Related papers: Semantics of Division for Polynomial Solvers
We consider the age-old problem of allocating items among different agents in a way that is efficient and fair. Two papers, by Dolev et al. and Ghodsi et al., have recently studied this problem in the context of computer systems. Both…
Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to…
The integer division of a numerator n by a divisor d gives a quotient q and a remainder r. Optimizing compilers accelerate software by replacing the division of n by d with the division of c * n (or c * n + c) by m for convenient integers c…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
Consider a binary classification problem solved using a feed-forward artificial neural network (ANN). Let the ANN be composed of a ReLU layer and several linear layers (convolution, sum-pooling, or fully connected). We assume the network…
Sumterms are introduced as syntactic entities, and sumtuples are introduced as semantic entities. Equipped with these concepts a new description is obtained of the notion of a sum as (the name for) a role which can be played by a number.…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
It is well known that we can use structural proof theory to refine, or generalize, existing paradigmatic computational primitives, or to discover new ones. Under such a point of view we keep developing a programme whose goal is establishing…
Game semantics aim at describing the interactive behaviour of proofs by interpreting formulas as games on which proofs induce strategies. In this article, we introduce a game semantics for a fragment of first order propositional logic. One…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
We give a criterion for a real divisor to be rational and semiample.
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
We revisit the foundations of fairness and its interplay with utility and efficiency in settings where the training data contain richer labels, such as individual types, rankings, or risk estimates, rather than just binary outcomes. In this…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
We survey a burgeoning and promising new research area that considers the online nature of many practical fair division problems. We identify wide variety of such online fair division problems, as well as discuss new mechanisms and…
In this paper we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in [J. F. Bonnans and H. Ram\'irez C., Math. Program. 104 (2005), no. 2-3, Ser. B,…
The theory of algorithmic fair allocation is within the center of multi-agent systems and economics in the last decade due to its industrial and social importance. At a high level, the problem is to assign a set of items that are either…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…