Related papers: Truth Table Minimization of Computational Models
Black-box complexity is a complexity theoretic measure for how difficult a problem is to be optimized by a general purpose optimization algorithm. It is thus one of the few means trying to understand which problems are tractable for genetic…
We suggest two new methodologies for the design of efficient secure protocols, that differ with respect to their underlying computational models. In one methodology we utilize the communication complexity tree (or branching for f and…
The information complexity of a function $f$ is the minimum amount of information Alice and Bob need to exchange to compute the function $f$. In this paper we provide an algorithm for approximating the information complexity of an arbitrary…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
According to the Church-Turing Thesis (CTT), effective formal behaviours can be simulated by Turing machines; this has naturally led to speculation that physical systems can also be simulated computationally. But is this wider claim true,…
In spite of several claims stating that some models are more interpretable than others -- e.g., "linear models are more interpretable than deep neural networks" -- we still lack a principled notion of interpretability to formally compare…
We propose a decision-theoretic framework for computational complexity, complementary to classical theory: moving from syntactic exactness (Turing / Shannon) to semantic simulability (Le Cam). While classical theory classifies problems by…
Model interpretability has become an important problem in machine learning (ML) due to the increased effect that algorithmic decisions have on humans. Counterfactual explanations can help users understand not only why ML models make certain…
Black-box complexity theory provides lower bounds for the runtime of black-box optimizers like evolutionary algorithms and serves as an inspiration for the design of new genetic algorithms. Several black-box models covering different…
Datasets can be biased due to societal inequities, human biases, under-representation of minorities, etc. Our goal is to certify that models produced by a learning algorithm are pointwise-robust to potential dataset biases. This is a…
In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The…
In situations where explanations of black-box models may be useful, the fairness of the black-box is also often a relevant concern. However, the link between the fairness of the black-box model and the behavior of explanations for the…
Although many investigators affirm a desire to build reasoning systems that behave consistently with the axiomatic basis defined by probability theory and utility theory, limited resources for engineering and computation can make a complete…
Classical complexity theory measures the cost of computing a function, but many computational tasks require committing to one valid output among several. We introduce determination depth -- the minimum number of sequential layers of…
We develop a notion of computability and complexity of functions over the reals, which seems to be very natural when one tries to determine just how "difficult" a certain function is. This notion can be viewed as an extension of both BSS…
In system analysis and design optimization, multiple computational models are typically available to represent a given physical system. These models can be broadly classified as high-fidelity models, which provide highly accurate…
A general condition determining the optimal performance of a complex system has not yet been found and the possibility of its existence is unknown. To contribute in this direction, an optimization algorithm as a complex system is presented.…
Computation plays a major role in decision making. Even if an agent is willing to ascribe a probability to all states and a utility to all outcomes, and maximize expected utility, doing so might present serious computational problems.…
Fuzzy optimization deals with the problem of determining 'optimal'solutions of an optimization problem when some of the elements that appear in the problem are not precise. In real situations it is usual to have information, in systems…
This paper is devoted to the complexity of the Boolean satisfiability problem. We consider a version of this problem, where the Boolean formula is specified in the conjunctive normal form. We prove an unexpected result that the…