Related papers: A Computational Complexity-Theoretic Elaboration o…

Complexity theory offers a variety of concise computational models for computing boolean functions - branching programs, circuits, decision trees and ordered binary decision diagrams to name a few. A natural question that arises in this…

The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…

Computable reducibility is a well-established notion that allows to compare the complexity of various equivalence relations over the natural numbers. We generalize computable reducibility by introducing degree spectra of reducibility and…

The recently initiated approach called computability logic is a formal theory of interactive computation. See a comprehensive online source on the subject at http://www.cis.upenn.edu/~giorgi/cl.html . The present paper contains a soundness…

Interpretable representations are the backbone of many explainers that target black-box predictive systems based on artificial intelligence and machine learning algorithms. They translate the low-level data representation necessary for good…

One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…

We derive computationally tractable methods to select a small subset of experiment settings from a large pool of given design points. The primary focus is on linear regression models, while the technique extends to generalized linear models…

Real-life agents seldom have unlimited reasoning power. In this paper, we propose and study a new formal notion of computationally bounded strategic ability in multi-agent systems. The notion characterizes the ability of a set of agents to…

Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…

The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

Many techniques for handling missing data have been proposed in the literature. Most of these techniques are overly complex. This paper explores an imputation technique based on rough set computations. In this paper, characteristic…

Within the program of finding axiomatizations for various parts of computability logic, it was proved earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting's intuitionistic calculus. That sort…

One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are…

This article presents a formal model demonstrating that genuine autonomy, the ability of a system to self-regulate and pursue objectives, fundamentally implies computational unpredictability from an external perspective. we establish…

Counterfactual explanations are emerging as an attractive option for providing recourse to individuals adversely impacted by algorithmic decisions. As they are deployed in critical applications (e.g. law enforcement, financial lending), it…

Dimensionality reduction and clustering techniques are frequently used to analyze complex data sets, but their results are often not easy to interpret. We consider how to support users in interpreting apparent cluster structure on scatter…

Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…

In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these…

This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…