Related papers: Wadge degrees of $\Delta^0_2$ omega-powers

We establish character formulae for representations of the one-parameter family of simple Lie superalgebras $D(2|1;\zeta)$. We provide a complete description of the Verma flag multiplicities of the tilting modules and the projective modules…

In this paper, we primarily investigate the following symmetric presentation of the surface group $\pi_1(\Sigma_g)=\left\langle c_1,\dots, c_{2g}\mid c_1\cdots c_{2g}c_1^{-1}\cdots c_{2g}^{-1}\right\rangle$. For every nontrivial element…

We investigate the topological complexity of non Borel recognizable tree languages with regard to the difference hierarchy of analytic sets. We show that, for each integer $n \geq 1$, there is a $D_{\omega^n}({\bf \Sigma}^1_1)$-complete…

We study tree languages that can be defined in \Delta_2 . These are tree languages definable by a first-order formula whose quantifier prefix is forall exists, and simultaneously by a first-order formula whose quantifier prefix is . For the…

This is a review of several results related to distribution of powers and combination of powers modulo 1. We include a proof that given a sequence of real numbers $\theta_n$, it is possible to get an $\alpha$ (given $\lambda \ne 0$), or a…

We present a polynomial time algorithm that constructs a deterministic parity automaton (DPA) from a given set of positive and negative ultimately periodic example words. We show that this algorithm is complete for the class of…

Let G be a powerful finite p-group. In this note, we give a short elementary proof of the following facts for all $i\ge 0$: (i) $\exp \Omega_-i(G)\le p^i$ for odd p, and $\exp \Omega_-i(G)\le 2^{i+1}$ for p = 2; (ii) the index $|G:G^{p^i}|$…

A new class of languages of infinite words is introduced, called the max-regular languages, extending the class of $\omega$-regular languages. The class has two equivalent descriptions: in terms of automata (a type of deterministic counter…

We show that there are $\Sigma_3^0$-complete languages of infinite words accepted by non-deterministic Petri nets with B\"uchi acceptance condition, or equivalently by B\"uchi blind counter automata. This shows that omega-languages accepted…

We investigate the expressive power of regular expressions for languages of countable words and establish their expressive equivalence with logical and algebraic characterizations. Our goal is to extend the classical theory of regular…

We consider extensions of monadic second order logic over $\omega$-words, which are obtained by adding one language that is not $\omega$-regular. We show that if the added language $L$ has a neutral letter, then the resulting logic is…

Iteration semirings are Conway semirings satisfying Conway's group identities. We show that the semirings $\N^{\rat}\llangle \Sigma^* \rrangle$ of rational power series with coefficients in the semiring $\N$ of natural numbers are the free…

In a functional calculus, the so called \Omega-rule states that if two terms P and Q applied to any closed term <i>N</i> return the same value (i.e. PN = QN), then they are equal (i.e. P = Q holds). As it is well known, in the…

Let S be a complete star-omega semiring and Sigma be an alphabet. For a weighted omega-pushdown automaton P with stateset 1...n, n greater or equal to 1, we show that there exists a mixed algebraic system over a complete semiring-semimodule…

We ask whether $\mathbf{\Delta^1_2}$ or $\mathbf{\Sigma^1_2}$ equivalence relations with $I$-small classes for $I$ a $\sigma$-ideal must have perfectly many classes. We show that for a wide class of ccc $\sigma$-ideals, a positive answer…

Let Y be a weighted homogeneous (singular) subvariety of C^n. The main objective of this paper is to present a class of explicit integral formulae for solving the d-bar-equation $\omega=\dbar\lambda$ on the regular part of Y, where $\omega$…

We obtain new omega results for the error terms in two classical lattice point problems. These results are likely to be the best possible.

We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $\zeta(2n+1)$ in terms of zeta at other fractional points. This paper also…

For an increasing weighted tree $G_\omega$, we obtain an asymptotic value and a sharp bound on the index stability of the depth function of its edge ideal $I(G_\omega)$. Moreover, if $G_\omega$ is a strictly increasing weighted tree, we…

In this article, we give a full description of the Wadge degrees of Borel functions from $\omega^\omega$ to a better quasi ordering $\mathcal{Q}$. More precisely, for any countable ordinal $\xi$, we show that the Wadge degrees of…