Related papers: Solitons in 3-State Mealy Automata
We introduce the notion of multipass automata as a generalization of pushdown automata and study the classes of languages accepted by such machines. The class of languages accepted by deterministic multipass automata is exactly the Boolean…
We provide a categorical notion called uncertain bisimilarity, which allows to reason about bisimilarity in combination with a lack of knowledge about the involved systems. Such uncertainty arises naturally in automata learning algorithms,…
An L operator is presented related to an infinite dimensional limit of the fusion R matrices for U_q(A^{(1)}_{n-1}) and U_q(D^{(1)}_n). It is factorized into the local propagation operators which quantize the deterministic dynamics of…
Quantum and classical integrable systems share common mathematical structures, and the phenomena appearing in them are interrelated. Solitons, which universally appear in classical integrable systems, also appear in quantum integrable…
A general family of $D$-dimensional, $K$-state cellular automata is proposed where the update rule is sequentially applied in each dimension. This includes the Biham--Middleton--Levine traffic model, which is a 2D cellular automaton with 3…
Solitons in general are configurations of extended fields which move like isolated particles. Vector bright solitons can occur in a two-component self-attractive Bose-Einstein condensate. If the components of the condensate have different…
By means of variational methods and systematic numerical analysis, we demonstrate the existence of stable solitons in three-dimensional (3D) free space, in the context of binary atomic condensates combining contact self-attraction and…
A solvable vertex model in ferromagnetic regime gives rise to a soliton cellular automaton which is a discrete dynamical system in which site variables take on values in a finite set. We study the scattering of a class of soliton cellular…
We extend the usual definition of cellular automaton on a group in order to deal with a new kind of cellular automata, like cellular automata in the hyperbolic plane and we explore some properties of these cellular automata. This definition…
Multi-valued logics have a long tradition in the literature on system verification, including run-time verification. However, comparatively fewer model-checking tools have been developed for multi-valued specification languages. We present…
We consider a class of finite state three-tape transducers which models the operation of shuffling and splitting words. We present them as automata over the so-called Shuffling Monoid. These automata can be seen as either shufflers or…
A deautonomized version of the two-dimensional Toda lattice equation is presented. Its ultra-discrete analogue and soliton solutions are also discussed.
Classification of groups generated by 3-state automata over a 2-letter alphabet started in the first paper (see http://www.arxiv.org/abs/math/0612178) is continued.
In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also…
Integer lattice gas automata can be utilized as building blocks in statistical mechanics. The presented deterministic and reversible automaton generates semiclassical statistical distributions. A possible approach to Bose-Einstein…
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…
Some direct relations between soliton solutions of integrable hierarchies and thermodynamical quantities of the Coulomb plasmas on the plane are revealed. We find that certain soliton solutions of the Kadomtsev-Petviashvili (KP) and B-type…
We study subsystems of open induction which are strongly connected to methods of automated inductive theorem proving. Specifically, we consider systems obtained from restricting induction to atoms, literals, clauses, and dual clauses. We…
We consider ideals and Boolean combinations of ideals. For the regular languages within these classes we give expressively complete automaton models. In addition, we consider general properties of regular ideals and their Boolean…
In recent work, several classes of solitonic solutions of string theory with higher-membrane structure have been obtained. These solutions can be classified according to the symmetry possessed by the solitons in the subspace of the…