Related papers: Game interpretation of Kolmogorov complexity

We illustrate how one can use basic combinatorial theory and computer programming technique (Python) to analyze the combinatorial game: Mahjong. The results confirm some folklore concerning the game, and expose some unexpected results.…

We introduce orderings between total functions f,g: N -> N which refine the pointwise "up to a constant" ordering <=cte and also insure that f(x) is often much less thang(x). With such orderings, we prove a strong hierarchy theorem for…

If no optimal propositional proof system exists, we (and independently Pudl\'ak) prove that ruling out length $t$ proofs of any unprovable sentence is hard. This mapping from unprovable to hard-to-prove sentences powerfully translates facts…

In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C^*-algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the…

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.

In the mentioned paper we presented results of the estimation of Kolmogorov complexity of sequences of random numbers generated in a famous Bell's experiment, aimed to study the security of QKD. We focused on series of time differences…

We give a tighter lifting theorem for security games in the quantum random oracle model. At the core of our main result lies a novel measure-and-reprogram framework that we call coherent reprogramming. This framework gives a tighter lifting…

We prove a Kolmogorov complexity variant of the birthday paradox. Sufficiently sized random subsets of strings are guaranteed to have two members x and y with low K(x/y). To prove this, we first show that the minimum conditional Kolmogorov…

Is it possible to find a shortest description for a binary string? The well-known answer is "no, Kolmogorov complexity is not computable." Faced with this barrier, one might instead seek a short list of candidates which includes a laconic…

Link prediction in graphs is an important task in the fields of network science and machine learning. We investigate a flexible means of regularization for link prediction based on an approximation of the Kolmogorov complexity of graphs…

We suggest necessary conditions of soficness of multidimensional shifts formulated in termsof resource-bounded Kolmogorov complexity. Using this technique we provide examples ofeffective and non-sofic shifts on $\mathbb{Z}^2$ with very low…

Diverse applications of Kolmogorov complexity to learning [CIKK16], circuit complexity [OPS19], cryptography [LP20], average-case complexity [Hir21], and proof search [Kra22] have been discovered in recent years. Since the running time of…

Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…

We introduce a natural Turing-complete extension of first-order logic FO. The extension adds two novel features to FO. The first one of these is the capacity to add new points to models and new tuples to relations. The second one is the…

We consider the computational complexity of the question whether a certain strategy can be removed from a game by means of iterated elimination of dominated strategies. In particular, we study the influence of different definitions of…

With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…

Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural…

An extractor is a function that receives some randomness and either "improves" it or produces "new" randomness. There are statistical and algorithmical specifications of this notion. We study an algorithmical one called Kolmogorov…

The multitime probability distributions obtained by repeatedly probing a quantum system via the measurement of an observable generally violate Kolmogorov's consistency property. Therefore, one cannot interpret such distributions as the…

We provide another proof to the EL Theorem. We show the tradeoff between compressibility of codebooks and their communication capacity. A resource bounded version of the EL Theorem is proven. This is used to prove three instances of…