Related papers: Orbit automata as a new tool to attack the order p…
The transition structure of an automaton can be used to create a natural topology to the set of states of an automaton, generating, this way, a topological space. Probabilistic automata can also be modeled in terms of measure theory. A…
The notion of an automaton over a changing alphabet $X=(X_i)_{i\geq 1}$ is used to define and study automorphism groups of the tree $X^*$ of finite words over $X$. The concept of bi-reversibility for Mealy-type automata is extended to…
We study natural linear representations of self-similar groups over finite fields. In particular, we show that if the group is generated by a finite automaton, then obtained matrices are automatic. This shows a new relation between two…
A new design of an AI assistant that has become increasingly popular is that of an "aggregated assistant" -- realized as an orchestrated composition of several individual skills or agents that can each perform atomic tasks. In this paper,…
First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, however, have yet to realize the same utility. In this paper I…
We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of…
Let G be a Lie group, $g = Lie(G)$ - its Lie algebra, $g*$ - the dual vector space and $\widehat G$ - the set of equivalence classes of unitary irreducible representations of $G$. The orbit method [1] establishes a correspondence between…
We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.
We describe a simple algorithm for classifying orbits into orbit families. This algorithm works by finding patterns in the sign changes of the principal coordinates. Orbits in the logarithmic potential are studied as an application; we…
This paper proposes a distributed on-orbit spacecraft assembly algorithm, where future spacecraft can assemble modules with different functions on orbit to form a spacecraft structure with specific functions. This form of spacecraft…
We give a survey of various recent developments in orbit equivalence and measured group theory. This subject aims at studying infinite countable groups through their measure preserving actions.
Trained humans exhibit highly agile spatial skills, enabling them to operate vehicles with complex dynamics in demanding tasks and conditions. Prior work shows that humans achieve this performance by using strategies such as satisficing,…
One of the major open problems in automata and logic is the following: is there an algorithm which inputs a regular tree language and decides if the language can be defined in first-order logic? The goal of this paper is to present this…
Path planning through complex obstacle spaces is a fundamental requirement of many mobile robot applications. Recently a rapid convergence path planning algorithm, Batch Informed Trees (BIT*), was introduced. This work serves as a concise…
A finitary automaton group is a group generated by an invertible, deterministic finite-state letter-to-letter transducer whose only cycles are self-loops at an identity state. We show that, for this presentation of finite groups, the…
In this chapter, we propose a novel approach for solving the coordination of a fleet of mobile robots, which consists of finding a set of collision-free trajectories for individual robots in the fleet. This problem is studied for several…
We extend the notion of activity for automaton semigroups and monoids introduced by Bartholdi, Godin, Klimann and Picantin to a more general setting. Their activity notion was already a generalization of Sidki's activity hierarchy for…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
A mimic computing oriented automaton can directly portray the behaviors of a mimic computing system. In this paper, we investigate the following theoretical problems on this type of automata: operational semantics and computational ability.…
Evolution by natural selection, which is one of the most compelling themes of modern science, brought forth evolutionary algorithms and evolutionary computation, applying mechanisms of evolution in nature to various problems solved by…