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Reconfiguration is one of the central mechanisms in distributed systems. Due to failures and connectivity disruptions, the very set of service replicas (or servers) and their roles in the computation may have to be reconfigured over time.…
A family of formal power series, such that its coefficients satisfy a recursion formula, is characterized in terms of the summability, in the sense of J. P. Ramis, of its elements along certain well chosen directions. We describe a set of…
The purpose of a program analysis is to compute an abstract meaning for a program which approximates its dynamic behaviour. A compositional program analysis accomplishes this task with a divide-and-conquer strategy: the meaning of a program…
We present a hierarchical framework to solve robot planning as an input control problem. At the lowest level are temporary closed control loops, ("tasks"), each representing a behaviour, contingent on a specific sensory input and therefore…
Multi-task learning is a learning paradigm which seeks to improve the generalization performance of a learning task with the help of some other related tasks. In this paper, we propose a regularization formulation for learning the…
Finite determinacy for mappings has been classically thoroughly studied in numerous scenarios in the real- and complex-analytic category and in the differentiable case. It means that the map-germ is determined, up to a given equivalence…
A heap is a structure with a ternary operation which is intuitively a group with forgotten unit element. Quantum heaps are associative algebras with a ternary cooperation which are to the Hopf algebras what heaps are to groups, and, in…
In this article, we show that the now classical protocol complex approach to distributed task solvability of Herlihy et al. can be understood in standard categorical terms. First, protocol complexes are functors, from chromatic (semi-)…
By introducing the concepts of a loop and a loop formula, Lin and Zhao showed that the answer sets of a nondisjunctive logic program are exactly the models of its Clark's completion that satisfy the loop formulas of all loops. Recently,…
This paper advances the theoretical understanding of active learning label complexity for decision trees as binary classifiers. We make two main contributions. First, we provide the first analysis of the disagreement coefficient for…
This paper contributes to the mathematical foundations of logic programming by introducing and studying the sequential composition of answer set programs. On the semantic side, we show that the immediate consequence operator of a program…
This paper explores the problem of task learning and planning, contributing the Action-Category Representation (ACR) to improve computational performance of both Planning and Reinforcement Learning (RL). ACR is an algorithm-agnostic,…
The use of function contracts to specify the behavior of functions often remains limited to the scope of a single function call. Relational properties link several function calls together within a single specification. They can express more…
Algebraic effects offer a versatile framework that covers a wide variety of effects. However, the family of operations that delimit scopes are not algebraic and are usually modelled as handlers, thus preventing them from being used freely…
The set of formal power series with coefficients in an associative but noncommutative algebra becomes a loop with the substitution product. We initiate the study of this loop by describing certain Lie and Sabinin algebras related to it.…
We introduce the resolvent composition, a monotonicity-preserving operation between a linear operator and a set-valued operator, as well as the proximal composition, a convexity-preserving operation between a linear operator and a function.…
In order theory, a rank function measures the vertical "level" of a poset element. It is an integer-valued function on a poset which increments with the covering relation, and is only available on a graded poset. Defining a vertical measure…
Auxiliary learning is an effective method for enhancing the generalization capabilities of trained models, particularly when dealing with small datasets. However, this approach may present several difficulties: (i) optimizing multiple…
The relative algebraic monodromy of abelian logarithms (defined as the kernel of a map between algebraic monodromy groups attached to an abelian scheme with and without a section) was computed in \cite{A1}: under natural assumptions, this…
Resource-bounded measure is a generalization of classical Lebesgue measure that is useful in computational complexity. The central parameter of resource-bounded measure is the {\it resource bound} $\Delta$, which is a class of functions.…