Related papers: Wadge Degrees of Infinitary Rational Relations
We consider $\omega^n$-automatic structures which are relational structures whose domain and relations are accepted by automata reading ordinal words of length $\omega^n$ for some integer $n\geq 1$. We show that all these structures are…
We present a general coalgebraic setting in which we define finite and infinite behaviour with B\"uchi acceptance condition for systems whose type is a monad. The first part of the paper is devoted to presenting a construction of a monad…
This paper is a continuation of the study of topological properties of omega context free languages (omega-CFL). We proved before that the class of omega-CFL exhausts the hierarchy of Borel sets of finite rank, and that there exist some…
We introduce partially ordered two-way B\"uchi automata and characterize their expressive power in terms of fragments of first-order logic FO[<]. Partially ordered two-way B\"uchi automata are B\"uchi automata which can change the direction…
Infinite time Turing machine models with tape length $\alpha$, denoted $T_\alpha$, strengthen the machines of Hamkins and Kidder [HL00] with tape length $\omega$. A new phenomenon is that for some countable ordinals $\alpha$, some cells…
The $\omega$-power of a finitary language L over a finite alphabet $\Sigma$ is the language of infinite words over $\Sigma$ defined by L $\infty$ := {w 0 w 1. .. $\in$ $\Sigma$ $\omega$ | $\forall$i $\in$ $\omega$ w i $\in$ L}. The…
1-way quantum finite state automata are reversible in nature, which greatly reduces its accepting property. In fact, the set of languages accepted by 1-way quantum finite automata is a proper subset of regular languages. We introduce 2-tape…
Altenbernd, Thomas and W\"ohrle have considered in [ATW02] acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the B\"uchi and Muller ones,…
We prove in this paper that the length of the Wadge hierarchy of omega context free languages is greater than the Cantor ordinal epsilon_omega, which is the omega-th fixed point of the ordinal exponentiation of base omega. The same result…
A central question in the theory of automata is which classes of automata can be minimized in polynomial time. We close the remaining gaps for deterministic and history-deterministic automata over infinite words by proving that…
We revisit here congruence relations for B\"uchi automata, which play a central role in the automata-based verification. The size of the classical congruence relation is in $3^{\mathcal{O}(n^2)}$, where $n$ is the number of states of a…
We study the Borel-reducibility of isomorphism relations of complete first order theories and show the consistency of the following: For all such theories T and T', if T is classifiable and T' is not, then the isomorphism of models of T' is…
A non-deterministic automaton running on infinite trees is unambiguous if it has at most one accepting run on every tree. The class of languages recognisable by unambiguous tree automata is still not well-understood. In particular,…
We prove that the B\"uchi topology and the automatic topology are Polish. We also show that this cannot be fully extended to the case of a space of infinite labelled binary trees; in particular the B\"uchi and the Muller topologies are not…
We consider the temporal logic with since and until modalities. This temporal logic is expressively equivalent over the class of ordinals to first-order logic by Kamp's theorem. We show that it has a PSPACE-complete satisfiability problem…
In this article we consider two-way two-tape (alternating) automata accepting pairs of words and we study some closure properties of this model. Our main result is that such alternating automata are not closed under complementation for…
Recently data trees and data words have received considerable amount of attention in connection with XML reasoning and system verification. These are trees or words that, in addition to labels from a finite alphabet, carry data values from…
We describe the basic theory of infinite time Turing machines and some recent developments, including the infinite time degree theory, infinite time complexity theory, and infinite time computable model theory. We focus particularly on the…
We present a unified translation of LTL formulas into deterministic Rabin automata, limit-deterministic B\"uchi automata, and nondeterministic B\"uchi automata. The translations yield automata of asymptotically optimal size (double or…
Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of omega-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is…