Related papers: Recursed is not Recursive: A Jarring Result
In this paper we use the Recursion Theorem to show the existence of various infinite sequences and sets. Our main result is that there is an increasing sequence e_0, e_1, e_2 .. such that W_{e_n}={e_{n+1}} for every n. Similarly, we prove…
Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…
Reversible computation opens up the possibility of overcoming some of the hardware's current physical limitations. It also offers theoretical insights, as it enriches multiple paradigms and models of computation, and sometimes…
We prove that a particular pushing-blocks puzzle is intractable in 2D, improving an earlier result that established intractability in 3D [OS99]. The puzzle, inspired by the game *PushPush*, consists of unit square blocks on an integer…
Regret Matching+ (RM+) and its variants are important algorithms for solving large-scale games. However, a theoretical understanding of their success in practice is still a mystery. Moreover, recent advances on fast convergence in games are…
Game solving aims to find the optimal strategies for all players and determine the theoretical outcome of a game. However, due to the exponential growth of game trees, many games remain unsolved, even though methods like AlphaZero have…
Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits.…
Recursive filters are treated as linear time-invariant (LTI) systems but they are not: uninitialised, they have an infinite number of outputs for any given input, while if initialised, they are not time-invariant. This short tutorial…
This study introduces "Haunted House" a novel text-based game designed to compare the performance of humans and large language models (LLMs) in model-based reasoning. Players must escape from a house containing nine rooms in a 3x3 grid…
Using the recently introduced universal computing model, called orchestrated machine, that represents computations in a dissipative environment, we consider a new kind of interpretation of Turing's Imitation Game. In addition we raise the…
We show that autoregressive decoding of a transformer-based language model can realize universal computation, without external intervention or modification of the model's weights. Establishing this result requires understanding how a…
We develop a framework for resource efficient compilation of higher-level programs into lower-level reversible circuits. Our main focus is on optimizing the memory footprint of the resulting reversible networks. This is motivated by the…
Conway Checkers is a game played with a checker placed in each square of the lower half of an infinite checkerboard. Pieces move by jumping over an adjacent checker, removing the checker jumped over. Conway showed that it is not possible to…
The relationship between the complexity classes P and NP is a question that has not yet been answered by the Theory of Computation. The existence of a language in NP, proven not to belong to P, is sufficient evidence to establish the…
Neural reasoners such as Tiny Recursive Models (TRMs) solve complex problems by combining neural backbones with specialized inference schemes. Such inference schemes have been a central component of stochastic reasoning systems, where…
Cirquent calculus is a proof system manipulating circuit-style constructs rather than formulas. Using it, this article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic (the…
We construct quantum games from a table of non-factorizable joint probabilities, coupled with a symmetry constraint, requiring symmetrical payoffs between the players. We give the general result for a Nash equilibrium and payoff relations…
I give an analysis of the simplest non-commutative quantum game, which is a gambling game much like Heads or Tails. The quantum gamespace displays strategies which are not interpretable through direct-product strategies of the two players.…
Regret-based algorithms are highly efficient at finding approximate Nash equilibria in sequential games such as poker games. However, most regret-based algorithms, including counterfactual regret minimization (CFR) and its variants, rely on…
A non-deterministic recursion scheme recognizes a language of finite trees. This very expressive model can simulate, among others, higher-order pushdown automata with collapse. We show decidability of the diagonal problem for schemes. This…