Related papers: Wadge Degrees of Infinitary Rational Relations

We define a class of ranked tree automata TABG generalizing both the tree automata with local tests between brothers of Bogaert and Tison (1992) and with global equality and disequality constraints (TAGED) of Filiot et al. (2007). TABG can…

We present a direct transformation of weak alternating $\omega$-automata into equivalent backward deterministic $\omega$-automata and show (1) how it can be used to obtain a transformation of non-deterministic B\"uchi automata into…

We introduce the notion of feedback computable functions from $2^\omega$ to $2^\omega$, extending feedback Turing computation in analogy with the standard notion of computability for functions from $2^\omega$ to $2^\omega$. We then show…

We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite…

We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to 'recover' the properties of classical…

We show that polynomial time Turing equivalence and a large class of other equivalence relations from computational complexity theory are universal countable Borel equivalence relations. We then discuss ultrafilters on the invariant Borel…

Visibly pushdown automata are input-driven pushdown automata that recognize some non-regular context-free languages while preserving the nice closure and decidability properties of finite automata. Visibly pushdown automata with multiple…

We investigate the descriptive complexity of order convergence in separable Banach lattices. While uniform convergence is Borel and $\sigma$-order convergence is known to be ${\bf \Delta}^1_2$, it is unclear in general when $\sigma$-order…

We introduce a weight assignment logic for reasoning about quantitative languages of infinite words. This logic is an extension of the classical MSO logic and permits to describe quantitative properties of systems with multiple weight…

Let $\Gamma$ be a centerless irreducible higher rank arithmetic lattice in characteristic zero. We prove that if $\Gamma$ is either non-uniform or is uniform of orthogonal type and dimension at least 9, then $\Gamma$ is bi-interpretable…

We investigate the language classes recognized by group automata over matrix groups. For the case of $2 \times 2 $ matrices, we prove that the corresponding group automata for rational matrix groups are more powerful than the corresponding…

An $\omega$-regular language is Eve-positional if, in all games with this language as objective, the existential player can play optimally without keeping any information from the previous moves. This notion plays a crucial role in…

The cyclotomic Birman-Murakami-Wenzl (BMW) algebras B_n^k, introduced by R. H\"aring-Oldenburg, are a generalisation of the BMW algebras associated with the cyclotomic Hecke algebras of type G(k,1,n) (aka Ariki-Koike algebras) and type B…

The extension of the Wagner hierarchy to blind counter automata accepting infinite words with a Muller acceptance condition is effective. We determine precisely this hierarchy.

This paper establishes an explicit obstruction to constructing algebraic cycles from automorphic cohomology classes on Shimura varieties. We produce a rational Hodge class $\Omega_E$ in the intersection cohomology of the Baily-Borel…

We use erasers-like basic operations on words to construct a set that is both Borel and above Delta^0_omega, built as a set V^\omega where V is a language of finite words accepted by a pushdown automaton. In particular, this gives a first…

This paper is the extended version of On the Complexity of Infinite Advice Strings (ICALP 2018). We investigate a notion of comparison between infinite strings. In a general way, if M is a computation model (e.g. Turing machines) and C a…

We present a number of results concerning infinite-exponent partition relations on linear orders of the form $\langle {}^\alpha 2,<_{\text{lex}}\rangle$ for $\alpha$ an ordinal, generalising the setting of the real line, working throughout…

The main observational equivalences of the untyped lambda-calculus have been characterized in terms of extensional equalities between B\"ohm trees. It is well known that the lambda-theory H*, arising by taking as observables the head normal…

In this paper we consider non-archimedean abelian Polish groups whose orbit equivalence relations are all Borel. Such groups are called tame. We show that a non-archimedean abelian Polish group is tame if and only if it does not involve…