Zobrazeno 1 - 10
of 10 968
pro vyhledávání: '"Worrell A"'
We prove transcendence of the Hecke-Mahler series $\sum_{n=0}^\infty f(\lfloor n\theta+\alpha \rfloor) \beta^{-n}$, where $f(x) \in \mathbb{Z}[x]$ is a non-constant polynomial $\alpha$ is a real number, $\theta$ is an irrational real number, and $\be
Externí odkaz:
http://arxiv.org/abs/2412.07908
We study decidability of the following problems for both discrete-time and continuous-time linear dynamical systems. Suppose we are given a matrix $M$, a set $S$ of starting points, and a set $T$ of unsafe points. (a) Does there exist $\varepsilon >
Externí odkaz:
http://arxiv.org/abs/2410.13053
Hilbert's Nullstellensatz is a fundamental result in algebraic geometry that gives a necessary and sufficient condition for a finite collection of multivariate polynomials to have a common zero in an algebraically closed field. Associated with this r
Externí odkaz:
http://arxiv.org/abs/2408.13027
Multi-priced timed automata (MPTA) are timed automata with observer variables whose derivatives can change from one location to another. Observers are write-only variables, that is, they do not affect the control flow of the automaton; thus MPTA lie
Externí odkaz:
http://arxiv.org/abs/2407.18131
In this paper we introduce holonomic tree automata: a common extension of weighted tree automata and holonomic recurrences. We show that the generating function of the tree series represented by such an automaton is differentially algebraic. Converse
Externí odkaz:
http://arxiv.org/abs/2407.08218
We prove that for any integers $\alpha, \beta > 1$, the existential fragment of the first-order theory of the structure $\langle \mathbb{Z}; 0,1,<, +, \alpha^{\mathbb{N}}, \beta^{\mathbb{N}}\rangle$ is decidable (where $\alpha^{\mathbb{N}}$ is the se
Externí odkaz:
http://arxiv.org/abs/2407.05191
Computational problems concerning the orbit of a point under the action of a matrix group occur in numerous subfields of computer science, including complexity theory, program analysis, quantum computation, and automata theory. In many cases the focu
Externí odkaz:
http://arxiv.org/abs/2407.04626
Nonuniformly sampled signals are prevalent in real-world applications, but their power spectra estimation, usually from a finite number of samples of a single realization, presents a significant challenge. The optimal solution, which uses Bronez Gene
Externí odkaz:
http://arxiv.org/abs/2407.01943
Autor:
Berthé, Valérie, Karimov, Toghrul, Nieuwveld, Joris, Ouaknine, Joël, Vahanwala, Mihir, Worrell, James
We investigate the decidability of the monadic second-order (MSO) theory of the structure $\langle \mathbb{N};<,P_1, \ldots,P_k \rangle$, for various unary predicates $P_1,\ldots,P_k \subseteq \mathbb{N}$. We focus in particular on "arithmetic" predi
Externí odkaz:
http://arxiv.org/abs/2405.07953
We consider numbers of the form $S_\beta(\boldsymbol{u}):=\sum_{n=0}^\infty \frac{u_n}{\beta^n}$, where $\boldsymbol{u}=\langle u_n \rangle_{n=0}^\infty$ is an infinite word over a finite alphabet and $\beta\in \mathbb{C}$ satisfies $|\beta|>1$. Our
Externí odkaz:
http://arxiv.org/abs/2405.05279