Related papers: Plane-Walking Automata
Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered…
We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the…
This article studies the complexity of the word problem in groups of automorphisms of subshifts. We show in particular that for any Turing degree, there exists a subshift whose automorphism group contains a subgroup whose word problem has…
We define sets of coulourings of the infinite discrete plane using monadic second order (MSO) formulas. We determine the complexity of deciding whether such a formula defines a subshift, parametrized on the quantifier alternation complexity…
In low dimensional topology, we have some invariants defined by using solutions of some nonlinear elliptic operators. The invariants could be understood as Euler class or degree in the ordinary cohomology, in infinite dimensional setting.…
The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language…
Transformers have demonstrated remarkable capabilities in multi-step reasoning tasks. However, understandings of the underlying mechanisms by which they acquire these abilities through training remain limited, particularly from a…
This article conducts a large dimensional study of a simple yet quite versatile classification model, encompassing at once multi-task and semi-supervised learning, and taking into account uncertain labeling. Using tools from random matrix…
For a subshift over a finite alphabet, a measure of the complexity of the system is obtained by counting the number of nonempty cylinder sets of length $n$. When this complexity grows exponentially, the automorphism group has been shown to…
We start with comparisons of hierarchies in Biology and relate it to Quan- tum Field Theories. Thereby we discover many similarities and translate them into rich mathematical correspondences. The basic connection goes via scale…
Combining ideas from distributed algorithms and alternating automata, we introduce a new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order logic. By restricting…
This paper seeks to build on the extensive connections that have arisen between automata theory, combinatorics on words, fractal geometry, and model theory. Results in this paper establish a characterization for the behavior of the fractal…
Deterministic one-way time-bounded multi-counter automata are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the…
We study trees where each successor set is equipped with some additional structure. We introduce a family of automaton models for such trees and prove their equivalence to certain fixed-point logics. As a consequence we obtain…
We study the relation between the standard two-way automata and more powerful devices, namely, two-way finite automata with an additional "pebble" movable along the input tape. Similarly as in the case of the classical two-way machines, it…
In this paper we study finite higher-dimensional automata (HDAs) from the logical point of view. Languages of HDAs are sets of finite bounded-width interval pomsets with interfaces (iiPoms<=k) closed under order extension. We prove that…
It is known that the alternation hierarchy of least and greatest fixpoint operators in the mu-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of…
We study the Monadic Second Order (MSO) Hierarchy over infinite pictures, that is tilings. We give a characterization of existential MSO in terms of tilings and projections of tilings. Conversely, we characterise logic fragments…
This chapter presents some of the links between automata theory and symbolic dynamics. The emphasis is on two particular points. The first one is the interplay between some particular classes of automata, such as local automata and results…
We introduce a new type of nonuniform two--way automaton that can use a different transition function for each tape square. We also enhance this model by allowing to shuffle the given input at the beginning of the computation. Then we…