7 Search Results for "McKay, Dylan M."

Document
DOI: 10.4230/LIPIcs.ITCS.2026.37
New Algebrization Barriers to Circuit Lower Bounds via Communication Complexity of Missing-String

Authors: Lijie Chen, Yang Hu, and Hanlin Ren

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

Abstract
The algebrization barrier, proposed by Aaronson and Wigderson (STOC '08, ToCT '09), captures the limitations of many complexity-theoretic techniques based on arithmetization. Notably, several circuit lower bounds that overcome the relativization barrier (Buhrman-Fortnow-Thierauf, CCC '98; Vinodchandran, TCS '05; Santhanam, STOC '07, SICOMP '09) remain subject to the algebrization barrier. In this work, we establish several new algebrization barriers to circuit lower bounds by studying the communication complexity of the following problem, called XOR-Missing-String: For m < 2^{n/2}, Alice gets a list of m strings x₁, … , x_m ∈ {0, 1}ⁿ, Bob gets a list of m strings y₁, … , y_m ∈ {0, 1}ⁿ, and the goal is to output a string s ∈ {0, 1}ⁿ that is not equal to x_i⊕ y_j for any i, j ∈ [m]. 1) We construct an oracle A₁ and its multilinear extension A₁̃ such that PostBPE^{A₁̃} has linear-size A₁-oracle circuits on infinitely many input lengths. That is, proving PostBPE ̸ ⊆ i.o.- SIZE[O(n)] requires non-algebrizing techniques. This barrier follows from a PostBPP communication lower bound for XOR-Missing-String. This is in contrast to the well-known algebrizing lower bound MA_E (⊆ PostBPE) ̸ ⊆ P/_poly. 2) We construct an oracle A₂ and its multilinear extension A₂̃ such that BPE^{A₂̃} has linear-size A₂-oracle circuits on all input lengths. Previously, a similar barrier was demonstrated by Aaronson and Wigderson, but in their result, A₂̃ is only a multiquadratic extension of A₂. Our results show that communication complexity is more useful than previously thought for proving algebrization barriers, as Aaronson and Wigderson wrote that communication-based barriers were "more contrived". This serves as an example of how XOR-Missing-String forms new connections between communication lower bounds and algebrization barriers. 3) Finally, we study algebrization barriers to circuit lower bounds for MA_E. Buhrman, Fortnow, and Thierauf proved a sub-half-exponential circuit lower bound for MA_E via algebrizing techniques. Toward understanding whether the half-exponential bound can be improved, we define a natural subclass of MA_E that includes their hard MA_E language, and prove the following result: For every super-half-exponential function h(n), we construct an oracle A₃ and its multilinear extension A₃̃ such that this natural subclass of MA_E^{A₃̃} has h(n)-size A₃-oracle circuits on all input lengths. This suggests that half-exponential might be the correct barrier for MA_E circuit lower bounds w.r.t. algebrizing techniques.
Cite as

Lijie Chen, Yang Hu, and Hanlin Ren. New Algebrization Barriers to Circuit Lower Bounds via Communication Complexity of Missing-String. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 37:1-37:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chen_et_al:LIPIcs.ITCS.2026.37,
  author =	{Chen, Lijie and Hu, Yang and Ren, Hanlin},
  title =	{{New Algebrization Barriers to Circuit Lower Bounds via Communication Complexity of Missing-String}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{37:1--37:20},
  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.2026.37},
  URN =		{urn:nbn:de:0030-drops-253246},
  doi =		{10.4230/LIPIcs.ITCS.2026.37},
  annote =	{Keywords: circuit lower bound, algebrization barrier, missing string, communication complexity}
}
Document
DOI: 10.4230/OASIcs.SLATE.2025.1
From Prediction to Precision: Leveraging LLMs for Equitable and Data-Driven Writing Placement in Developmental Education

Authors: Miguel Da Corte and Jorge Baptista

Published in: OASIcs, Volume 135, 14th Symposium on Languages, Applications and Technologies (SLATE 2025)

Abstract
Accurate text classification and placement remain challenges in U.S. higher education, with traditional automated systems like Accuplacer functioning as "black-box" models with limited assessment transparency. This study evaluates Large Language Models (LLMs) as complementary placement tools by comparing their classification performance against a human-rated gold standard and Accuplacer. A 450-essay corpus was classified using Claude, Gemini, GPT-3.5-turbo, and GPT-4o across four prompting strategies: Zero-shot, Few-shot, Enhanced, and Enhanced+ (definitions with examples). Two classification approaches were tested: (i) a 1-step, 3 class classification task, distinguishing DevEd Level 1, DevEd Level 2, and College-level texts in one single run; and (ii) a 2-step classification task, first separating College vs. Non-College texts before further classifying Non-College texts into DevEd sublevels. The results show that structured prompt refinement improves the precision of LLMs' classification, with Claude Enhanced + achieving 62.22% precision (1 step) and Gemini Enhanced + reaching 69.33% (2 step), both surpassing Accuplacer (58.22%). Gemini and Claude also demonstrated strong correlation with human ratings, with Claude achieving the highest Pearson scores (ρ = 0.75; 1-step, ρ = 0.73; 2-step) vs. Accuplacer (ρ = 0.67). While LLMs show promise for DevEd placement, their precision remains a work in progress, highlighting the need for further refinement and safeguards to ensure ethical and equitable placement.
Cite as

Miguel Da Corte and Jorge Baptista. From Prediction to Precision: Leveraging LLMs for Equitable and Data-Driven Writing Placement in Developmental Education. In 14th Symposium on Languages, Applications and Technologies (SLATE 2025). Open Access Series in Informatics (OASIcs), Volume 135, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dacorte_et_al:OASIcs.SLATE.2025.1,
  author =	{Da Corte, Miguel and Baptista, Jorge},
  title =	{{From Prediction to Precision: Leveraging LLMs for Equitable and Data-Driven Writing Placement in Developmental Education}},
  booktitle =	{14th Symposium on Languages, Applications and Technologies (SLATE 2025)},
  pages =	{1:1--1:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-387-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{135},
  editor =	{Baptista, Jorge and Barateiro, Jos\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SLATE.2025.1},
  URN =		{urn:nbn:de:0030-drops-236817},
  doi =		{10.4230/OASIcs.SLATE.2025.1},
  annote =	{Keywords: Large Language Models (LLMs), Developmental Education (DevEd), writing assessment, text classification, English writing proficiency}
}
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.ITCS.2023.99
On Oracles and Algorithmic Methods for Proving Lower Bounds

Authors: Nikhil Vyas and Ryan Williams

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

Abstract
This paper studies the interaction of oracles with algorithmic approaches to proving circuit complexity lower bounds, establishing new results on two different kinds of questions. 1) We revisit some prominent open questions in circuit lower bounds, and provide a clean way of viewing them as circuit upper bound questions. Let Missing-String be the (total) search problem of producing a string that does not appear in a given list L containing M bit-strings of length N, where M < 2ⁿ. We show in a generic way how algorithms and uniform circuits (from restricted classes) for Missing-String imply complexity lower bounds (and in some cases, the converse holds as well). We give a local algorithm for Missing-String, which can compute any desired output bit making very few probes into the input, when the number of strings M is small enough. We apply this to prove a new nearly-optimal (up to oracles) time hierarchy theorem with advice. We show that the problem of constructing restricted uniform circuits for Missing-String is essentially equivalent to constructing functions without small non-uniform circuits, in a relativizing way. For example, we prove that small uniform depth-3 circuits for Missing-String would imply exponential circuit lower bounds for Σ₂ EXP, and depth-3 lower bounds for Missing-String would imply non-trivial circuits (relative to an oracle) for Σ₂ EXP problems. Both conclusions are longstanding open problems in circuit complexity. 2) It has been known since Impagliazzo, Kabanets, and Wigderson [JCSS 2002] that generic derandomizations improving subexponentially over exhaustive search would imply lower bounds such as NEXP ̸ ⊂ 𝖯/poly. Williams [SICOMP 2013] showed that Circuit-SAT algorithms running barely faster than exhaustive search would imply similar lower bounds. The known proofs of such results do not relativize (they use techniques from interactive proofs/PCPs). However, it has remained open whether there is an oracle under which the generic implications from circuit-analysis algorithms to circuit lower bounds fail. Building on an oracle of Fortnow, we construct an oracle relative to which the circuit approximation probability problem (CAPP) is in 𝖯, yet EXP^{NP} has polynomial-size circuits. We construct an oracle relative to which SAT can be solved in "half-exponential" time, yet exponential time (EXP) has polynomial-size circuits. Improving EXP to NEXP would give an oracle relative to which Σ₂ 𝖤 has "half-exponential" size circuits, which is open. (Recall it is known that Σ₂ 𝖤 is not in "sub-half-exponential" size, and the proof relativizes.) Moreover, the running time of the SAT algorithm cannot be improved: relative to all oracles, if SAT is in "sub-half-exponential" time then EXP does not have polynomial-size circuits.
Cite as

Nikhil Vyas and Ryan Williams. On Oracles and Algorithmic Methods for Proving Lower Bounds. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 99:1-99:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{vyas_et_al:LIPIcs.ITCS.2023.99,
  author =	{Vyas, Nikhil and Williams, Ryan},
  title =	{{On Oracles and Algorithmic Methods for Proving Lower Bounds}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{99:1--99:26},
  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.2023.99},
  URN =		{urn:nbn:de:0030-drops-176021},
  doi =		{10.4230/LIPIcs.ITCS.2023.99},
  annote =	{Keywords: oracles, relativization, circuit complexity, missing string, exponential hierarchy}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.70
Beyond Natural Proofs: Hardness Magnification and Locality

Authors: Lijie Chen, Shuichi Hirahara, Igor C. Oliveira, Ján Pich, Ninad Rajgopal, and Rahul Santhanam

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
Hardness magnification reduces major complexity separations (such as EXP ⊈ NC^1) to proving lower bounds for some natural problem Q against weak circuit models. Several recent works [Igor Carboni Oliveira and Rahul Santhanam, 2018; Dylan M. McKay et al., 2019; Lijie Chen and Roei Tell, 2019; Igor Carboni Oliveira et al., 2019; Lijie Chen et al., 2019; Igor Carboni Oliveira, 2019; Lijie Chen et al., 2019] have established results of this form. In the most intriguing cases, the required lower bound is known for problems that appear to be significantly easier than Q, while Q itself is susceptible to lower bounds but these are not yet sufficient for magnification. In this work, we provide more examples of this phenomenon, and investigate the prospects of proving new lower bounds using this approach. In particular, we consider the following essential questions associated with the hardness magnification program: - Does hardness magnification avoid the natural proofs barrier of Razborov and Rudich [Alexander A. Razborov and Steven Rudich, 1997]? - Can we adapt known lower bound techniques to establish the desired lower bound for Q? We establish that some instantiations of hardness magnification overcome the natural proofs barrier in the following sense: slightly superlinear-size circuit lower bounds for certain versions of the minimum circuit size problem MCSP imply the non-existence of natural proofs. As a corollary of our result, we show that certain magnification theorems not only imply strong worst-case circuit lower bounds but also rule out the existence of efficient learning algorithms. Hardness magnification might sidestep natural proofs, but we identify a source of difficulty when trying to adapt existing lower bound techniques to prove strong lower bounds via magnification. This is captured by a locality barrier: existing magnification theorems unconditionally show that the problems Q considered above admit highly efficient circuits extended with small fan-in oracle gates, while lower bound techniques against weak circuit models quite often easily extend to circuits containing such oracles. This explains why direct adaptations of certain lower bounds are unlikely to yield strong complexity separations via hardness magnification.
Cite as

Lijie Chen, Shuichi Hirahara, Igor C. Oliveira, Ján Pich, Ninad Rajgopal, and Rahul Santhanam. Beyond Natural Proofs: Hardness Magnification and Locality. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 70:1-70:48, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chen_et_al:LIPIcs.ITCS.2020.70,
  author =	{Chen, Lijie and Hirahara, Shuichi and Oliveira, Igor C. and Pich, J\'{a}n and Rajgopal, Ninad and Santhanam, Rahul},
  title =	{{Beyond Natural Proofs: Hardness Magnification and Locality}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{70:1--70:48},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.70},
  URN =		{urn:nbn:de:0030-drops-117550},
  doi =		{10.4230/LIPIcs.ITCS.2020.70},
  annote =	{Keywords: Hardness Magnification, Natural Proofs, Minimum Circuit Size Problem, Circuit Lower Bounds}
}
Document
DOI: 10.4230/LIPIcs.CCC.2019.30
Relations and Equivalences Between Circuit Lower Bounds and Karp-Lipton Theorems

Authors: Lijie Chen, Dylan M. McKay, Cody D. Murray, and R. Ryan Williams

Published in: LIPIcs, Volume 137, 34th Computational Complexity Conference (CCC 2019)

Abstract
A frontier open problem in circuit complexity is to prove P^{NP} is not in SIZE[n^k] for all k; this is a necessary intermediate step towards NP is not in P_{/poly}. Previously, for several classes containing P^{NP}, including NP^{NP}, ZPP^{NP}, and S_2 P, such lower bounds have been proved via Karp-Lipton-style Theorems: to prove C is not in SIZE[n^k] for all k, we show that C subset P_{/poly} implies a "collapse" D = C for some larger class D, where we already know D is not in SIZE[n^k] for all k. It seems obvious that one could take a different approach to prove circuit lower bounds for P^{NP} that does not require proving any Karp-Lipton-style theorems along the way. We show this intuition is wrong: (weak) Karp-Lipton-style theorems for P^{NP} are equivalent to fixed-polynomial size circuit lower bounds for P^{NP}. That is, P^{NP} is not in SIZE[n^k] for all k if and only if (NP subset P_{/poly} implies PH subset i.o.- P^{NP}_{/n}). Next, we present new consequences of the assumption NP subset P_{/poly}, towards proving similar results for NP circuit lower bounds. We show that under the assumption, fixed-polynomial circuit lower bounds for NP, nondeterministic polynomial-time derandomizations, and various fixed-polynomial time simulations of NP are all equivalent. Applying this equivalence, we show that circuit lower bounds for NP imply better Karp-Lipton collapses. That is, if NP is not in SIZE[n^k] for all k, then for all C in {Parity-P, PP, PSPACE, EXP}, C subset P_{/poly} implies C subset i.o.-NP_{/n^epsilon} for all epsilon > 0. Note that unconditionally, the collapses are only to MA and not NP. We also explore consequences of circuit lower bounds for a sparse language in NP. Among other results, we show if a polynomially-sparse NP language does not have n^{1+epsilon}-size circuits, then MA subset i.o.-NP_{/O(log n)}, MA subset i.o.-P^{NP[O(log n)]}, and NEXP is not in SIZE[2^{o(m)}]. Finally, we observe connections between these results and the "hardness magnification" phenomena described in recent works.
Cite as

Lijie Chen, Dylan M. McKay, Cody D. Murray, and R. Ryan Williams. Relations and Equivalences Between Circuit Lower Bounds and Karp-Lipton Theorems. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 30:1-30:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chen_et_al:LIPIcs.CCC.2019.30,
  author =	{Chen, Lijie and McKay, Dylan M. and Murray, Cody D. and Williams, R. Ryan},
  title =	{{Relations and Equivalences Between Circuit Lower Bounds and Karp-Lipton Theorems}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{30:1--30:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-116-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{137},
  editor =	{Shpilka, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2019.30},
  URN =		{urn:nbn:de:0030-drops-108525},
  doi =		{10.4230/LIPIcs.CCC.2019.30},
  annote =	{Keywords: Karp-Lipton Theorems, Circuit Lower Bounds, Derandomization, Hardness Magnification}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.56
Quadratic Time-Space Lower Bounds for Computing Natural Functions with a Random Oracle

Authors: Dylan M. McKay and Richard Ryan Williams

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
We define a model of size-S R-way branching programs with oracles that can make up to S distinct oracle queries over all of their possible inputs, and generalize a lower bound proof strategy of Beame [SICOMP 1991] to apply in the case of random oracles. Through a series of succinct reductions, we prove that the following problems require randomized algorithms where the product of running time and space usage must be Omega(n^2/poly(log n)) to obtain correct answers with constant nonzero probability, even for algorithms with constant-time access to a uniform random oracle (i.e., a uniform random hash function): - Given an unordered list L of n elements from [n] (possibly with repeated elements), output [n]-L. - Counting satisfying assignments to a given 2CNF, and printing any satisfying assignment to a given 3CNF. Note it is a major open problem to prove a time-space product lower bound of n^{2-o(1)} for the decision version of SAT, or even for the decision problem Majority-SAT. - Printing the truth table of a given CNF formula F with k inputs and n=O(2^k) clauses, with values printed in lexicographical order (i.e., F(0^k), F(0^{k-1}1), ..., F(1^k)). Thus we have a 4^k/poly(k) lower bound in this case. - Evaluating a circuit with n inputs and O(n) outputs. As our lower bounds are based on R-way branching programs, they hold for any reasonable model of computation (e.g. log-word RAMs and multitape Turing machines).
Cite as

Dylan M. McKay and Richard Ryan Williams. Quadratic Time-Space Lower Bounds for Computing Natural Functions with a Random Oracle. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 56:1-56:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{mckay_et_al:LIPIcs.ITCS.2019.56,
  author =	{McKay, Dylan M. and Williams, Richard Ryan},
  title =	{{Quadratic Time-Space Lower Bounds for Computing Natural Functions with a Random Oracle}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{56:1--56:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.56},
  URN =		{urn:nbn:de:0030-drops-101493},
  doi =		{10.4230/LIPIcs.ITCS.2019.56},
  annote =	{Keywords: branching programs, random oracles, time-space tradeoffs, lower bounds, SAT, counting complexity}
}
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