Related papers: On the Borel Inseparability of Game Tree Languages
We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…
The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…
We consider the problem of computing the measure of a regular set of infinite binary trees. While the general case remains unsolved, we show that the measure of a language can be computed when the set is given in one of the following three…
Parikh's game logic is a PDL-like fixpoint logic interpreted on monotone neighbourhood frames that represent the strategic power of players in determined two-player games. Game logic translates into a fragment of the monotone…
We address questions of logic and expressibility in the context of random rooted trees. Infiniteness of a rooted tree is not expressible as a first order sentence, but is expressible as an existential monadic second order sentence (EMSO).…
We show that graphs generated by collapsible pushdown systems of level 2 are tree-automatic. Even if we allow epsilon-contractions and reachability predicates (with regular constraints) for pairs of configurations, the structures remain…
Finitary Idealized Concurrent Algol (FICA) is a prototypical programming language combining functional, imperative, and concurrent computation. There exists a fully abstract game model of FICA, which in principle can be used to prove…
A tree automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. Words can be regarded as specific…
We study the separability problem for automatic relations (i.e., relations on finite words definable by synchronous automata) in terms of recognizable relations (i.e., finite unions of products of regular languages). This problem takes as…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
Sturmian words are infinite binary words with many equivalent definitions: They have a minimal factor complexity among all aperiodic sequences; they are balanced sequences (the labels 0 and 1 are as evenly distributed as possible) and they…
We study tree games developed recently by Matteo Mio as a game interpretation of the probabilistic $\mu$-calculus. With expressive power comes complexity. Mio showed that tree games are able to encode Blackwell games and, consequently, are…
One of the major open problems in automata and logic is the following: is there an algorithm which inputs a regular tree language and decides if the language can be defined in first-order logic? The goal of this paper is to present this…
Deterministic game-solving algorithms are conventionally analyzed in the light of their average-case complexity against a distribution of random game-trees, where leaf values are independently sampled from a fixed distribution. This…
So-called separation automata are in the core of several recently invented quasi-polynomial time algorithms for parity games. An explicit $q$-state separation automaton implies an algorithm for parity games with running time polynomial in…
This paper presents a decidable characterization of tree languages that can be defined by a boolean combination of Sigma_1 sentences. This is a tree extension of the Simon theorem, which says that a string language can be defined by a…
Saturation is a fundamental game-semantic property satisfied by strategies that interpret higher-order concurrent programs. It states that the strategy must be closed under certain rearrangements of moves, and corresponds to the intuition…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
In this paper we show that given a max-plus automaton (over trees, and with real weights) computing a function $f$ and a min-plus automaton (similar) computing a function $g$ such that $f\leqslant g$, there exists effectively an unambiguous…
We study alternating automata with qualitative semantics over infinite binary trees: alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the…