Average-case complexity

About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.

Algorithmic Specified Complexity

Abstract: Engineers like to think that they produce something different from that of a chaotic system. The Eiffel tower is fundamentally different from the same components lying in a heap on the ground. Mt. Rushmore is fundamentally different from a random mountainside. But engineers lack a good method for quantifying this idea. This has led some to reject the idea that engineered or designed systems can be detected. Various methods have been proposed, each of which has various faults. Some have trouble distinguishing noise from data, some are subjective, etc. For this study, conditional Kolmogorov complexity is used to measure the degree of specification of an object. The Kolmogorov complexity of an object is the length of the shortest computer program required to describe that object. Conditional Kolmogorov complexity is Kolmogorov complexity with access to a context. The program can extract information from the context in a variety of ways allowing more compression. The more compressible an object is, the greater the evidence that the object is specified. Random noise is incompressible, and so compression indicates that the object is not simply random noise. This model is intended to launch further dialog on use of conditional Kolmogorov complexity in the measurement of specified complexity.

A statistical test for stream ciphers based on the maximum order complexity

Abstract: The maximum order complexity determines the shortest feedback shift register which can generate a given sequence utilising a memoryless, possibly non-linear, feedback function. The maximum order complexity of a sequence is a potentially useful measure of the randomness of 8 sequence. In this paper a statistical test based on the maximum order complexity is proposed. The proposed test requires that the distribution of the maximum order complexity of a random sequence of arbitrary length is known. Erdmann and Murphy (1997) derived an expression which approximates the distribution of the maximum order complexity. Evaluating this expression is computationally expensive and an alternative approximation to the distribution of the maximum order complexity is proposed. The alternative approximation is then used to construct a computationally efficient statistical test which may be used to evaluate the randomness of a sequence. The proposed test is specifically concerned with binary sequences and the distribution of the maximum order complexity of binary sequences.

A note on blum static complexity measures

Abstract: Dual complexity measures have been developed by Burgin, under the influence of the axiomatic system proposed by Blum in [3]. The concept of dual complexity measure is a generalization of Kolmogorov/Chaitin complexity, also known as algorithmic or static complexity. In this paper we continue this effort by extending some of the well known results for plain and prefix-free complexities to the general case of Blum universal static complexity. We also extend some results obtained by Calude in [9] to a larger class of computable measures, proving that transducer complexity is a dual (Blum static) complexity measure.