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We define a notion of complexity, which quantifies the nonlinearity of the computation of a neural network, as well as a complementary measure of the effective dimension of feature representations. We investigate these observables both for…

Machine Learning · Computer Science 2021-03-18 Romuald A. Janik , Przemek Witaszczyk

Probabilistic program analysis aims to quantify the probability that a given program satisfies a required property. It has many potential applications, from program understanding and debugging to computing program reliability, compiler…

Programming Languages · Computer Science 2017-09-08 Aleksandar S. Dimovski

Program comprehension concerns the ability of an individual to make an understanding of an existing software system to extend or transform it. Software systems comprise of data that are noisy and missing, which makes program understanding…

Software Engineering · Computer Science 2019-02-05 Amir Saeidi , Jurriaan Hage , Ravi Khadka , Slinger Jansen

This paper proposes a theory of encapsulation, establishing a relationship between encapsulation and information hiding through the concept of potential structural complexity (P.S.C.), the maximum possible number of source code dependencies…

Software Engineering · Computer Science 2008-07-29 Edmund Kirwan

Software testing is a complex, intellectual activity based (at least) on analysis, reasoning, decision making, abstraction and collaboration performed in a highly demanding environment. Naturally, it uses and allocates multiple cognitive…

Software Engineering · Computer Science 2020-12-10 Eduard Enoiu , Gerald Tukseferi , Robert Feldt

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…

Computational Complexity · Computer Science 2023-01-10 Chuyu Xiong

Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or…

Other Computer Science · Computer Science 2021-10-05 Luciano da F. Costa , Guilherme S. Domingues

While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…

Computational Complexity · Computer Science 2018-01-23 Akitoshi Kawamura , Martin Ziegler

When writing programs, people have the ability to tackle a new complex task by decomposing it into smaller and more familiar subtasks. While it is difficult to measure whether neural program synthesis methods have similar capabilities, what…

Machine Learning · Computer Science 2023-10-31 Kensen Shi , Joey Hong , Manzil Zaheer , Pengcheng Yin , Charles Sutton

There is a cognitive limit in Human Mind. This cognitive limit has played a decisive role in almost all fields including computer sciences. The cognitive limit replicated in computer sciences is responsible for inherent Computational…

Other Computer Science · Computer Science 2022-12-22 Asad Malik

In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…

Logic in Computer Science · Computer Science 2014-02-25 Dusko Pavlovic

Measuring software complexity plays an important role to meet the demands of complex software. The cyclomatic complexity is one of most used and renowned metric among the other three proposed and researched metrics that are namely: Line of…

Software Engineering · Computer Science 2014-12-22 Ankita Garg

Multivariate information theory provides a general and principled framework for understanding how the components of a complex system are connected. Existing analyses are coarse in nature -- built up from characterizations of discrete…

Information Theory · Computer Science 2025-05-30 Kieran A. Murphy , Yujing Zhang , Dani S. Bassett

Mathematical Program Networks (MPNs) are introduced in this work. An MPN is a collection of interdependent Mathematical Programs (MPs) which are to be solved simultaneously, while respecting the connectivity pattern of the network defining…

Optimization and Control · Mathematics 2024-04-24 Forrest Laine

The theory of asymptotic complexity provides an approach to characterizing the behavior of programs in terms of bounds on the number of computational steps executed or use of computational resources. We describe work using ACL2 to prove…

Computational Complexity · Computer Science 2022-05-25 William D. Young

Defining process standards by integrating, harmonizing, and standardizing heterogeneous and often implicit processes is an important task, especially for large development organizations. However, many challenges exist, such as limiting the…

Software Engineering · Computer Science 2014-02-03 Ove Armbrust , Masafumi Katahira , Yuko Miyamoto , Jürgen Münch , Haruka Nakao , Alexis Ocampo

In computability theory and computable analysis, finite programs can compute infinite objects. Presenting a computable object via any program for it, provides at least as much information as presenting the object itself, written on an…

Logic in Computer Science · Computer Science 2014-09-25 Mathieu Hoyrup , Cristobal Rojas

A program is usually represented as a word chain. It is exactly a word chain that appears as the lexical analyzer output and is parsed. The work shows that a program can be syntactically represented as an oriented word tree, that is a…

Programming Languages · Computer Science 2012-03-23 Alex Shkotin

Complex software systems are among most sophisticated human-made systems, yet only little is known about the actual structure of 'good' software. We here study different software systems developed in Java from the perspective of network…

Social and Information Networks · Computer Science 2013-05-24 Lovro Šubelj , Marko Bajec

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.…

Data Analysis, Statistics and Probability · Physics 2013-01-18 Eugene Perevalov , David Grace