear condensers for OBF sources.
Cite as

Dean Doron and Ori Fridman. Bit-Fixing Extractors for Almost-Logarithmic Entropy. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 33:1-33:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{doron_et_al:LIPIcs.APPROX/RANDOM.2025.33,
  author =	{Doron, Dean and Fridman, Ori},
  title =	{{Bit-Fixing Extractors for Almost-Logarithmic Entropy}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{33:1--33:19},
  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.2025.33},
  URN =		{urn:nbn:de:0030-drops-243994},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.33},
  annote =	{Keywords: Seedless extractors, oblivious bit-fixing sources}
}
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
DOI: 10.4230/LIPIcs.ITCS.2025.30
Provability of the Circuit Size Hierarchy and Its Consequences

Authors: Marco Carmosino, Valentine Kabanets, Antonina Kolokolova, Igor C. Oliveira, and Dimitrios Tsintsilidas

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
The Circuit Size Hierarchy (CSH^a_b) states that if a > b ≥ 1 then the set of functions on n variables computed by Boolean circuits of size n^a is strictly larger than the set of functions computed by circuits of size n^b. This result, which is a cornerstone of circuit complexity theory, follows from the non-constructive proof of the existence of functions of large circuit complexity obtained by Shannon in 1949. Are there more "constructive" proofs of the Circuit Size Hierarchy? Can we quantify this? Motivated by these questions, we investigate the provability of CSH^a_b in theories of bounded arithmetic. Among other contributions, we establish the following results: i) Given any a > b > 1, CSH^a_b is provable in Buss’s theory 𝖳²₂. ii) In contrast, if there are constants a > b > 1 such that CSH^a_b is provable in the theory 𝖳¹₂, then there is a constant ε > 0 such that 𝖯^NP requires non-uniform circuits of size at least n^{1 + ε}. In other words, an improved upper bound on the proof complexity of CSH^a_b would lead to new lower bounds in complexity theory. We complement these results with a proof of the Formula Size Hierarchy (FSH^a_b) in PV₁ with parameters a > 2 and b = 3/2. This is in contrast with typical formalizations of complexity lower bounds in bounded arithmetic, which require APC₁ or stronger theories and are not known to hold even in 𝖳¹₂.
Cite as

Marco Carmosino, Valentine Kabanets, Antonina Kolokolova, Igor C. Oliveira, and Dimitrios Tsintsilidas. Provability of the Circuit Size Hierarchy and Its Consequences. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 30:1-30:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{carmosino_et_al:LIPIcs.ITCS.2025.30,
  author =	{Carmosino, Marco and Kabanets, Valentine and Kolokolova, Antonina and C. Oliveira, Igor and Tsintsilidas, Dimitrios},
  title =	{{Provability of the Circuit Size Hierarchy and Its Consequences}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{30:1--30:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.30},
  URN =		{urn:nbn:de:0030-drops-226586},
  doi =		{10.4230/LIPIcs.ITCS.2025.30},
  annote =	{Keywords: Bounded Arithmetic, Circuit Complexity, Hierarchy Theorems}
}
Document
DOI: 10.4230/LIPIcs.CCC.2021.6
On the Power and Limitations of Branch and Cut

Authors: Noah Fleming, Mika Göös, Russell Impagliazzo, Toniann Pitassi, Robert Robere, Li-Yang Tan, and Avi Wigderson

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)

Abstract
The Stabbing Planes proof system [Paul Beame et al., 2018] was introduced to model the reasoning carried out in practical mixed integer programming solvers. As a proof system, it is powerful enough to simulate Cutting Planes and to refute the Tseitin formulas - certain unsatisfiable systems of linear equations od 2 - which are canonical hard examples for many algebraic proof systems. In a recent (and surprising) result, Dadush and Tiwari [Daniel Dadush and Samarth Tiwari, 2020] showed that these short refutations of the Tseitin formulas could be translated into quasi-polynomial size and depth Cutting Planes proofs, refuting a long-standing conjecture. This translation raises several interesting questions. First, whether all Stabbing Planes proofs can be efficiently simulated by Cutting Planes. This would allow for the substantial analysis done on the Cutting Planes system to be lifted to practical mixed integer programming solvers. Second, whether the quasi-polynomial depth of these proofs is inherent to Cutting Planes. In this paper we make progress towards answering both of these questions. First, we show that any Stabbing Planes proof with bounded coefficients (SP*) can be translated into Cutting Planes. As a consequence of the known lower bounds for Cutting Planes, this establishes the first exponential lower bounds on SP*. Using this translation, we extend the result of Dadush and Tiwari to show that Cutting Planes has short refutations of any unsatisfiable system of linear equations over a finite field. Like the Cutting Planes proofs of Dadush and Tiwari, our refutations also incur a quasi-polynomial blow-up in depth, and we conjecture that this is inherent. As a step towards this conjecture, we develop a new geometric technique for proving lower bounds on the depth of Cutting Planes proofs. This allows us to establish the first lower bounds on the depth of Semantic Cutting Planes proofs of the Tseitin formulas.
Cite as

Noah Fleming, Mika Göös, Russell Impagliazzo, Toniann Pitassi, Robert Robere, Li-Yang Tan, and Avi Wigderson. On the Power and Limitations of Branch and Cut. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 6:1-6:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{fleming_et_al:LIPIcs.CCC.2021.6,
  author =	{Fleming, Noah and G\"{o}\"{o}s, Mika and Impagliazzo, Russell and Pitassi, Toniann and Robere, Robert and Tan, Li-Yang and Wigderson, Avi},
  title =	{{On the Power and Limitations of Branch and Cut}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{6:1--6:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.6},
  URN =		{urn:nbn:de:0030-drops-142809},
  doi =		{10.4230/LIPIcs.CCC.2021.6},
  annote =	{Keywords: Proof Complexity, Integer Programming, Cutting Planes, Branch and Cut, Stabbing Planes}
}
Document
DOI: 10.4230/OASIcs.LDK.2019.22
Opening Digitized Newspapers Corpora: Europeana’s Full-Text Data Interoperability Case

Authors: Nuno Freire, Antoine Isaac, Twan Goosen, Daan Broeder, Hugo Manguinhas, and Valentine Charles

Published in: OASIcs, Volume 70, 2nd Conference on Language, Data and Knowledge (LDK 2019)

Abstract
Cultural heritage institutions hold collections of printed newspapers that are valuable resources for the study of history, linguistics and other Digital Humanities scientific domains. Effective retrieval of newspapers content based on metadata only is a task nearly impossible, making the retrieval based on (digitized) full-text particularly relevant. Europeana, Europe’s Digital Library, is in the position to provide access to large newspapers collections with full-text resources. Full-text corpora are also relevant for Europeana’s objective of promoting the usage of cultural heritage resources for use within research infrastructures. We have derived requirements for aggregating and publishing Europeana’s newspapers full-text corpus in an interoperable way, based on investigations into the specific characteristics of cultural data, the needs of two research infrastructures (CLARIN and EUDAT) and the practices being promoted in the International Image Interoperability Framework (IIIF) community. We have then defined a "full-text profile" for the Europeana Data Model, which is being applied to Europeana’s newspaper corpus.
Cite as

Nuno Freire, Antoine Isaac, Twan Goosen, Daan Broeder, Hugo Manguinhas, and Valentine Charles. Opening Digitized Newspapers Corpora: Europeana’s Full-Text Data Interoperability Case. In 2nd Conference on Language, Data and Knowledge (LDK 2019). Open Access Series in Informatics (OASIcs), Volume 70, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{freire_et_al:OASIcs.LDK.2019.22,
  author =	{Freire, Nuno and Isaac, Antoine and Goosen, Twan and Broeder, Daan and Manguinhas, Hugo and Charles, Valentine},
  title =	{{Opening Digitized Newspapers Corpora: Europeana’s Full-Text Data Interoperability Case}},
  booktitle =	{2nd Conference on Language, Data and Knowledge (LDK 2019)},
  pages =	{22:1--22:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-105-4},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{70},
  editor =	{Eskevich, Maria and de Melo, Gerard and F\"{a}th, Christian and McCrae, John P. and Buitelaar, Paul and Chiarcos, Christian and Klimek, Bettina and Dojchinovski, Milan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.LDK.2019.22},
  URN =		{urn:nbn:de:0030-drops-103869},
  doi =		{10.4230/OASIcs.LDK.2019.22},
  annote =	{Keywords: Metadata, Full-text, Interoperability, Data aggregation, Cultural Heritage, Research Infrastructures}
}
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