相关论文: Algebraic Elimination of epsilon-transitions

We establish new combinatorial transcendence criteria for continued fraction expansions. Let $\alpha = [0; a_1, a_2,...]$ be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients…

We study a quantum cellular automaton (QCA) whose time-evolution is defined from global transition function of classical cellular automata (CA). In order to investigate natural transformations from CA to QCA, the present QCA includes CA…

We present an elementary algorithm for the dynamics of recently introduced soliton cellular automata associated with quantum affine algebra U_q(g_n) at q=0. For g_n = A^{(1)}_n, the rule reproduces the ball-moving algorithm in…

In this paper, we give a Nivat-like characterization for weighted alternating automata over commutative semirings (WAFA). To this purpose we prove that weighted alternating can be characterized as the concatenation of weighted finite tree…

This work introduces a new kind of affine semigroups called $P$-semigroups. Within the framework of $\mathcal C$-semigroups, we define a finite-state automaton associated to them. Moreover, this automaton determines whether a $\mathcal…

We prove K-theoretic and shifted K-theoretic analogues of the bijection of Stanton and White between domino tableaux and pairs of semistandard tableaux. As a result, we obtain product formulas for pairs of stable Grothendieck polynomials…

This text aims to provide a self-contained, comprehensive, and reasonably detailed presentation of the theory of Stallings automata and some of its main applications.

Various forms of the $q$-boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator. Both the one-component and the multicomponent $q$-bosons are discussed. As a byproduct, we obtain a new…

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 article, we propose a $p$-adic analogue of complex Hilbert space and consider generalizations of some well-known theorems from functional analysis and the basic study of operators on Hilbert spaces. We compute the $K$-theory of the…

In this paper, we shall describe all the Rota-Baxter operators with any weight on split semi-quaternion algebra. Firstly, we give the matrix characterization of the Rota-Baxter operator on split semi-quaternion algebra. Then we give the…

We revisit the complexity of procedures on SFAs (such as intersection, emptiness, etc.) and analyze them according to the measures we find suitable for symbolic automata: the number of states, the maximal number of transitions exiting a…

By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…

For computation, there existed Turing machine and later-matured automata theory. For low-level parallel computation, there existed variants of Turing machine, such as two-tapes Turing machine and multi-tapes Turing machine. In the…

The Kleene theorem establishes a fundamental link between automata and expressions over the free monoid. Numerous generalisations of this result exist in the literature. Lifting this result to a weighted setting has been widely studied.…

We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as…

We introduce a spacetime discretization of the Dirac equation that has the form of a quantum automaton and that is invariant upon changing the representation of the Clifford algebra, as the Dirac equation itself. Our derivation follows…

In this expository article, we give a self-contained introduction to the wonderfully well-behaved class of pseudocompact algebras, focusing on the foundational classes of semisimple and separable algebras. We give characterizations of such…

We compare the K-theories of symplectic quotients with respect to a compact connected Lie group and with respect to its maximal torus, and in particular we give a method for computing the former in terms of the latter. More specifically,…

Rota-Baxter operators are an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota-Baxter operators and integrals in the case of the polynomial algebra $\mathbf{k}[x]$. We consider…