Related papers: Using games and universal trees to characterise th…
The parity index problem of tree automata asks, given a regular tree language L, what is the least number of priorities of a nondeterministic parity tree automaton that recognises L. This is a long-standing open problem, also known as the…
For a given regular language of infinite trees, one can ask about the minimal number of priorities needed to recognize this language with a non-deterministic, alternating, or weak alternating parity automaton. These questions are known as,…
The game tree languages can be viewed as an automata-theoretic counterpart of parity games on graphs. They witness the strictness of the index hierarchy of alternating tree automata, as well as the fixed-point hierarchy over binary trees.…
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,…
This work is a study of the expressive power of unambiguity in the case of automata over infinite trees. An automaton is called unambiguous if it has at most one accepting run on every input, the language of such an automaton is called an…
The complexity of parity games is a long standing open problem that saw a major breakthrough in 2017 when two quasi-polynomial algorithms were published. This article presents a third, independent approach to solving parity games in…
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…
The following problem is shown undecidable: given regular languages L,K of finite trees, decide if there exists a deterministic tree-walking automaton which accepts all trees in L and rejects all trees in K. The proof uses a technique of…
The HOM problem, which asks whether the image of a regular tree language under a given tree homomorphism is again regular, is known to be decidable [Godoy & Gim\'enez: The HOM problem is decidable. JACM 60(4), 2013]. However, the problem…
Several distinct techniques have been proposed to design quasi-polynomial algorithms for solving parity games since the breakthrough result of Calude, Jain, Khoussainov, Li, and Stephan (2017): play summaries, progress measures and register…
The Strahler number of a rooted tree is the largest height of a perfect binary tree that is its minor. The Strahler number of a parity game is proposed to be defined as the smallest Strahler number of the tree of any of its attractor…
$\mu$-Calculus and automata on infinite trees are complementary ways of describing infinite tree languages. The correspondence between $\mu$-Calculus and alternating tree automaton is used to solve the satisfiability and model checking…
We show that it is decidable whether two regular languages of infinite trees are separable by a deterministic language, resp., a game language. We consider two variants of separability, depending on whether the set of priorities of the…
We define the class of explorable automata on finite or infinite words. This is a generalization of History-Deterministic (HD) automata, where this time non-deterministic choices can be resolved by building finitely many simultaneous runs…
Parity games have witnessed several new quasi-polynomial algorithms since the breakthrough result of Calude et al. (STOC 2017). The combinatorial object underlying these approaches is a universal tree, as identified by Czerwi\'nski et al.…
Recently, five quasi-polynomial-time algorithms solving parity games were proposed. We elaborate on one of the algorithms, by Lehtinen (2018). Czerwi\'nski et al. (2019) observe that four of the algorithms can be expressed as constructions…
An attractor decomposition meta-algorithm for solving parity games is given that generalises the classic McNaughton-Zielonka algorithm and its recent quasi-polynomial variants due to Parys (2019), and to Lehtinen, Schewe, and Wojtczak…
Register automata are finite automata equipped with a finite set of registers ranging over the domain of some relational structure like $(\mathbb N;=)$ or $(\mathbb Q;<)$. Register automata process words over the domain, and along a run of…
The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class $\Game (D\_n({\bf\Sigma}^0\_2))$ for some natural number $n\geq 1$, where $\Game$ is the game quantifier. We first give…
History-deterministic automata are a restricted class of nondeterministic automata where the nondeterminism while reading an input can be resolved successfully based on the prefix read so far. History-deterministic automata are…