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Showing 1 to 13 of 13 for “"Pseudorandomness"”.
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Algebraic methods in randomness and pseudorandomness
… progress on several questions in randomness and pseudorandomness. The technical ingredients we introduce include: " Multiplicity-enhanced versions of the Schwartz-Zippel lenina and the "polynomial method", extending their applicability to "higher-degree" polynomials. " Conditions for polynomials …
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Algebraic methods in pseudorandomness and circuit complexity
… concerning extractors for algebraic sets, AC⁰-pseudorandomness, the recursive Fourier sampling problem, and VC dimension. We present a new construction of an extractor which works for algebraic sets defined by polynomials over F₂ of substantially higher degree than the previous state-of-the-art …
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Minimum distance of error correcting codes versus encoding complexity, symmetry, and pseudorandomness
We study the minimum distance of binary error correcting codes from the following perspectives: * The problem of deriving bounds on the minimum distance of a code given constraints on the computational complexity of its encoder. * The minimum distance of linear codes that are symmetric in the sense …
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Random and exact structures in combinatorics
… and probability. One central notion, the pseudorandomness-structure dichotomy, has played a key role in additive combinatorics and extremal graph theory. More generally, however, such notions come into play in the study of combinatorial probability and the use of random processes in …
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Better Hardness via Algorithms, and New Forms of Hardness versus Randomness
… of functions that are hard to compute) and pseudorandomness (the procedure that converts randomized algorithms into equivalent deterministic algorithms). In one direction, from the classic works of Nisan-Widgerson and Impagliazzo-Widgerson, we know certain hardness hypothesis (circuit lower …
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Polynomial identity testing of read-once oblivious algebraic branching programs
… this is analogous (in the terminology of boolean pseudorandomness) to a seed-length of lg2 S, which is the seed length of the pseudorandom generators of Nisan [Nis92] and Impagliazzo-Nisan-Wigderson [INW94] for read-once oblivious boolean branching programs. Thus our work can be seen as an …
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Testability of linear-invariant properties
… had significant impact on complexity theory, pseudorandomness, coding theory, computational learning theory, and extremal combinatorics. In the history of the area, a particularly important role has been played by linearinvariant properties, i.e., properties of Boolean functions on the …
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Sparse regularity and relative Szemerédi theorems
… Szemerédi theorem, showing that a much weaker pseudorandomness condition is sufficient. Finally, we give a short simple proof of a multidimensional Szemerédi theorem in the primes, which states that any positive proportion subset of Pd (where P denotes the primes) contains constellations of any …
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Seedless Extractors
… our extractors, we exploit new reductions within pseudorandomness, and unearth new connections to extremal combinatorics, communication complexity, and coding theory. Along the way, we unlock exciting new applications in cryptography, complexity theory, and beyond.
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From Quantum Information to Cosmic Censorship: Emergent Spacetimes and Their Surfaces
… show a connection between event horizons and CFT pseudorandomness, and we construct a new measure of the size of a naked singularity. We conjecture that quantum gravity only forbids macroscopic naked singularities, according to this measure. In the second part, we derive new properties of various …
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Imperfect gaps in Gap-ETH and PCPs
… studied in parallel repetition [21] and pseudorandomness [141. We also investigate the time complexity of approximating perfectly satisfiable instances of 3SAT versus those with imperfect completeness. We show that the Gap-ETH conjecture without perfect completeness is equivalent to …
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Security proofs for the MD6 hash function mode of operation
… resistance, and for keyed hash functions, pseudorandomness. This work presents proofs of security for the mode of operation of the MD6 cryptographic hash function [32] - a candidate for the SHA-3 competition - which differs greatly from the modes of operation of many commonly-used hash …
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Explicit pseudorandom distributions for restricted models of computation
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms