Related papers: The Consequences of Eliminating NP Solutions
Imposing constraints on the output of a Deep Neural Net is one way to improve the quality of its predictions while loosening the requirements for labeled training data. Such constraints are usually imposed as soft constraints by adding new…
In this paper we evaluate how constructive heuristics degrade when a problem transits from P to NP-hard. This is done by means of the linear ordering problem. More specifically, for this problem we prove that the objective function can be…
This paper concerns both anaphora resolution and prepositional phrase (PP) attachment that are the most frequent ambiguities in natural language processing. Several methods have been proposed to deal with each phenomenon separately, however…
The reliable fraction of information is an attractive score for quantifying (functional) dependencies in high-dimensional data. In this paper, we systematically explore the algorithmic implications of using this measure for optimization. We…
The snags in Nucci(1996)REDUCE algorithm are the intrinsic computational efforts and the ability to recognize the ignorable variable(s) during the reduction process of the algorithm. An inappropriate choice of the ignorable variable(s)may…
Neural networks are becoming a popular tool for solving many real-world problems such as object recognition and machine translation, thanks to its exceptional performance as an end-to-end solution. However, neural networks are complex…
This paper studies the complexity of query evaluation for databases whose relations are partially ordered; the problem commonly arises when combining or transforming ordered data from multiple sources. We focus on queries in a useful…
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it…
In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in…
While looking for abductive explanations of a given set of manifestations, an ordering between possible solutions is often assumed. The complexity of finding/verifying optimal solutions is already known. In this paper we consider the…
In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…
Reductions---rules that reduce input size while maintaining the ability to compute an optimal solution---are critical for developing efficient maximum independent set algorithms in both theory and practice. While several simple reductions…
Here we briefly discuss how negative numbers, or "negative probabilities", can naturally arise in probabilistic expressions and be given an operational interpretation. Like the use of negative numbers in arithmetical expressions, the use of…
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…
We study the optimization of functions with $n>2$ arguments that have a representation as a sum of several functions that have only $2$ of the $n$ arguments each, termed sums of bivariates, on finite domains. The complexity of optimizing…
It is a long-standing objective to ease the computation burden incurred by the decision making process. Identification of this mechanism's sensitivity to simplification has tremendous ramifications. Yet, algorithms for decision making under…
This paper presents a novel and straight formulation, and gives a complete insight towards the understanding of the complexity of the problems of the so called NP-Class. In particular, this paper focuses in the Searching of the Optimal…
Reduction of combinatorial filters involves compressing state representations that robots use. Such optimization arises in automating the construction of minimalist robots. But exact combinatorial filter reduction is an NP-complete problem…
The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…
We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is…