Related papers: Kolmogorov complexity as a combinatorial tool
Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…
Chaitin's incompleteness theorem states that sufficiently rich formal systems cannot prove lower bounds on Kolmogorov complexity. In this paper we extend this theorem by showing theories that prove the Kolmogorov complexity of a large (but…
This paper introduces a simple type system for combinatory logic in which combinators have at most one type, whose polymorphism is revealed by application. The combinatory types exactly describe the structure of their values, which may be…
We briefly show how the use of topological spaces and $\sigma$-algebras in physics can be rederived and understood as the fundamental requirement of experimental verifiability. We will see that a set of experimentally distinguishable…
When agents are acting together, they may need a simple mechanism to decide on joint actions. One possibility is to have the agents express their preferences in the form of a ballot and use a voting rule to decide the winning action(s).…
In this paper we survey the computational time complexity of assorted simple stochastic game problems, and we give an overview of the best known algorithms associated with each problem.
Information entropy is used to summarize transcriptome data, but ignoring zero count data contained them. Ignoring zero count data causes loss of information and sometimes it was difficult to distinguish between multiple transcriptomes.…
This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct…
We study in which way Kolmogorov complexity and instance complexity affect properties of r.e. sets. We show that the well-known 2log n upper bound on the Kolmogorov complexity of initial segments of r.e.\ sets is optimal and characterize…
This work presents a study of Kolmogorov complexity for general quantum states from the perspective of deterministic-control quantum Turing Machines (dcq-TM). We extend the dcq-TM model to incorporate mixed state inputs and outputs, and…
Black-box complexity is a complexity theoretic measure for how difficult a problem is to be optimized by a general purpose optimization algorithm. It is thus one of the few means trying to understand which problems are tractable for genetic…
Solovay proved that there exists a computable upper bound f of the prefix-free Kolmogorov complexity function K such that f (x) = K(x) for infinitely many x. In this paper, we consider the class of computable functions f such that K(x) <= f…
Computability logic (CoL) is a formal theory of interactive computation. It understands computational problems as games played by two players: a machine and its environment, uses logical formalism to describe valid principles of…
Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables,…
Two-party one-way quantum communication has been extensively studied in the recent literature. We target the size of minimal information that is necessary for a feasible party to finish a given combinatorial task, such as distinction of…
We study the computational complexity of an important property of simple, regular and weighted games, which is decisiveness. We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness…
We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
Ball, Liu, Mazor and Pass proved that the existence of key-agreement protocols is equivalent to the hardness of a certain problem about interactive Kolmogorov complexity. We generalize the statement and give a short proof of the difficult…