Complexity and Randomness
ON INITIAL SEGMENT COMPLEXITY AND DEGREES OF RANDOMNESS
... higher initial segment prefix-free complexity than X (up to a constant). Formally, (∀n) K(X n) ≤ K(Y n) + O(1). The induced partial order is called the K- degrees. Define the C-degrees in the same way. This brings ...
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Complexity leads to randomness in chaotic systems
... Pseudorandom or chaotic numbers are nowadays used in many areas of contemporary technology such as modern communication systems and engineering applications. Efficient Chaotic Pseudo Random Number Generators (CPRNG) have ...
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Entanglement, quantum randomness, and complexity beyond scrambling
... Abstract: Scrambling is a process by which the state of a quantum system is effec- tively randomized due to the global entanglement that “hides” initially localized quantum information. Closely related notions include ...
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A Rigorous Take on Randomness: Defining 1-Randomness using Complexity, Measure Theory, and Martingales
... 5 The Equivalence of our Approaches to Randomness So far, we have characterized randomness using prefix-free complexity, Martin-L¨ of tests, and mar- tingales. The first roughly said that random ...
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A Note on the Communication Complexity of Multiparty Computation in the Correlated Randomness Model
... correlated randomness model, which states (informally) that they evaluate the function in a “gate-by-gate” fashion, and require communication for every multiplication ...communication complexity of secure ...
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Structure and Randomness in Complexity Theory and Additive Combinatorics
... Theorem 2.3.3. For every ε > 0 it holds that M(ε) ≥ twr(b1/16εc). 2.3.2 Explicit construction of pseudorandom objects One of the greatest questions in computer science is whether randomness helps speed up ...
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CiteSeerX — The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms
... With this definition, all random sequences without exception satisfy all conceivable effectively verifiable laws of probability theory, since for any such law we can arrange a test that [r] ...
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Randomness and intractability in Kolmogorov complexity
... Kolmogorov complexity investigated in other works (see ...allowing randomness in the computation is somewhat counter-intuitive, given that Kolmogorov complexity tries to capture how far from random ...
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Randomness complexity as a family feature of rolling bearings’ degradation
... the complexity can be traced back to 1940s when Shannon first developed information theory and proposed Shannon entropy ...Kolmogorov complexity (KC) is proposed by Kolmogorov in 1965, which can measure ...
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A Note on 'Further Improving Efficiency of Higher-Order Masking Scheme by Decreasing Randomness Complexity'
... The bias we exhibit is quite small, but exists, and therefore contradicts the claims of perfect probing security made by the original authors. 4. Analysis, Discussion and Conclusions In this short note, we have exhibited ...
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On the randomness that generates biased samples: The limited randomness approach
... time complexity of Step is equal to ...no randomness is inserted into the scheme, and the position of the cursor becomes deterministic for all the future time ...
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Algorithmic Randomness
... algorithmic randomness in the Cantor space C of the infinite binary ...algorithmic randomness concept one specifies a set of elements of C, each of which is assigned the property of being ...of ...
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Randomness and Computability
... In Part I of this thesis we investigate the relationship between randomness and computability for finite strings. In Chapter 2 we will see that there are many different types of Kolmogorov complexities. Two of ...
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Randomness and Solovay degrees
... Solovay reducibility Our central notion is Solovay reducibility ≤ S . Informally, for left-r.e. reals α, β , α ≤ S β expresses that α is no harder to approximate from the left than β . A formal definition will be given ...
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Randomness Extractors -- An Exposition
... 2016 Randomness Extractors – An Exposition Wei Dai Abstract. Randomness is crucial to computer science, both in theory and applica- ...In complexity theory, randomness augments computers to ...
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Algorithmic randomness and analysis
... We begin with the effective dimension of Euclidean points. We show that the techniques from algorithmic information can be used successfully to study problems in fractal geometry. Specifically, we investigate the ...
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On the Randomness of the Editing Generator
... linear complexity, symbol distribution and security analysis are discussed in the same ar- ...the randomness results of the edited sequence for general cases, we do not restrict the base sequence and the ...
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True-Randomness and Pseudo-Randomness in Ring Oscillator-Based True Random Number Generators
... the complexity of the detection circuitry would rise with the square of number of rings and it would thus limit the practical use of the generator, which is already penalized by the fact that the number of rings ...
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CiteSeerX — Hardness vs. randomness
... This construction reveals an equivalence between the problem of proving lower bounds and the problem of generating good pseudorandom sequences. Our construction has many consequences. The most direct one is that ...
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Linear Transformations for Randomness Extraction
... Index Terms—Randomness Extraction, Linear Transforma- tions, Sparse Random Matrices. I. I NTRODUCTION R ANDOMNESS plays an important role in many fields, including complexity theory, cryptography, ...
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