相关论文: Logic Blog 2020
The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, \textit{Complexity of finite semigroups}, Annals of Mathematics (2) \textbf{88} (1968), 128--160, motivated by the…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
Relativizing computations of Turing machines to an oracle is a central concept in the theory of computation, both in complexity theory and in computability theory(!). Inspired by lowness notions from computability theory, Allender…
We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and…
This volume contains a selection of papers presented at Linearity&TLLA 2020, namely the Second Joint International Workshop on Linearity & Trends in Linear Logic and Applications, held on June 29-30, 2020 online. (The workshop was supposed…
If $(T_t)$ is a semigroup of Markov operators on an $L^1$-space that admits a non-trivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as $t \to \infty$. In this article we…
We develop a semigroup approach to representation theory for pro-Lie groups satisfying suitable amenability conditions. As an application of our approach, we establish a one-to-one correspondence between equivalence classes of unitary…
In recent years, much work has been done to measure and compare the complexity of orbit equivalence relations, especially for certain classes of Polish groups. We start by introducing some language to organize this previous work, namely the…
Coalition Logic is primarily concerned with what coalitions can achieve, whereas what coalitions cannot achieve -- their \emph{inability} -- has received comparatively little explicit attention. This asymmetry matters in artificial…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
Group polarization, the phenomenon where individuals become more extreme after interacting, has been gaining attention, especially with the rise of social media shaping people's opinions. Recent interest has emerged in formal reasoning…
We prove a characterization of the amenability of countable Borel equivalence relations in terms of the uniform Liouville property for group actions on their classes. Furthermore, inspired by a well-known amenability criterion for locally…
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…
Algebras of Logic deal with some algebraic structures, often bounded lattices, considered as models of certain logics, including logic as a domain of order theory. There are well known their importance and applications in social life to…
Finite group extensions offer a natural language to quantum computing. In a nutshell, one roughly describes the action of a quantum computer as consisting of two finite groups of gates: error gates from the general Pauli group P and…
The history of computability theory and and the history of analysis are surprisingly intertwined since the beginning of the twentieth century. For one, \'Emil Borel discussed his ideas on computable real number functions in his introduction…
Machine learning models have become more and more complex in order to better approximate complex functions. Although fruitful in many domains, the added complexity has come at the cost of model interpretability. The once popular k-nearest…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
In this paper we address the question: How many pairwise non-isomorphic extremely amenable groups are there which are separable metrizable or even Polish? We show that there are continuum many such groups. In fact we construct continuum…
Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth. This approach was initiated very recently in "Introduction to computability logic" (Annals of Pure and…