-
Discrete Mathematics in a Nutshell or Theoretical Foundations of Computer Science
Yuliya Lierler
Contents 1. Basic Structures: Sets, Function, Sequences, Sums 4 1.1. Sets Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2. Sets Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3. Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4. Sequences and Summations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2. Elements of Mathematica Logic and Proofs 15 2.1. Syntax and Semantics of Propositional Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2. Tautologies, Equivalence, Satisfiability and Entailment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3. Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4. Elements of Predicate Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5. Predicate Logic, Formally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.6. Elements of Mathematical Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3. Growth of Functions 38 3.1. Calculus Notion of Function Growth Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2. Big-O Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4. Elements on Algorithms and the Complexity 42 4.1. Algorithms and their Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.2. Time Complexity of Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5. Induction and Recursive Definitions 45 5.1. Proofs by Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.2. Strong and Structural Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 6. Recursive Definitions 51 7. Counting 54 7.1. The Product Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 7.2. The Sum Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 7.3. The Pigeonhole Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 7.4. Premutation and Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 8. Relations 58 8.1. Relations and their Kinds: Reflexive, Symmetric, Transitive . . . . . . . . . . . . . . . . . . . . . . . . . 58 8.2. Equivalence Relations and Partitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 9. Graphs 61 9.1. Undirected Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 9.2. Directed Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 10. Elements on Proving Partial Correctness of Programs 63
-
Handout on Algorithms in Backtracking Search behind SAT and ASP
Yuliya Lierler
We now turn out attention to search algorithms underlying ASP technology. In particular, we will focus on the techniques employed by answer set solver such as clasp. Recall that clasp is only one building block of an answer set system clingo that also incorporates grounder called gringo. In the scope of this course we ignore the details behind grounders, but note that these are highly nontrivial systems solving a complex and computationally intense task of intelligent instantiation. The algorithms behind majority answer set solvers fall into group of so called backtracking search algorithms. Backtracking is a general algorithm for finding all (or some) solutions to some computational problem, that incrementally builds candidates to the solutions, and abandons each partial candidate c (”backtracks”) as soon as it determines that c cannot possibly be completed to a valid solution. (Wikipedia) The Davis-Putnam-Logemann-Loveland (DPLL) procedure is a classic example of backtracking search algorithms. DPLL is a method for deciding the satisfiability of propositional logic formula in conjunctive normal form, or, in other words, for solving the propositional satisfiability problem. Algorithms used by answer set solvers share a lot in common with DPLL. In this handout, we thus begin by presenting DPLL procedure. We then discuss its extensions suitable for computing answer sets of a program in place.
-
Handout on Answer Set Programming Paradigm
Yuliya Lierler
Answer set programming paradigm (ASP) is a form of declarative programming oriented towards difficult combinatorial search problems. It belongs to the group of so called constraint programming languages. The idea of ASP is to represent a given computational problem by a program whose answer sets correspond to solutions, and then use an answer set solver to generate answer sets for this program. In this note we discuss the methodology of answer set programming as well as the use of software systems for computing answer sets. First, a graph coloring problem is utilized to illustrate the use of answer set programming in practice. Then, solutions to Hamiltonian cycle and to n-queens problems are presented. Across the handout you are given problems to solve. This handout is self-contained: you are given all the definitions and links that are required in constructing solutions. In the text italics is primarily used to identify concepts that are being defined. Some definitions are identified by the word Definition. In this course we will use the answer set system clingo1 that incorporates answer set solver clasp1 with its front-end grounder gringo1 (user guide is available online at https://sourceforge.net/projects/potassco/ files/guide/2.0/guide-2.0.pdf/download). You may access system clingo via web interface available at https://potassco.org/clingo/run/ or download an executable for clingo version 5 from the url listed at footnote 1. Answer set programming practitioners develop applications that rely on ASP languages, which allow variables. Yet, common ASP solvers, including clasp (a subsystem of clingo) process propositional logic programs only. We now re-introduce such programs and restate the definition of an answer set in the form convenient for this part of the course.
-
Handout on Basics behind Answer Sets
Yuliya Lierler
Answer set programming (ASP) is a form of declarative programming oriented towards modeling i intelligent agents in knowledge representation and reasoning and ii difficult combinatorial search problems. It belongs to the group of so called constraint programming languages. ASP has been applied to a variety of applications including plan generation and product configuration problems in artificial intelligence and graph-theoretic problems arising in VLSI design and in historical linguistics [1]. Syntactically, ASP programs look like logic programs in Prolog, but the computational mechanisms used in ASP are different: they are based on the ideas stemming from the development of satisfiability solvers for propositional logic. This document presents the concept of an answer set for programs in their simplest form: no variables, no classical negation symbol, no disjunction in the heads of rules. The textbooks [?, 2] provide an account for general definition of this concept that assumes rules of the general form that includes all the features mentioned above. Yet, it is useful to first consider as simple programs as possible to build intuitions about answer sets. In this note italics is primarily used to identify concepts that are being defined. Some definitions are identified by the word Definition.
-
Digital Media in Teaching and its Added Value
David F. Conway, Stephanie A. Hillen, Melodie Landis, Mary T. Schlegelmilch, Peter Wolcott, Deepak Khazanchi, Bjørn Erik Munkvold, Aleksandra Lazareva, Jeanne L. Surface, Mary T. Schlegelmilch, Phyllis K. Adcock, Victor L. Winter, Paul J.A. van Vliet, and Jeremy Harris Lipschultz
Editors: David F. Conway (UNO faculty member), Stefanie Hillen, Melodee Landis, Mary T. Schlegelmilch, Peter Wolcott (UNO faculty member)
Chapter, The Value of Investigating Information Technology Applications for Teaching and Learning Purposes, co-authored by David F. Conway and Peter Wolcott, UNO faculty members.
Chapter, Towards a Contingency Theory of eLearning, co-authored by Deepak Khazanchi, UNO faculty member.
Chapter, Collaborative Technologies and Digital Media in Teaching and Learning: Starting Small and Learning Along the Way, co-authored by Jeanne Surface and Phyllis Adcock, UNO faculty members.
Chapter, Information Technology for Development: Service Learning from Classroom to Community and Back Again, co-authored by Peter Wolcott, UNO faculty member.
Chapter, The World Needs More Computer Science! What to do?, authored by Victor Winter, UNO faculty member.
Chapter, Building an Online Systems Development Course – Experiences with Content and Interaction Design, authored by Paul J. A. van Vliet UNO faculty member.
Chapter, Social Media Communication in the Classroom: A Pedagogical Case Study of Social Network Analysis, authored by Jeremy Harris Lipschultz, UNO faculty member.
This book project was initiated in fall 2013 at the University of Nebraska at Omaha (UNO), Nebraska during a Global Engagement Research and Teaching Workshop between faculty from UNO and the University of Agder (UiA), Norway.
The anthology presents articles that center on the application of digital technologies that add value to the teaching and learning process in a globalized context. The unique focus of the book is the intersection between pedagogy and technology, specifically the innovative use of technology to improve higher education teaching and learning. With the increased mobility of faculty and students, more diversity among our students and faculty, increased cross-disciplinary designs, alternative environments enabled by technology, and greater demand from the millennial generation for increased access and flexibility, it is important to share accounts where technology has made a positive impact on the instructional process.
Topics that are discussed are local studies with implications for the global environment and the innovative use of technology to improve higher education teaching and learning.
The target audiences for the book are researchers, teachers and stakeholders in learning organizations interested in using IT for teaching and learning. -
Bioinformatics and Biomedical Engineering
Francisco Ortuño, Ignacio Rojas, Kathryn Dempsey Cooper, Sachin Pawaskar, and Hesham Ali
Editors: Francisco Ortuño, Ignacio Rojas
Chapter, Identification of Biologically Significant Elements Using Correlation Networks in High Performance Computing Environments, co-authored by Kathryn Dempsey Cooper, Sachin Pawaskar, and Hesham Ali, UNO faculty members.
The two volume set LNCS 9043 and 9044 constitutes the refereed proceedings of the Third International Conference on Bioinformatics and Biomedical Engineering, IWBBIO 2015, held in Granada, Spain in April 2015. The 134 papers presented were carefully reviewed and selected from 268 submissions. The scope of the conference spans the following areas: bioinformatics for healthcare and diseases, biomedical engineering, biomedical image analysis, biomedical signal analysis, computational genomics, computational proteomics, computational systems for modelling biological processes, eHealth, next generation sequencing and sequence analysis, quantitative and systems pharmacology, Hidden Markov Model (HMM) for biological sequence modeling, advances in computational intelligence for bioinformatics and biomedicine, tools for next generation sequencing data analysis, dynamics networks in system medicine, interdisciplinary puzzles of measurements in biological systems, biological networks, high performance computing in bioinformatics, computational biology and computational chemistry, advances in drug discovery and ambient intelligence for bio emotional computing.
-
Optimization and Security Challenges in Smart Power Grids
Vijay Pappu, Marco Carvalho, Panos M. Pardalos, William Sousan, Qiuming Zhu, Robin Ghandi, and William Mahoney
Editors: Vijay Pappu, Marco Carvalho, Panos Pardalos
Chapter, Smart Grid Tamper Detection using Learned Event Patterns, co-authored by William L. Sousan, Qiuming Zhu, and William Mahoney, UNO faculty members.
This book provides an overview of state-of-the-art research on “Systems and Optimization Aspects of Smart Grid Challenges.” The authors have compiled and integrated different aspects of applied systems optimization research to smart grids, and also describe some of its critical challenges and requirements.
The promise of a smarter electricity grid could significantly change how consumers use and pay for their electrical power, and could fundamentally reshape the current Industry. Gaining increasing interest and acceptance, Smart Grid technologies combine power generation and delivery systems with advanced communication systems to help save energy, reduce energy costs and improve reliability. Taken together, these technologies support new approaches for load balancing and power distribution, allowing optimal runtime power routing and cost management. Such unprecedented capabilities, however, also present a set of new problems and challenges at the technical and regulatory levels that must be addressed by Industry and the Research Community.
-
Correct Reasoning: Essays on Logic-Based AI in Honour of Vladimir Lifschitz
Esta Erdem, Joohyung Lee, Yuliya Lierler, and David Pearce
Co-edited by Yuliya Lierler, UNO faculty member.
Essay, Parsing Combinatory Categorial Grammar via Planning in Answer Set Programming, co-authored by Yuliya Lierler, UNO faculty member.
This Festschrift published in honor of Vladimir Lifschitz on the occasion of his 65th birthday presents 39 articles by colleagues from all over the world with whom Vladimir Lifschitz had cooperation in various respects. The 39 contributions reflect the breadth and the depth of the work of Vladimir Lifschitz in logic programming, circumscription, default logic, action theory, causal reasoning and answer set programming.
-
Parsing Combinatory Categorial Grammar via Planning in Answer Set Programming
Yuliya Lierler and Peter Schueller
Essay, Parsing Combinatory Categorial Grammar via Planning in Answer Set Programming, from Correct reasoning: essays on logic-based AI in honour of Vladimir Lifschitz, co-authored by Yuliya Lierler, UNO faculty member. Combinatory categorial grammar (CCG) is a grammar formalism used for natural language parsing. CCG assigns structured lexical categories to words and uses a small set of combinatory rules to combine these categories to parse a sentence. In this work we propose and implement a new approach to CCG parsing that relies on a prominent knowledge representation formalism, answer set programming (ASP) - a declarative programming paradigm. We formulate the task of CCG parsing as a planning problem and use an ASP computational tool to compute solutions that correspond to valid parses. Compared to other approaches, there is no need to implement a specific parsing algorithm using such a declarative method. Our approach aims at producing all semantically distinct parse trees for a given sentence. From this goal, normalization and efficiency issues arise, and we deal with them by combining and extending existing strategies. We have implemented a CCG parsing tool kit - AspCcgTk - that uses ASP as its main computational means. The C&C supertagger maybe used as a preprocessor within AspCcgTk that allows us to achieve wide-coverage natural language parsing.
-
Handbook of Knowledge Representation
Frank Van Harmelen, Vladimir Lifschitz, Bruce Porter, and Yuliya Lierler
Chapter 20, Knowledge Representation and Question Answering, co-authored by Yuliya Lierler, UNO faculty member.
Knowledge Representation, which lies at the core of Artificial Intelligence, is concerned with encoding knowledge on computers to enable systems to reason automatically. The Handbook of Knowledge Representation is an up-to-date review of twenty-five key topics in knowledge representation, written by the leaders of each field.
This book is an essential resource for students, researchers and practitioners in all areas of Artificial Intelligence.
* Make your computer smarter
* Handle qualitative and uncertain information
* Improve computational tractability to solve your problems easily -
The IEBM Handbook of Information Technology in Business
Milan Zeleny and Qiuming Zhu
Editor: Milan Zeleny
Chapter, Face Recognition, authored by Qiuming Zhu, UNO faculty member
Chapter, Voice Recognition, authored by Qiuming Zhu, UNO faculty member
Chapter, Computer Vision, authored by Qiuming Zhu, UNO faculty member
Information technology and management information systems are assuming an ever greater importance in the arena of business and management. Traditional areas of the work place are being redefined while MIS and IT are becoming the most potent productive forces and sources of competitive advantage. "The IEBM Handbook of IT in Business" explains these new developments and puts them into the wider business context. Coverage includes clear explanations of the new technological developments in the business world, how and why they are being applied, and the new strategies and infrastructures involved.
-
Foundations of Intelligent Systems
Zbigniew W. Ras, Andrzej Skowron, Qiuming Zhu, and Z. Chen
Editors: Zbigniew W. Ras and Andrzej Skowron
Chapter, Knowledge Discovery from Databases with the Guidance of a Causal Network, co-authored by Qiuming Zhu, UNO faculty member
This book constitutes the refereed proceedings of the 10th International Symposium on Methodologies for Intelligent Systems, ISMIS'97, held in Charlotte, NC, USA, in October 1997. The 57 revised full papers were selected from a total of 117 submissions. Also included are four invited papers. Among the topics covered are intelligent information systems, approximate reasoning, evolutionary computation, knowledge representation and integration, learning and knowledge discovery, AI-Logics, discovery systems, data mining, query processing, etc.
-
Computer Graphics 1987: Proceedings of CG International '8
Tosiyasu L. Kunii and Qiuming Zhu
Editor: Tosiyasu L. Kunii
Chapter, A Two-phase Fast Hidden-line Removal Algorithm, authored by Qiuming Zhu, UNO faculty member.
Recent developments in computer graphics have largely involved the following: Integration of computer graphics and image analysis through computer data structure; integration of CAD/CAM as computer-integrated manufacturing (CIM) through the design and simulation of manufacturing processes using computer graphics; progress in basic research on the modeling of complex and mathematical graphic objects, such as computational geometry, graphic data bases, hierarchical windows, and texture; use of computer graphics as an improved human interface to present information visually and multidimensionally; and advancement of industrial technology and computer art based on developments in the areas listed above. These trends are strongly reflected in the contents of the present volume either as papers dealing with one particular aspect of research or as multifaceted studies involving several different areas. The proceedings comprise thirty selected, previously unpublished original papers presented in nine chapters.
Books and monographs by Computer Science Department faculty members are collected here.
Printing is not supported at the primary Gallery Thumbnail page. Please first navigate to a specific Image before printing.