Related papers: Eve-positional languages: putting order into B\"uc…
We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
Vision-Language-Action (VLA) models enable robots to perform manipulation tasks directly from natural language instructions and are increasingly viewed as a foundation for generalist robotic policies. However, their reliability under…
Since the 1970s with the work of McNaughton, Papert and Sch\"utzenberger, a regular language is known to be definable in the first-order logic if and only if its syntactic monoid is aperiodic. This algebraic characterisation of a…
Some decidable winning conditions of arbitrarily high finite Borel complexity for games on finite graphs or on pushdown graphs have been recently presented by O. Serre in [ Games with Winning Conditions of High Borel Complexity, in the…
We study alternating good-for-games (GFG) automata, i.e., alternating automata where both conjunctive and disjunctive choices can be resolved in an online manner, without knowledge of the suffix of the input word still to be read. We show…
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown languages over finite words. In VLDL one can, e.g., express that a function resets a…
Reasoning is a central capability of human intelligence. In recent years, with the advent of large-scale datasets, pretrained large language models have emerged with new capabilities, including reasoning. However, these models still…
At the beginning of a dynamic game, players may have exogenous theories about how the opponents are going to play. Suppose that these theories are commonly known. Then, players will refine their first-order beliefs, and challenge their own…
Probabilistic B\"uchi automata are a natural generalization of PFA to infinite words, but have been studied in-depth only rather recently and many interesting questions are still open. PBA are known to accept, in general, a class of…
Answer-set programming (ASP) is a successful problem-solving approach in logic-based AI. In ASP, problems are represented as declarative logic programs, and solutions are identified through their answer sets. Equilibrium logic (EL) is a…
In the context of multi-agent systems, the rational verification problem is concerned with checking which temporal logic properties will hold in a system when its constituent agents are assumed to behave rationally and strategically in…
Vision-Language-Action (VLA) policies have emerged as a versatile paradigm for generalist robotic manipulation. However, precise object placement under compositional language instructions remains a major challenge for modern monolithic VLA…
Random experiments that are simple and clear enough to be performed by human agents feature prominently in the teaching of elementary stochastics as well as in games. We present Alea, a domain-specific language for the specification of…
Transformer language models have made tremendous strides in natural language understanding tasks. However, the complexity of natural language makes it challenging to ascertain how accurately these models are tracking the world state…
We use erasers-like basic operations on words to construct a set that is both Borel and above Delta^0_omega, built as a set V^\omega where V is a language of finite words accepted by a pushdown automaton. In particular, this gives a first…
In this thesis, we study the place of regular languages within the communication complexity setting. In particular, we are interested in the non-deterministic communication complexity of regular languages. We show that a regular language…
Analogous to regular string and tree languages, regular languages of directed acyclic graphs (DAGs) are defined in the literature. Although called regular, those DAG-languages are more powerful and, consequently, standard problems have a…
The states of a deterministic finite automaton A can be identified with collections of words in Pf(L(A)) -- the set of prefixes of words belonging to the regular language accepted by A. But words can be ordered and among the many possible…
As a contribution to the challenge of building game-playing AI systems, we develop and analyse a formal language for representing and reasoning about strategies. Our logical language builds on the existing general Game Description Language…