Live briefing
Everything about Algorithmically random sequence
Binary sequence
Intuitively, an algorithmically random sequence is a sequence of binary digits that appears random to any algorithm running on a universal Turing machine. The notion can be applied analogously to sequences on any finite alphabet. Random sequences are key objects of study in algorithmic information theory. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Algorithmically random sequenceA 5-minute orientation
- Skim a recent paper: Aptamers from random sequence space: Accomplishments, gaps and future considerationsInfluential work since 2022
- Pick up a classic book: Random sums and branching stochastic processesThe most-reprinted book on the subject
- Read the landmark paper: Functional proteins from a random-sequence libraryCited 486 times
- Go sideways: K-trivial setA closely related topic
- Go sideways: Random sequenceA closely related topic
📖 Definitions
Noun A sequence of identically distributed random variables.
🏆 Landmark papers (most cited)
Functional proteins from a random-sequence library
Random sequence generation by cellular automata
On the concept of a random sequence
NUCLEIC ACID SEQUENCE PHYLOGENY AND RANDOM OUTGROUPS
Random graphs with a given degree sequence
Sequence-Corrected 15N "Random Coil" Chemical Shifts
Cloning of random-sequence oligodeoxynucleotides
Some Aspects of the Random Sequence
🆕 Influential since 2022
Aptamers from random sequence space: Accomplishments, gaps and future considerations
Toehold-Mediated Strand Displacement in Random Sequence Pools
Experimental characterization of de novo proteins and their unevolved random-sequence counterparts
Combined Pseudo-Random Sequence Generator for Cybersecurity
Sequence Design of Random Heteropolymers as Protein Mimics
📚 Books worth reading
Random sums and branching stochastic processesIbrahim Rahimov · 1995
Stationary sequences and random fieldsMurray Rosenblatt · 1985- 📕Statistical properties of fast Fourier transform coefficients computed from real-valued, covariance-stationary, periodic random sequencesLeon E. Borgman · 1973
Limit theory for mixing dependent random variablesZhengyan Lin, Lin Zhengyan · 1996
Independent and stationary sequences of random variablesI. A. Ibragimov · 1971- 📕On the effect of a mixing table on a stationary random sequenceAarni Perko · 1971
Neural network identification of keystream generatorsJeffery J. Leader · 1993- 📕Raspoznavanie sluchaĭnykh posledovatelʹnosteĭ · 1978
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- K-trivial set In mathematics, a set of natural numbers is called a K-trivial set if its initial segments viewed as binary strings are easy to describe: the prefix-free…
- Random sequence The concept of a random sequence is essential in probability theory and statistics. The concept generally relies on the notion of a sequence of random…
- Chaitin's constant In the computer science subfield of algorithmic information theory, a Chaitin constant, Chaitin omega number, or halting probability is a real number that…
- Algorithmic information theory Algorithmic information theory (AIT) is a branch of theoretical computer science that concerns itself with the relationship between computation and information…
- Effective dimension In mathematics, effective dimension is a modification of Hausdorff dimension and other fractal dimensions that places it in a computability theory setting…
- Resource-bounded measure Lutz's resource-bounded measure is a generalisation of Lebesgue measure to complexity classes. It was originally developed by Jack Lutz. Just as Lebesgue…
- Algorithmic probability In algorithmic information theory, algorithmic probability, also known as Solomonoff probability, is a mathematical method of assigning a prior probability…
- Universality probability Universality probability is an abstruse probability measure in computational complexity theory that concerns universal Turing machines. A Turing machine…