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First-order (FO) transition systems have recently attracted attention for the verification of parametric systems such as network protocols, software-defined networks or multi-agent workflows like conference management systems. Desirable…
We study conformal inference in non-exchangeable environments through the lens of Blackwell's theory of approachability. We first recast adaptive conformal inference (ACI, Gibbs and Cand\`es, 2021) as a repeated two-player vector-valued…
We consider regret minimization in repeated games with a very large number of actions. Such games are inherent in the setting of AI Safety via Debate \cite{irving2018ai}, and more generally games whose actions are language-based. Existing…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…
With edge intelligence, AI models are increasingly pushed to the edge to serve ubiquitous users. However, due to the drift of model, data, and task, AI model deployed at the edge suffers from degraded accuracy in the inference serving…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
This work studies constrained stochastic optimization problems where the objective and constraint functions are convex and expressed as compositions of stochastic functions. The problem arises in the context of fair classification, fair…
We prove sharp, computable error estimates for the propagation of errors in the numerical solution of ordinary differential equations. The new estimates extend previous estimates of the influence of data errors and discretisation errors…
A variety of practical problems can be modeled by the decision-making process in multi-player games where a group of self-interested players aim at optimizing their own local objectives, while the objectives depend on the actions taken by…
Programming languages with countable nondeterministic choice are computationally interesting since countable nondeterminism arises when modeling fairness for concurrent systems. Because countable choice introduces non-continuous behaviour,…
We prove decidability of the boundedness problem for monadic least fixed-point recursion based on positive monadic second-order (MSO) formulae over trees. Given an MSO-formula phi(X,x) that is positive in X, it is decidable whether the…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
The development of data-driven approaches for solving differential equations has been followed by a plethora of applications in science and engineering across a multitude of disciplines and remains a central focus of active scientific…
While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the properties that optimal solutions need to have, and devised a…
Integer octagonal constraints (a.k.a. ``Unit Two Variables Per Inequality'' or ``UTVPI integer constraints'') constitute an interesting class of constraints for the representation and solution of integer problems in the fields of constraint…
Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this…
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
Enclosing depth is a recently introduced depth measure which gives a lower bound to many depth measures studied in the literature. So far, enclosing depth has only been studied from a combinatorial perspective. In this work, we give the…
Ordinal classification problems, where labels exhibit a natural order, are prevalent in high-stakes fields such as medicine and finance. Accurate uncertainty quantification, including the decomposition into aleatoric (inherent variability)…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…