Related papers: Highly Undecidable Problems about Recognizability …
In this paper, based on results of exact learning and test theory, we study arbitrary infinite binary information systems each of which consists of an infinite set of elements and an infinite set of two-valued functions (attributes) defined…
We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…
We study word structures of the form $(D,<,P)$ where $D$ is either $\mathbb{N}$ or $\mathbb{Z}$, $<$ is the natural linear ordering on $D$ and $P\subseteq D$ is a predicate on $D$. In particular we show: (a) The set of recursive…
We consider two decision problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem} (are all but finitely many terms of a…
Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…
Alternating timed automata on infinite words are considered. The main result is a characterization of acceptance conditions for which the emptiness problem for these automata is decidable. This result implies new decidability results for…
We prove that the inhabitation problem for rank two intersection types is decidable, but (contrary to common belief) EXPTIME-hard. The exponential time hardness is shown by reduction from the in-place acceptance problem for alternating…
The purpose of this article is to study the algorithmic complexity of the Besicovitch stability of noisy subshifts of finite type, a notion studied in a previous article. First, we exhibit an unstable aperiodic tiling, and then see how it…
The Chinese Remainder Theorem for the integers says that every system of congruence equations is solvable as long as the system satisfies an obvious necessary condition. This statement can be generalized in a natural way to arbitrary…
We prove that one cannot algorithmically decide whether a finitely presented $\mathbb{Z}$-extension admits a finitely generated base group, and we use this fact to prove the undecidability of the BNS invariant. Furthermore, we show the…
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…
Probabilistic B\"uchi Automata (PBA) are randomized, finite state automata that process input strings of infinite length. Based on the threshold chosen for the acceptance probability, different classes of languages can be defined. In this…
We prove the universality of the regular realizability problems for several classes of filters. The filters are encodings of finite relations on the set of non-negative integers in the format proposed by P. Wolf and H. Fernau. The…
Parametric timed automata extend the standard timed automata with the possibility to use parameters in the clock guards. In general, if the parameters are real-valued, the problem of language emptiness of such automata is undecidable even…
The Regular Post Embedding Problem extended with partial (co)directness is shown decidable. This extends to universal and/or counting versions. It is also shown that combining directness and codirectness in Post Embedding problems leads to…
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 propose the Transcendental Encoding Conjecture for decision problems, which asserts that every language in complexity class P encodes to an algebraic real (possibly rational or algebraic irrational) under its binary characteristic…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
We construct examples of finitely generated decidable group presentations that satisfy certain combinations of solvability for the word problem, solvability for the bounded word problem, and computablity for the Dehn function. We prove that…
Deciding if a given set of Wang tiles admits a tiling of the plane is decidable if the number of Wang tiles (or the number of colors) is bounded, for a trivial reason, as there are only finitely many such tilesets. We prove however that the…