The Kolmogorov complexity of random reals

The Kolmogorov complexity of random reals

Kolmogorov Complexity Theory over the Reals

Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and computational complexity theory— in the discrete setting of bits and Turing machines. Over real numbers, on the other hand, the BSS-machine (aka real-RAM) has been established as a major model of computation. This real realm has turned out to exhibit natural counterparts to many notions and resul...

Oscillation in the Initial Segment Complexity of Random Reals

We study oscillation in the prefix-free complexity of initial segments of 1-random reals. For upward oscillations, we prove that P n∈ω 2 −g(n) diverges iff (∃∞n) K(X n) > n+g(n) for every 1-random X ∈ 2ω . For downward oscillations, we characterize the functions g such that (∃∞n) K(X n) < n+g(n) for almost every X ∈ 2ω . The proof of this result uses an improvement of Chaitin’s counting theorem...

the effect of task complexity on lexical complexity and grammatical accuracy of efl learners’ argumentative writing

بر اساس فرضیه شناخت رابینسون (2001 و 2003 و 2005) و مدل ظرفیت توجه محدود اسکهان (1998)، این تحقیق تاثیر پیچیدگی تکلیف را بر پیچیدگی واژگان و صحت گرامری نوشتار مباحثه ای 60 نفر از دانشجویان زبان انگلیسی بررسی کرد. میزان پیچیدگی تکلیف از طریق فاکتورهای پراکندگی-منابع تعیین شد. همه ی شرکت کنندگان به صورت نیمه تصادفی به یکی از سه گروه: (1) گروه موضوع، (2) گروه موضوع + اندیشه و (3) گروه موضوع + اندی...

On Kolmogorov Complexity of Random Very Long Braided Words

Any positive word comprised of random sequence of tokens from a finite alphabet can be reduced (without change of length) using an appropriate size Braid group relationships. Surprisingly the Braid relationships dramatically reduce the Kolmogorov Complexity of the original random word and do so in distinct ‘bands’ of (rate of change) values with gaps in between. Distribution of these bands are ...