Related papers: Game interpretation of Kolmogorov complexity
We consolidate two widely believed conjectures about tautologies -- no optimal proof system exists, and most require superpolynomial size proofs in any system -- into a $p$-isomorphism-invariant condition satisfied by all paddable…
The class of algorithmically computable simple games (i) includes the class of games that have finite carriers and (ii) is included in the class of games that have finite winning coalitions. This paper characterizes computable games,…
Consider QBF, the Quantified Boolean Formula problem, as a combinatorial game ruleset. The problem is rephrased as determining the winner of the game where two opposing players take turns assigning values to boolean variables. In this…
Faraday complexity describes whether a spectropolarimetric observation has simple or complex magnetic structure. Quickly determining the Faraday complexity of a spectropolarimetric observation is important for processing large, polarised…
Coalitional games are mathematical models suited to analyze scenarios where players can collaborate by forming coalitions in order to obtain higher worths than by acting in isolation. A fundamental problem for coalitional games is to single…
We consider one-round games between a classical verifier and two provers who share entanglement. We show that when the constraints enforced by the verifier are `unique' constraints (i.e., permutations), the value of the game can be well…
Is the universe computable? If so, it may be much cheaper in terms of information requirements to compute all computable universes instead of just ours. I apply basic concepts of Kolmogorov complexity theory to the set of possible…
Coalitional voting games appear in different forms in multi-agent systems, social choice and threshold logic. In this paper, the complexity of comparison of influence between players in coalitional voting games is characterized. The…
Kolmogorov complexity is the length of the ultimately compressed version of a file (that is, anything which can be put in a computer). Formally, it is the length of a shortest program from which the file can be reconstructed. We discuss the…
Value methods for solving stochastic games with partial observability model the uncertainty about states of the game as a probability distribution over possible states. The dimension of this belief space is the number of states. For many…
We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation selected according to internal random coins. We describe several problems that are impossible to solve classically but can…
The Bodirsky-Pinsker conjecture asserts a P vs. NP-complete dichotomy for the computational complexity of Constraint Satisfaction Problems (CSPs) of first-order reducts of finitely bounded homogeneous structures. Prominently, two structures…
It is well known that many theorems in recursion theory can be "relativized". This means that they remain true if partial recursive functions are replaced by functions that are partial recursive relative to some fixed oracle set. Uspensky…
We study a robust Dynkin game over a set of mutually singular probabilities. We first prove that for the conservative player of the game, her lower and upper value processes coincide (i.e. She has a value process $V $ in the game). Such a…
The paper is devoted to inverse Stackelberg games with many players. We consider both static and differential games. The main assumption of the paper is the compactness of the strategy sets. We obtain the characterization of inverse…
We show that any cooperative game can be represented by an assignment of costly facilities to players, in which it is intuitively obvious how to allocate the total cost in an equitable manner. This equitable solution turns out to be the…
Algorithmic statistics studies explanations of observed data that are good in the algorithmic sense: an explanation should be simple i.e. should have small Kolmogorov complexity and capture all the algorithmically discoverable regularities…
Hyperproperties generalize traditional trace properties by relating multiple execution traces rather than reasoning about individual runs in isolation. They provide a unified way to express important requirements such as information flow…
Online game playing algorithms produce high-quality strategies with a fraction of memory and computation required by their offline alternatives. Continual Resolving (CR) is a recent theoretically sound approach to online game playing that…
A growing number of machine learning architectures, such as Generative Adversarial Networks, rely on the design of games which implement a desired functionality via a Nash equilibrium. In practice these games have an implicit complexity…