We give a simpler proof using automata theory of a recent result of Kapovich, Weidmann and Myasnikov according to which socalled benign graphs of groups preserve decidability of the generalized word problem. These include graphs of groups in which edge groups are polycyclic-by-finite and vertex groups are either locally quasiconvex hyperbolic or polycyclic-by-finite and so in particular chordal...

The simulation of pedestrian dynamics is a consolidated area of application for cellular automata based models: successful case studies can be found in the literature and off-the-shelf simulators are commonly employed by end-users, decision makers and consultancy companies. These models, however, generally consider individuals, their interactions with the environment and among themselves, but t...

We consider Turing machines as actions over configurations in ΣZ d which only change them locally around a marked position that can move and carry a particular state. In this setting we study the monoid of Turing machines and the group of reversible Turing machines. We also study two natural subgroups, namely the group of finite-state automata, which generalizes the topological full groups stud...

We present a general coalgebraic setting in which we define finite and infinite behaviour with B\"uchi acceptance condition for systems whose type is monad. The first part of the paper devoted to presenting construction monad suitable modelling (in)finite behaviour. second focuses on concepts (coalgebraic) automaton its ($\omega$-) end Kleene-type theorems regular input. framework instantiated ...

in this paper an application of cellular learning automata (cla) to vlsi placement is presented. the cla, which is introduced for the first time in this paper, is different from standard cellular learning automata in two respects. it has input and the cell neighborhood varies during the operation of cla. the proposed cla based algorithm for vlsi placement is tested on number of placement proble...

Toric ideals to hierarchical models are invariant under the action of a product symmetric groups. Taking number factors, say m, into account, we introduce and study filtrations their equivariant Hilbert series. We present condition that guarantees series is rational function in m+1 variables with coefficients. Furthermore give explicit formulas for functions coefficients field an algorithm dete...

We explore the dual version of Gottschalk’s conjecture recently introduced by Capobianco, Kari, and Taati, notion surjunctivity in general. show that surjunctive groups satisfy Kaplansky’s direct finiteness for all fields positive characteristic. By quantifying notions injectivity post-surjectivity cellular automata, we image full topological shift under an injective automaton is a subshift fin...

Clustering, an unsupervised machine learning technique, plays a crucial role in partitioning unlabeled data into meaningful groups. K-means, known for its simplicity, has gained popularity as clustering method. However, both K-means and the LAC algorithm, which utilize automata, are sensitive to selection of initial points. To overcome this limitation, we propose enhanced algorithm based on K-H...