Index problems for game automata

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, respectively, the non-deterministic, alternating, and weak Rabin-Mostowski index problems. Whether they can be answered effectively is a long-standing open problem, solved so far only for languages recognizable by deterministic automata (the alternating variant trivializes). We investigate a wider class of regular languages, recognizable by so-called game automata, which can be seen as the closure of deterministic ones under complementation and composition. Game automata are known to recognize languages arbitrarily high in the alternating Rabin-Mostowski index hierarchy; that is, the alternating index problem does not trivialize any more. Our main contribution is that all three index problems are decidable for languages recognizable by game automata. Additionally, we show that it is decidable whether a given regular language can be recognized by a game automaton

Bayesian phylolinguistics infers the internal structure and the time-depth of the Turkic language family

Despite more than 200 years of research, the internal structure of the Turkic language family remains subject to debate. Classifications of Turkic so far are based on both classical historical–comparative linguistic and distance-based quantitative approaches. Although these studies yield an internal structure of the Turkic family, they cannot give us an understanding of the statistical robustness of the proposed branches, nor are they capable of reliably inferring absolute divergence dates, without assuming constant rates of change. Here we use computational Bayesian phylogenetic methods to build a phylogeny of the Turkic languages, express the reliability of the proposed branches in terms of probability, and estimate the time-depth of the family within credibility intervals. To this end, we collect a new dataset of 254 basic vocabulary items for thirty-two Turkic language varieties based on the recently introduced Leipzig–Jakarta list. Our application of Bayesian phylogenetic inference on lexical data of the Turkic languages is unprecedented. The resulting phylogenetic tree supports a binary structure for Turkic and replicates most of the conventional sub-branches in the Common Turkic branch. We calculate the robustness of the inferences for subgroups and individual languages whose position in the tree seems to be debatable. We infer the time-depth of the Turkic family at around 2100 years before present, thus providing a reliable quantitative basis for previous estimates based on classical historical linguistics and lexicostatistics

Growth Series and Random Walks on Some Hyperbolic Graphs

Consider the tesselation of the hyperbolic plane by m-gons, l per vertex. In its 1-skeleton, we compute the growth series of vertices, geodesics, tuples of geodesics with common extremities. We also introduce and enumerate "holly trees", a family of reduced loops in these graphs. We then apply Grigorchuk's result relating cogrowth and random walks to obtain lower estimates on the spectral radius of the Markov operator associated with a symmetric random walk on these graphs.Comment: 21 pages. to appear in monash. mat

Visualizing the Boni dialects with Historical Glottometry

This paper deals with the historical relations between dialects of Boni, a Cushitic language of Kenya and Somalia. Boni forms the subject of Volume 10 of the Language and Dialect Atlas of Kenya (Heine & Möhlig 1982). Heine presents evidence for three subgroups within Boni, as well as several areas of convergence between dialects belonging to different proposed subgroups. In reviewing his evidence, I find that two of the three splits are not supported by the data, and therefore his conclusions on convergence must also be reinterpreted. Given the presence of numerous intersecting isoglosses, the tree diagram is an inappropriate model for describing the relations between Boni dialects, and I turn to Historical Glottometry (Kalyan & François 2018) to provide a visualization of the data