scholarly journals A Decomposition Method for Global Evaluation of Shannon Entropy and Local Estimations of Algorithmic Complexity

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 605 ◽  
Author(s):  
Hector Zenil ◽  
Santiago Hernández-Orozco ◽  
Narsis Kiani ◽  
Fernando Soler-Toscano ◽  
Antonio Rueda-Toicen ◽  
...  
Keyword(s):  
Programming Languages ◽  
Shannon Entropy ◽  
Decomposition Method ◽  
Computer Programs ◽  
Algorithmic Complexity ◽  
Maximal Entropy ◽  
Small Computer ◽  
Algorithmic Randomness ◽  
Global Evaluation ◽  
Statistical Regularities

We investigate the properties of a Block Decomposition Method (BDM), which extends the power of a Coding Theorem Method (CTM) that approximates local estimations of algorithmic complexity based on Solomonoff–Levin’s theory of algorithmic probability providing a closer connection to algorithmic complexity than previous attempts based on statistical regularities such as popular lossless compression schemes. The strategy behind BDM is to find small computer programs that produce the components of a larger, decomposed object. The set of short computer programs can then be artfully arranged in sequence so as to produce the original object. We show that the method provides efficient estimations of algorithmic complexity but that it performs like Shannon entropy when it loses accuracy. We estimate errors and study the behaviour of BDM for different boundary conditions, all of which are compared and assessed in detail. The measure may be adapted for use with more multi-dimensional objects than strings, objects such as arrays and tensors. To test the measure we demonstrate the power of CTM on low algorithmic-randomness objects that are assigned maximal entropy (e.g., π ) but whose numerical approximations are closer to the theoretical low algorithmic-randomness expectation. We also test the measure on larger objects including dual, isomorphic and cospectral graphs for which we know that algorithmic randomness is low. We also release implementations of the methods in most major programming languages—Wolfram Language (Mathematica), Matlab, R, Perl, Python, Pascal, C++, and Haskell—and an online algorithmic complexity calculator.

PERANGKAT LUNAK KOMPUTER

2020 ◽  
Author(s):  
Cut Nabilah Damni
Keyword(s):  
Programming Languages ◽  
Programming Language ◽  
Operating Systems ◽  
Source Code ◽  
Computer Software ◽  
Computer Programs ◽  
Application Systems ◽  
Executable Programs

AbstrakSoftware komputer atau perangkat lunak komputer merupakan kumpulan instruksi (program atau prosedur) untuk dapat melaksanakan pekerjaan secara otomatis dengan cara mengolah atau memproses kumpulan intruksi (data) yang diberikan. (Yahfizham, 2019 : 19) Sebagian besar dari software komputer dibuat oleh (programmer) dengan menggunakan bahasa pemprograman. Orang yang membuat bahasa pemprograman menuliskan perintah dalam bahasa pemprograman seperti layaknya bahasa yang digunakan oleh orang pada umumnya dalam melakukan perbincangan. Perintah-perintah tersebut dinamakan (source code). Program komputer lainnya dinamakan (compiler) yang digunakan pada (source code) dan kemudian mengubah perintah tersebut kedalam bahasa yang dimengerti oleh komputer lalu hasilnya dinamakan program executable (EXE). Pada dasarnya, komputer selalu memiliki perangkat lunak komputer atau software yang terdiri dari sistem operasi, sistem aplikasi dan bahasa pemograman.AbstractComputer software or computer software is a collection of instructions (programs or procedures) to be able to carry out work automatically by processing or processing the collection of instructions (data) provided. (Yahfizham, 2019: 19) Most of the computer software is made by (programmers) using the programming language. People who make programming languages write commands in the programming language like the language used by people in general in conducting conversation. The commands are called (source code). Other computer programs called (compilers) are used in (source code) and then change the command into a language understood by the computer and the results are called executable programs (EXE). Basically, computers always have computer software or software consisting of operating systems, application systems and programming languages.

scholarly journals Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 534 ◽  
Author(s):  
Hector Zenil ◽  
Narsis Kiani ◽  
Jesper Tegnér
Keyword(s):  
Algorithmic Complexity ◽  
Information Theoretic ◽  
Algorithmic Probability ◽  
Graphs And Networks ◽  
Algorithmic Information ◽  
Statistical Regularities ◽  
Review Study ◽  
Causal Nature ◽  
Definition Of

We introduce a definition of algorithmic symmetry in the context of geometric and spatial complexity able to capture mathematical aspects of different objects using as a case study polyominoes and polyhedral graphs. We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov–Chaitin complexity) of graphs and networks based on the concept of Algorithmic Probability (AP). AP is a concept (and method) capable of recursively enumerate all properties of computable (causal) nature beyond statistical regularities. We explore the connections of algorithmic complexity—both theoretical and numerical—with geometric properties mainly symmetry and topology from an (algorithmic) information-theoretic perspective. We show that approximations to algorithmic complexity by lossless compression and an Algorithmic Probability-based method can characterize spatial, geometric, symmetric and topological properties of mathematical objects and graphs.

Jurnal PERANGKAT LUNAK KOMPUTER Ayubi Simatupang PMM-1

2020 ◽  
Author(s):  
S Mukhtar Ayubi Simatupang
Keyword(s):  
Programming Languages ◽  
Programming Language ◽  
Source Code ◽  
Computer Software ◽  
Computer Programs ◽  
Computer Hardware ◽  
Executable Programs

Abstrak- Perangkat lunak komputer atau yang sering disebut sebagai (software) mempunyai sifat yang berbeda dengan (hardware) atau perangkat keras komputer. Jika perangkat keras komputer dapat dilihat dan disentuh keberadaannya maka perangkat lunak pada suatu komputer hanya dapat dilihat saja tanpa dapat kita rasa atau raba bendanya. Lebih tepatnya, perangkat lunak tidak dapat disentuh dan memang secara fisik tidak tampak namun kita dapat mengoperasikannya. Namun walaupun tidak tampak secara fisik perangkat lunak sangat berguna dalam pengoperasiannya dengan adanya perangkat lunak suatu komputer dapat menjalankan suatu perintah. Sebagian besar dari software komputer dibuat oleh (programmer) dengan menggunakan bahasa pemprograman. Orang yang membuat bahasa pemprograman menuliskan perintah dalam bahasa pemprograman seperti layaknya bahasa yang digunakan oleh orang pada umumnya dalam melakukan perbincangan. Perintah-perintah tersebut dinamakan (source code). Program komputer lainnya dinamakan (compiler) yang digunakan pada (source code) dan kemudian mengubah perintah tersebut kedalam bahasa yang dimengerti oleh komputer lalu hasilnya dinamakan program executable (EXE).Kata Kunci: Software, ProgrammerAbstac t- Computer software or often referred to as (software) has different properties from (hardware) or computer hardware. If the computer hardware can be seen and touched, then the software on a computer can only be seen without our feeling or feeling. More precisely, the software cannot be touched and it is physically invisible but we can operate it. But even though the software does not appear physically very useful in its operation with the software a computer can run a command. Most of the computer software is made by (programmers) using the programming language. People who make programming languages write commands in the programming language like the language used by people in general in conducting conversation. The commands are called (source code). Other computer programs called (compilers) are used in (source code) and then change the command into a language understood by the computer and the results are called executable programs (EXE).Keywords: Software, Programmer

Logic and Proof in Computer Science

2017 ◽  
pp. 218-240
Author(s):  
John W. Coffey
Keyword(s):  
Computer Science ◽  
Computer Software ◽  
Computer Programs ◽  
Algorithmic Complexity ◽  
Proof Techniques ◽  
Historical Antecedents ◽  
Striking Fact ◽  
The Way

Computer software pervades our lives today. Nevertheless, software is one of the few products for which producers generally provide no express or implied warranties, a truly striking fact since peoples' lives depend in such fundamental ways on these products. This article addresses why such an unintuitive (and undesirable) situation might exist. It will catalog a range of computer science proof techniques and their historical antecedents, the purposes they serve, and several foundational concerns that elude proof techniques of any kind. Along the way, the concept of intractability and its role in computing will be explored as it pertains to algorithmic complexity and to proofs of the meanings of computer programs.

Decomposing a Delta Volume Into Maximal Convex Volumes and Sequencing Them for Machining

1994 ◽  
Author(s):  
Hiroshi Sakurai
Keyword(s):  
Computer Program ◽  
Decomposition Method ◽  
Complex Shape ◽  
Raw Material ◽  
Small Computer ◽  
Machining Efficiency ◽  
Finished Part ◽  
Volume Difference

Abstract A method has been developed to decompose a polyhedral delta volume, which is the volume difference between the raw material and the finished part, into maximal convex volumes by intersecting the halfspaces of the faces of the delta volume. The hypothesis behind this effort is that in machining a delta volume of complex shape it is more efficient to divide it into volumes of simple shapes and remove volume by volume with large cutters than to remove it as a single volume with a single small cutter. The maximality of a maximal convex volume represents the possibility of using a large cutter and its convexity represents the simplicity of the shape of the volume. To prove the utility of maximal convex volumes, a small computer program was developed that sequences the maximal convex volumes based on a few heuristics on machining efficiency and tested it with a few objects. It generated good machining sequences. The basic idea of the decomposition method is to intersect a polyhedral delta volume with the halfspaces of its faces having concave edges. The combinations of such halfspaces that result in maximal convex volumes when they are intersected with the delta volume are determined efficiently by examining the relationships among the halfspaces. This basic idea works well for polyhedral delta volumes but does not work for delta volumes having curved faces since curved faces cannot always be extended infinitely. To cope with the delta volumes having cylindrical faces, a separate decomposition method has been developed. This method works only for the delta volumes that can be decomposed into 2½D machining volumes.

Human Factors Aspects of Digital Computer Programming for Simulator Control

1965 ◽  
Vol 7 (5) ◽  
pp. 473-482
Author(s):  
Gilbert J. Spesock ◽  
Robert S. Lincoln
Keyword(s):  
Human Factors ◽  
Real Time ◽  
Program Development ◽  
Digital Computer ◽  
Computer Programming ◽  
Computer Programs ◽  
Small Computer ◽  
Simulation Methodology ◽  
Display Control ◽  
Significant Application

Because of the enormous present day effort devoted to the preparation of digital computer programs, special attention should be given to the human factors aspects of program development. Currently available program compilers represent a significant application of certain human factors principles, but are not generally applicable to problems of “real time” programming. Since the creation of appropriate compilers is important to simulation methodology, this report includes a detailed description of a “real time” compiler developed for display/control simulation on a small computer in a human factors laboratory.

Algorithmic complexity of points in dynamical systems

1993 ◽  
Vol 13 (4) ◽  
pp. 807-830 ◽  
Author(s):  
Homer S. White
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Topological Entropy ◽  
Invariant Probability Measure ◽  
Algorithmic Complexity ◽  
Maximal Entropy ◽  
Property A ◽  
Open Set ◽  
Unique Measure ◽  
Set Of Points

AbstractThis work is based on the author's dissertation. We examine the algorithmic complexity (in the sense of Kolmogorov and Chaitin) of the orbits of points in dynamical systems. Extending a theorem of A. A. Brudno, we note that for any ergodic invariant probability measure on a compact dynamical system, almost every trajectory has a limiting complexity equal to the entropy of the system. We use these results to show that for minimal dynamical systems, and for systems with the tracking property (a weaker version of specification), the set of points whose trajectories have upper complexity equal to the topological entropy is residual. We give an example of a topologically transitive system with positive entropy for which an uncountable open set of points has upper complexity equal to zero. We use techniques from universal data compression to prove a recurrence theorem: if a compact dynamical system has a unique measure of maximal entropy, then any point whose lower complexity is equal to the topological entropy is generic for that unique measure. Finally, we discuss algorithmic versions of the theorem of Kamae on preservation of the class of normal sequences under selection by sequences of zero Kamae-entropy.

PERANGKAT LUNAK KOMPUTER

2020 ◽  
Author(s):  
Cut Nabilah Damni
Keyword(s):  
Programming Languages ◽  
Programming Language ◽  
Operating Systems ◽  
Source Code ◽  
Computer Software ◽  
Computer Programs ◽  
Executable Programs

AbstrakSoftware komputer atau perangkat lunak komputer merupakan kumpulan instruksi (program atau prosedur) untuk dapat melaksanakan pekerjaan secara otomatis dengan cara mengolah atau memproses kumpulan intruksi (data) yang diberikan. (Yahfizham, 2019 : 19) Sebagian besar dari software komputer dibuat oleh (programmer) dengan menggunakan bahasa pemprograman. Orang yang membuat bahasa pemprograman menuliskan perintah dalam bahasa pemprograman seperti layaknya bahasa yang digunakan oleh orang pada umumnya dalam melakukan perbincangan. Perintah-perintah tersebut dinamakan (source code). Program komputer lainnya dinamakan (compiler) yang digunakan pada (source code) dan kemudian mengubah perintah tersebut kedalam bahasa yang dimengerti oleh komputer lalu hasilnya dinamakan program executable (EXE). Pada dasarnya, komputer selalu memiliki perangkat lunak komputer atau software yang terdiri dari sistem operasi, sistem aplikasi dan bahasa pemograman.AbstractComputer software or computer software is a collection of instructions (programs or procedures) to be able to carry out work automatically by processing or processing the collection of instructions (data) provided. (Yahfizham, 2019: 19) Most of the computer software is made by (programmers) using the programming language. People who make programming languages write commands in the programming language like the language used by people in general in conducting conversation. The commands are called (source code). Other computer programs called (compilers) are used in (source code) and then change the command into a language understood by the computer and the results are called executable programs (EXE). Basically, computers always have computer software or software consisting of operating systems, ap

The Long History of Software Patenting in the United States

2021 ◽  
pp. 278-318
Author(s):  
Gerardo Con Díaz
Keyword(s):  
United States ◽  
Programming Languages ◽  
Computer Programs ◽  
The United States ◽  
Electronic Components ◽  
Electronic Computing ◽  
History Of ◽  
Patent Applications

The patent protections available to computer programs are almost as old as modern electronic computing. In the late 1940s and early 1950s, when a computer’s programming was as tangible as the machine’s circuits, there was nothing unusual about the idea that a patent could protect a program. The main problem was not whether programs were patent-eligible but how to draft patent applications for them that could bypass well-established doctrinal obstacles. As programs increased in complexity and programming languages enabled their creation through texts, inventors and their lawyers relied on the means-plus claim structure—a claim that discloses a machine as the means to perform a given collection of functions—as a shorthand to disclose the kinds of physicality that their predecessors would have spelled out. Successful patent applications combined means-plus language with very specific descriptions of interconnected electronic components to secure patent protections for the computer programs at their core.

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