Related papers: Morphisms on infinite alphabets, countable states …
We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an…
We construct a projective variety with discrete, non-finitely generated automorphism group. As an application, we show that there exists a complex projective variety with infinitely many non-isomorphic real forms.
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…
In the classic problem of sequence prediction, a predictor receives a sequence of values from an emitter and tries to guess the next value before it appears. The predictor masters the emitter if there is a point after which all of the…
Words are sequences of letters over a finite alphabet. We study two intimately related topics for this object: quasi-randomness and limit theory. With respect to the first topic we investigate the notion of uniform distribution of letters…
Probabilistic B\"uchi Automata (PBA) are randomized, finite state automata that process input strings of infinite length. Based on the threshold chosen for the acceptance probability, different classes of languages can be defined. In this…
The paper explains the connection between topological theories for one-manifolds with defects and values in the Boolean semiring and automata and their generalizations. Finite state automata are closely related to regular languages. To each…
Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…
Any finite state automaton gives rise to a Boolean one-dimensional TQFT with defects and inner endpoints of cobordisms. This paper extends the correspondence to Boolean TQFTs where defects accumulate toward inner endpoints, relating such…
Uniformly finite homology is a coarse invariant for metric spaces; in particular, it is a quasi-isometry invariant for finitely generated groups. In this article, we study uniformly finite homology of finitely generated amenable groups and…
We introduce jacobian graphs, which are explicit families of regular graphs that are spectrally indistinguishable from random graphs, but whose local structure is very different from that of random graphs. The construction relies on the…
We establish sufficient conditions for perfect simulation of chains of infinite order on a countable alphabet. The new assumption, localized continuity, is formalized with the help of the notion of context trees, and includes the…
We show that if the automorphism group of a projective variety is torsion, then it is finite. Motivated by Lang's conjecture on rational points of hyperbolic varieties, we use this to prove that a projective variety with only finitely many…
The classification of separable operator spaces and systems is commonly believed to be intractable. We analyze this belief from the point of view of Borel complexity theory. On one hand we confirm that the classification problems for…
Given an order of the underlying alphabet we can lift it to the states of a finite deterministic automaton: to compare states we use the order of the strings reaching them. When the order on strings is the co-lexicographic one \emph{and}…
Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.
Fixed points ${\bf u}=\varphi({\bf u})$ of marked and primitive morphisms $\varphi$ over arbitrary alphabet are considered. We show that if ${\bf u}$ is palindromic, i.e., its language contains infinitely many palindromes, then some power…
Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs.…
We investigate (2,1):1 structures, which consist of a countable set $A$ together with a function $f: A \to A$ such that for every element $x$ in $A$, $f$ maps either exactly one element or exactly two elements of $A$ to $x$. These…