Related papers: Report on Generic Case Complexity
There is currently a rapid increase in the number of challenge problem, benchmarking datasets and algorithmic optimization tests for evaluating AI systems. However, there does not currently exist an objective measure to determine the…
We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…
We generalize the definition of a counter and counter reversal complexity and investigate the power of generalized deterministic counter automata in terms of language recognition.
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we…
Generalized Additive Models (GAMs) are commonly considered *interpretable* within the ML community, as their structure makes the relationship between inputs and outputs relatively understandable. Therefore, it may seem natural to…
Some examples are easier for humans to classify than others. The same should be true for deep neural networks (DNNs). We use the term example perplexity to refer to the level of difficulty of classifying an example. In this paper, we…
A good process model is expected not only to reflect the behavior of the process, but also to be as easy to read and understand as possible. Because preferences vary across different applications, numerous measures provide ways to reflect…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
We study a group of new methods to solve an open problem that is the shortest paths problem on a given fix-weighted instance. It is the real significance at a considerable altitude to reach our aim to meet these qualities of generic,…
The local and global interpretability of various ML models has been studied extensively in recent years. However, despite significant progress in the field, many known results remain informal or lack sufficient mathematical rigor. We…
In this paper we introduce a general framework for defining the depth of a sequence with respect to a class of observers. We show that our general framework captures all depth notions introduced in complexity theory so far. We review most…
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…
In the rapidly evolving field of quantum computing, quantifying circuit complexity remains a critical challenge. This paper introduces Character Complexity, a novel measure that bridges Group-theoretic concepts with practical quantum…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a…
Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number…
In this note we introduce a notion of a generically (strongly generically) NP-complete problem and show that the randomized bounded version of the halting problem is strongly generically NP-complete.
This paper presents a series of general properties of the r-Complexity calculus, a complexity measurement for assessing the performance and asymptotic behaviour of real-world algorithms. This research describes characteristics such as…