Computer Engineering Commons^™

Towards The Use Of Aesthetics In Decision Making: Kolmogorov Complexity Formalizes Birkhoff's Idea, Misha Kosheleva, Vladik Kreinovich, Yeung Yam

Departmental Technical Reports (CS)

Decision making is traditionally based on utilitarian criteria such as cost, efficiency, time, etc. These criteria are reasonably easy to formalize; hence, for such criteria, we can select the best decision by solving the corresponding well-defined optimization problem. In many engineering projects, however, e.g., in designing cars, building, airplanes, etc., an important additional criterion which needs to be satisfied is that the designed object should be good looking. This additional criterion is difficult to formalize and, because of that, it is rarely taken into consideration in formal decision making. In the 1930s, the famous mathematician G. D. Birkhoff has proposed …

Encryption Algorithms Made (Somewhat) More Natural (A Pedagogical Remark), Misha Kosheleva, Vladik Kreinovich, Luc Longpre

Departmental Technical Reports (CS)

Modern cryptographic algorithms, such as DES, IDEA, etc., are very complex and therefore difficult to learn. Textbooks explain in detail how these algorithms work, but they usually do not explain why these algorithms were designed as they were. In this paper, we explain why, and thus, hopefully, make cryptographic algorithms easier to learn.

An Operationalistic Reformulation Of Einstein's Equivalence Principle, Vladik Kreinovich, R. R. Zapatrine

Departmental Technical Reports (CS)

No abstract provided.

On How To Merge Sorted Lists Coming From Different Web Search Tools, Ronald R. Yager, Vladik Kreinovich

Departmental Technical Reports (CS)

Different web search tools often complement each other. So, if we want to have a good coverage of all relevant web items, a reasonable strategy is to use different search tools and then merge the resulting lists. How to merge them? In this paper, we describe reasonable axioms for the merging procedure and describe all mergings that satisfy these reasonable axioms.

Optimal Choices Of Potential Functions In Fuzzy Clustering, Vladik Kreinovich, Hung T. Nguyen, Yeung Yam

Departmental Technical Reports (CS)

Fuzzy logic-based clustering techniques are widely used in situations where statistical assumptions are not valid. Whether in estimating cluster centers for model identification purposes or in determining clusters the existing techniques are essentially based upon the choice of some potential functions. As in any design problems of this kind, the choice of such a function has to be justified on a theoretical basis. In this work, we set up a decision frame work and show that optimal potential functions are the ones which are used in current techniques.

Human Visual Perception And Kolmogorov Complexity: Revisited, Vladik Kreinovich, Luc Longpre

Departmental Technical Reports (CS)

Experiments have shown that we can only memorize images up to a certain complexity level, after which, instead of memorizing the image itself, we, sort of, memorize a probability distribution in terms of which this image is "random" (in the intuitive sense of this word), and next time, we reproduce a "random" sample from this distribution. This random sample may be different from the original image, but since it belongs to the same distribution, it, hopefully, correctly reproduces the statistical characteristics of the original image.

The reason why a complex image cannot be accurately memorized is, probably, that our memory …

Run-Time Correctness Checking Is Algorithmically Undecidable For Pointer Data Structures, Mikhail Auguston, Vladik Kreinovich, Luc Longpre

Departmental Technical Reports (CS)

Programs routinely use complicated pointer (linked list-type) data structures such as linked lists, doubly linked lists, different types of trees, etc. These data structures are usually defined {\it inductively}: e.g., a tree can be defined as a structure that results from an empty tree by an arbitrary sequence of adding and deleting elements.

When the program runs, these data structures take dynamically changing shapes. To test program correctness, it is important to check, at run-time, whether a current shape is a correct implementation of the corresponding structure. Algorithms are known for checking the ``shape correctness'' for basic pointer-based data structures …

Telemanipulation: The Virtual Tool Approach And Its Interval-Based Justification, Vladik Kreinovich, Luic Olac Fuentes

Departmental Technical Reports (CS)

No abstract provided.

Application Of Kolmogorov Complexity To Image Compression: It Is Possible To Have A Better Compression, But It Is Not Possible To Have The Best One, Sanjeev Subbaramu, Ann Q. Gates, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Oo Or Not Oo: When Object-Oriented Is Better. Qualitative Analysis And Application To Satellite Image Processing, Ann Q. Gates, Leticia Sifuentes, Scott A. Starks

Departmental Technical Reports (CS)

No abstract provided.

Strong Negation: Its Relation To Intervals And Its Use In Expert Systems, Scott A. Starks, Vladik Kreinovich, Hung T. Nguyen, Hoang Phuong Nguyen, Mirko Navara

Departmental Technical Reports (CS)

No abstract provided.

Complexity Of Collective Decision Making Explained By Neural Network Universal Approximation Theorem, Raul A. Trejo, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Interval Approach To Non-Destructive Testing Of Aerospace Structures And To Mammography, Keith Worden, Roberto A. Osegueda, Carlos M. Ferregut, Soheil Nazarian, Eulalio Rodriguez, Debra L. George, Mary J. George, Vladik Kreinovich, Olga Kosheleva, Sergio Cabrera

Departmental Technical Reports (CS)

No abstract provided.

Alps: A Logic For Program Synthesis (Motivated By Fuzzy Logic), Daniel E. Cooke, Vladik Kreinovich, Scott A. Starks

Departmental Technical Reports (CS)

One of the typical problems in engineering and scientific applications is as follows: we know the values x1,...,xn of some quantities, we are interested in the values of some other quantities y1,...,ym, and we know the relationships between xi, yj, and, maybe, some auxiliary physical quantities z1,...,zk. For example, we may know an algorithm to compute y2 from x_1, x3, and y1; we may also know an equation F(x1,x2,y1)=0 that relates these values, etc. The question is: can we compute the values of yj, and, if we can, how to do it?

At first glance, this is a problem of …

A Modification Of Sugeno Integral Describes Stability And Smoothness Of Fuzzy Control, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

Sugeno integral was invented a few decades ago as a natural fuzzy analogue of the classical integral. Sugeno integral has many interesting applications. It is reasonable to expect that it can be used in all application areas where classical integrals are used, and in many such areas it is indeed useful. Surprisingly, however, it has never been used in fuzzy control, although in traditional control, classical integral is one of the main tools.

In this paper, we show that the appropriately modified Sugeno integral is indeed useful for fuzzy control: namely, it provides numerical characterization of stability and smoothness of …

Where To Bisect A Box? A Theoretical Explanation Of The Experimental Results, Vladik Kreinovich, R. Baker Kearfott

Departmental Technical Reports (CS)

No abstract provided.

Ordinal Explanation Of The Periodic System Of Chemical Elements, Eric R. Scerri, Vladik Kreinovich, Piotr Wojciechowski, Ronald R. Yager

Departmental Technical Reports (CS)

Textbooks often claim that quantum mechanics explained the periodic system: namely, the actual configuration of electronic orbits that is responsible for the element's chemical properties can be described as the one that minimizes the total energy, and the energy of each configuration can be computed by using quantum mechanics.

However, a careful analysis of this explanation reveals that, in addition to the basic equations of quantum mechanics, we need some heuristic rules that do not directly follow from quantum physics. One reason why additional heuristics are necessary is that the corresponding numerical equations are extremely difficult to solve, and as …

On Geometry Of Radio Antenna Placements, Olga Kosheleva, Vladik Kreinovich, Andrei M. Finkelstein, Steve Chan

Departmental Technical Reports (CS)

No abstract provided.

Coincidences Are Not Accidental: A Theorem, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we formalize and prove the statement that coincidences cannot be accidental, a statement that underlies many useful heuristics in mathematics and physics.

Our proof uses a version of Kolmogorov complexity, a technique originally developed to describe randomness and "accidentalness".

Why Kolmogorov Complexity In Physical Equations, Vladik Kreinovich, Luc Longpre

Departmental Technical Reports (CS)

Several researchers, including M. Gell-Mann, argue that the notion of Kolmogorov complexity, developed in the algorithmic information theory, is useful in physics (i.e., in the description of the physical world). Their arguments are rather convincing, but there seems to be a gap between traditional physical equations and Kolmogorov complexity: namely, it is not clear how the standard equations of physics can lead to algorithmic notions underlying Kolmogorov complexity. In this paper, this "gap" is bridged: we explain how Kolmogorov complexity naturally appear in physical equation.

From Fuzzification And Intervalization To Anglification: A New 5d Geometric Formalism For Physics And Data Processing, Scott A. Starks, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Spinal Cord Stimulation For Chronic Pain Management: Towards An Expert System, Kenneth M. Alo, Richard Alo, Andre De Korvin, Vladik Kreinovich

Departmental Technical Reports (CS)

Chronic pain is a serious health problem affecting millions of people worldwide. Currently, spinal cord simulation is one of the most effective methods of easing the chronic pain. For most patients, a careful selection of weak electric currents enables to drastically decrease the pain level. The first devices offered only a few possible regimes, and it was possible to choose an appropriate regime simply by exhaustive search. Continuous engineering progress leads to more and more flexible devices that offer a wide variety of millions of possible simulation regimes. With this variety, it is no longer possible to test all of …

From Expert Words Directly To Numerical Simulations: Group-Theoretic Approach To Computing With Words In Information/Intelligent Systems, Vladik Kreinovich, Brian Penn, Scott A. Starks

Departmental Technical Reports (CS)

In many real-life situations, e.g., when making an environmental decision, it is important to be able to predict long-term consequences of different decisions. Very often, these predictions must be done in the situation where the only available information consists of expert rules, which are formulated by words from natural language. One possible way to transform these expert words into numerical simulation (leading to prediction) is to use the fuzzy control methodology. However, there is a problem with using this methodology: it invokes replacing each word by a membership function, and this replacement drastically increases the required computer space (and thus, …

Identification And Classification Of Inconsistency In Relationship To Software Maintenance, Daniel Cooke, Luqi, Vladik Kreinovich

Departmental Technical Reports (CS)

This paper provides an overview of the relationship between recent work in logic programming and recent developments in software engineering. The relationship to software engineering is more specifically concerned with how formal specifications can be used to explain and represent the basis of software maintenance and evolution. Some of the results reviewed here have appeared in our previous papers. These previous results are summarized, extended, and made more general in this paper.

Strict Achimedean T-Norms And T-Conorms As Universal Approximators, Hung T. Nguyen, Vladik Kreinovich, Piotr Wojciechowski

Departmental Technical Reports (CS)

In knowledge representation, when we have to use logical connectives, various continuous t-norms and t-conorms are used. In this paper, we show that every continuous t-norm and t-conorm can be approximated, to an arbitrary degree of accuracy, by a strict Archimedean t-norm (t-conorm).

Computational Geometry And Artifical Neural Networks: A Hybrid Approach To Optimal Sensor Placement For Aerospace Nde, Roberto A. Osegueda, Carlos M. Ferregut, Mary J. George, Jose M. Gutierrez, Vladik Kreinovich

Departmental Technical Reports (CS)

The ideal design of an airplane should include built-in sensors that are pre-blended in the perfect aerodynamic shape. Each built-in sensor is expensive to blend in and requires continuous maintenance and data processing, so we would like to use as few sensors as possible. The ideal formulation of the corresponding optimization problem is, e.g., to minimize the average detection error for fault locations. However, there are two obstacles to this ideal formulation:

--First, this ideal formulation requires that we know the probabilities of different fault locations etc., and there are usually not enough statistics to determine these probabilities.

--Second, even …

The Challenge Of Hyper-Spectral Satellite Imaging And Integer-Valued Fuzzy Sets, Maria Beltran, Vladik Kreinovich, Scott A. Starks

Departmental Technical Reports (CS)

Satellite images already produce huge amounts of data, which makes their processing a serious computational challenge. This problem will become even more complicated with the launch of multi-spectral Earth-imaging satellites that will increase the amount of information by at least two orders of magnitude. With such a huge amount of information, it is necessary to come up with data processing methods that are as fast as possible. In particular, we show that for fuzzy processing techniques, this leads to the necessity to use integer-valued fuzzy sets.

Sensor Placement For Aerospace Non-Destructive Evaluation (Nde): Optimization Under Fuzzy Uncertainty, Roberto A. Osegueda, Carlos M. Ferregut, Mary J. George, Jose M. Gutierrez, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Which Algorithms Are Feasible? Maxent Approach, Daniel E. Cooke, Vladik Kreinovich, Luc Longpre

Departmental Technical Reports (CS)

It is well known that not all algorithms are feasible; whether an algorithm is feasible or not depends on how many computational steps this algorithm requires. The problem with the existing definitions of feasibility is that they are rather ad hoc. Our goal is to use the maximum entropy (MaxEnt) approach and get more motivated definitions.

If an algorithm is feasible, then, intuitively, we would expect the following to be true:

If we have a flow of problems with finite average length L, then we expect the average time T to be finite as well.

Thus, we can say …

We Must Choose The Simplest Physical Theory: Levin-Li-Vitanyi Theorem And Its Potential Physical Applications, Dirk Fox, Martin Schmidt, Misha Kosheleva, Vladik Kreinovich, Luc Longpre, Jeff Kuhn

Departmental Technical Reports (CS)

If several physical theories are consistent with the same experimental data, which theory should we choose? Physicists often choose the simplest theory; this principle (explicitly formulated by Occam) is one of the basic principles of physical reasoning. However, until recently, this principle was mainly a heuristic because it uses the informal notion of simplicity.

With the explicit notion of simplicity coming from the Algorithmic Information theory, it is possible not only to formalize this principle in a way that is consistent with its traditional usage in physics, but also to prove this principle, or, to be more precise, deduce it …