Related papers: Locally Finite Knowledge Structures
It has been suggested, on the one hand, that quantum states are just states of knowledge; and, on the other, that quantum theory is merely a theory of correlations. These suggestions are confronted with problems about the nature of…
In this article, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of two hat colors and a countably infinite number of players.…
In imperfect information games (e.g. Bridge, Skat, Poker), one of the fundamental considerations is to infer the missing information while at the same time avoiding the disclosure of private information. Disregarding the issue of protecting…
We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…
We give a new characterization of $\mathsf{NL}$ as the class of languages whose members have certificates that can be verified with small error in polynomial time by finite state machines that use a constant number of random bits, as…
Consider a game where Alice generates an integer and Bob wins if he can factor that integer. Traditional game theory tells us that Bob will always win this game even though in practice Alice will win given our usual assumptions about the…
The uncertainty principle may be considered as giving rise to the notion of incompatibility of observables. A pack of quantum measurements that cannot be measured simultaneously is said to form a set of incompatible measurements. Every set…
We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.
The Perfectly Transparent Equilibrium is algorithmically defined, for any game in normal form with perfect information and no ties, as the iterated deletion of non-individually-rational strategy profiles until at most one remains. In this…
Equilibrium notions for games with unawareness in the literature cannot be interpreted as steady-states of a learning process because players may discover novel actions during play. In this sense, many games with unawareness are…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
The rationalizability concept was introduced in \cite{Ber84} and \cite{Pea84} to assess what can be inferred by rational players in a non-cooperative game in the presence of common knowledge. However, this notion can be defined in a number…
Reasoning about knowledge seems to play a fundamental role in distributed systems. Indeed, such reasoning is a central part of the informal intuitive arguments used in the design of distributed protocols. Communication in a distributed…
The fixed template Promise Constraint Satisfaction Problem (PCSP) is a recently proposed significant generalization of the fixed template CSP, which includes approximation variants of satisfiability and graph coloring problems. All the…
Conscious states (states that there is something it is like to be in) seem both rich or full of detail, and ineffable or hard to fully describe or recall. The problem of ineffability, in particular, is a longstanding issue in philosophy…
Let us consider two companies A and B. Both of them are interested in buying a set of some goods. The company A is a big corporation and it knows the actual value of the good on the market and is able to observe the previous values of them.…
This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of…
Federated learning is a setting where agents, each with access to their own data source, combine models from local data to create a global model. If agents are drawing their data from different distributions, though, federated learning…
There are two reasons why uncertainty may not be adequately described by Probability Theory. The first one is due to unique or nearly-unique events, that either never realized or occurred too seldom for frequencies to be reliably measured.…
The Special Theory of Relativity and Quantum Mechanics merge in the key principle of Quantum Field Theory, the Principle of Locality. We review some examples of its ``unreasonable effectiveness'' (which shows up best in the formulation of…