相关论文: The Complexity of Modified Instances

Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…

While recent work has convincingly showed that sequence-to-sequence models struggle to generalize to new compositions (termed compositional generalization), little is known on what makes compositional generalization hard on a particular…

Constraint satisfaction problem (CSP) is a well-studied combinatorial search problem, in which we are asked to find an assignment of values to given variables so as to satisfy all of given constraints. We study a reconfiguration variant of…

The complexity of a computational problem is traditionally quantified based on the hardness of its worst case. This approach has many advantages and has led to a deep and beautiful theory. However, from the practical perspective, this…

One of the presuppositions of science since the times of Galileo, Newton, Laplace, and Descartes has been the predictability of the world. This idea has strongly influenced scientific and technological models. However, in recent decades,…

We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solution over a more restricted monoid exists. As a corollary, we obtain a complexity…

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…

Given a function based on the computation of an NP machine, can one in general eliminate some solutions? That is, can one in general decrease the ambiguity? This simple question remains, even after extensive study by many researchers over…

We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…

We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…

Optimization is a key task in a number of applications. When the set of feasible solutions under consideration is of combinatorial nature and described in an implicit way as a set of constraints, optimization is typically NP-hard.…

We study the P versus NP problem through properties of functions and monoids, continuing the work of [3]. Here we consider inverse monoids whose properties and relationships determine whether P is different from NP, or whether injective…

Models can be simple for different reasons: because they yield a simple and computationally efficient interpretation of a generic dataset (e.g. in terms of pairwise dependences) - as in statistical learning - or because they capture the…

Many NP-complete problems take integers as part of their input instances. These input integers are generally binarized, that is, provided in the form of the "binary" numeral representation, and the lengths of such binary forms are used as a…

Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…

A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…

Individuals have an intuitive perception of what makes a good coincidence. Though the sensitivity to coincidences has often been presented as resulting from an erroneous assessment of probability, it appears to be a genuine competence,…

The classical approach to solvability of a mathematical problem is to define a method which includes certain rules of operation or algorithms. Then using the defined method, one can show that some problems are solvable or not solvable or…

Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…

We introduce and investigate a series of matching problems for patterns with variables under Simon's congruence. Our results provide a thorough picture of these problems' computational complexity.