...Chapter 2 An Overview of Formal Methods Tools and Techniques The goal of this chapter is to give an overview of the different approaches and tools pertaining to formal methods. We do not attempt to be exhaustive, but focus instead on the main approaches. After reading the chapter the reader will be familiar with the terminology of the area, as well as with the most important concepts and techniques. Moreover the chapter will allow the reader to contextualise and put into perspective the topics that are covered in detail in the book. Why do we need an overview of formal methods? Why not just study one rigorous method for software development? This is a very pertinent and legitimate question. The behavioural essence of software is not captured by a unique unified mathematical theory. Such a general foundation is unlikely to exist. Think for instance about the diversity of programming language paradigms and theories, and the resulting jungle of existing computer programming languages. Is there a definite paradigm (or, even, language) that makes obsolete all the other ones? Clearly not. Different languages will be chosen by different people to solve the same problem, and someone may well use different languages to solve different problems. Similarly, depending on the goals of the software designers and of the verification process, one may prefer a theory over another one, and even use more than one theory (and related formal methods techniques and tools), in the context of the development...
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...Mon. 4:00–5:00 pm, Thurs: 3:00 - 4:00 pm DGD: Wed. 10–11:30 am. Textbook: K. H. Rosen, Discrete Mathematics and Its Applications, 6th Edition, McGrawHill. We’ll be covering most of Chapters 1, 2, and 9, and parts of Chapters 4, 5, and 8. The course may contain a small of amount of material not covered by the textbook. This text has been used in Discrete Math courses at Ottawa U. for many years, so secondhand copies can easily be found. Copies of the book are at the bookstore or available from Amazon. Coursework Evaluation: The final grade will be calculated as follows: • 5 homework assignments : 10% • Midterm exam: 30% • Final exam: 60% The midterm test is on February 17 . 1 Note that students must pass the final exam in order to pass the course. In the exceptional case that the student missed a midterm exam for a valid reason (see Policy on Missed Midterm Exams), the final exam will count for the combined percentage of the final and the missed midterm exam. Of the 5 homework assignments your best 4 will count 10% toward you final grade. All assignments are to be submitted in your DGD on the due date, or...
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...CARLESON POTENTIALS AND THE REPRODUCING KERNEL THESIS FOR EMBEDDING THEOREMS STEFANIE PETERMICHL 1 , SERGEI TREIL 2 , AND BRETT D. WICK 3 Abstract. In this note we present a new proof of the Carleson Embedding Theorem on the unit disc and unit ball in C n The only technical tool used in the proof of this fact is Green’s formula. The . starting point is that every Carleson measure gives rise to a bounded sub-harmonic function. Using this function we construct a new related Carleson measure that allows for a simple embedding. In the case of the disc D this gives the best known constant, with the previous best given by N. Nikolskii. 0. Introduction The famous Carleson Embedding Theorem for the unit disc states, in particular, that the embedding of the Hardy space H2 into a space L 2 (µ) can be checked on reproducing kernels of the Hardy space. Namely, it can be stated as follows: Theorem 0.1 (Carleson Embedding Theorem). Let µ be a non-negative measure in D. Then the following are equivalent: (i) The Hardy space H2 (D) is embedded in L 2 (µ), i.e. Z D |f(z)| 2 dµ(z) ≤ A 2 kfk 2 H2 (D) ∀f ∈ H2 (D). (ii) C(µ) 2 := sup z∈D kkzk 2 L2 (µ) = sup z∈D kPzkL1 (µ) < ∞, where kz(ξ) = (1−|z| 2 ( 1/2 1−ξz , is the normalized reproducing kernel for the Hardy space H2 (D). (iii) I(µ) := sup 1 r µ(D ∩ Q(ξ,...
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...for (P P T T F F Q) ^ (Q Q T F T F Truth Table for (P v Q) P T T F F Q T F T F P) P -> Q T F T T Q -> P T T F T (P Q) ^ (Q P^Q T F F F (P v Q) P) T F F T (P ^ Q) PvQ T T T F (P ^ Q) T F F T Hence shown that both expressions are logically equivalent. 3. Assuming this is a game in which animals attack each other, try to represent the following situation completely using first-order logic: You have to represent the following facts: a. The location (air/ground) of the animals b. The abilities of the animals (e.g. flying) c. The relative speed of the animals (slow/fast) d. Line-of-sight status (animal A is visible to animal B) Answers can be moderately different from the following suggested answer: is_at_location(turtle, ground) is_at_location(eagle, air) has_ability(turtle, hide_in_shell) has_ability(eagle, fly) has_speed(turtle, slow) has_speed(eagle, fast) can_see(eagle, turtle) ~can_see(turtle, eagle) 4. Answers are as follows: a. P ^ P ≡ P b. P ^ T ≡ P c. P ^ F ≡ F d. P v T ≡ T e. P ^ ~P ≡ F f. P v ~P ≡ T g. P P≡T 5. Draw a complete truth table for the following propositional logic statement: (P ^ Q) v (P Q)...
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...LEARNING OBJECTIVES: INTRODUCTION: Definitions Participative Leadership – involves efforts by a leader to encourage and facilitate participation by others in making important decisions Delegation – a distinct type of power sharing process that occurs when subordinates are given responsibility and authority for making some types of decisions formerly made by the manager Empowerment – involves the perception by members of an organization that they have the opportunity to determine their work roles, accomplish meaningful work and influence important events. VARIETIES OF PARTICIPATION: * Autocratic Decision * Consultation * Joint Decision * Delagation (Diagram) BENEFITS OF PARTICIPATION: * Decision Quality * Decision Acceptance * Satisfaction with the decision Process * Development of Participant Skill Research Effects of Participative Leadership Research Method: * Laboratory experiments * Field experiments * Correlation field studies * Qualitative case studies * Interviews with effective leaders and their subordinates Example Case: * Bragg and Andrews (1973) : Hospital Laundry Department Effects on Participation: * Research results have not been strong and conclusive. * Type of methodology blamed for inconsistency * E.g. Questionnaire data from survey of subordinates found positive effectives of participation, however, independent measure of outcome variables had weak...
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...omativityInformativity~ a text is more informative the mor eunexpected it is what u are told. Then theres three levels: 1)order: Trivial statements: that’s the first order iunformation 2) order: new info ------------------------------------------------- 3) order: violation: violation of world knowledge, it is unexpected. Open class elements vs closed class.: The closed class tend to be unnoticed. Also when we speak we use prepostions wrongly, and there seems to be no interprtation problems with regard ot that, people can still undertsand. The closed class possessess first order info, whereas the open class has second order. Time flies like an arrow; We read this sentence and we interperet it I the cliché way, we don’t think of it, for example, as an imperative sentence. The stress _______________________-- Types of expectations: a) Our knowledge about the world, that is, our model of the world. Frames give us expectations as well when we are talking, reading. b) The organization, we have an expectation with regard to the order of the words, don’t we?. c) How you arrange a text d) Text type or “genre”: I think of cortazars instructions e.g. how to blow ur nose Svend age madsen (danish writer who changes form one chafracter to another, or sth like that) Definitie article: we used because it is previusoly mentioned that objecvt. For example: aman….. and then I say the man…. Also if theres a certain frame being used, you don’t Hve to introduce...
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...Revising and Proofreading Checklist Item for Revision Circle One Notes for Revision Circle One Did I explore character traits and motivations by describing what the characters did, said, or how they interacted with others? Yes or No ONLY FOR CHARACTER Yes or No Did I identify and discuss a theme of the literary work I wrote about? Yes or No ONLY FOR THEME Yes or No Did I begin with an introduction that contains a strong thesis statement? Yes or No Yes or No Have I presented my ideas in a logical order? Yes or No Yes or No Did I use transitional words and phrases to make the ideas flow together smoothly? Yes or No Yes or No Do my topic sentences clearly support my thesis? Yes or No Yes or No Did I use textual evidence to support each topic sentence? Yes or No Yes or No Do all my arguments make sense? Yes or No Yes or No Is the tone consistent and appropriate for my audience? Yes or No Yes or No Items to Proofread Circle One Notes for Proofreading Circle One Have I indented every paragraph? Yes or No Yes or No Does each sentence in my essay express a complete thought? Yes or No Yes or No Have I capitalized everything in my essay correctly? Yes or No Yes or No Have I titled my essay appropriately and capitalized the title correctly? Yes or No Yes or No Have I used the appropriate punctuation throughout my essay? Yes or No Yes or No Have I corrected any misspellings and looked up the words that I...
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...for students to organize their research and show the topical areas that they will cover throughout the Research Project. By breaking down the literature into various sections, topics, sub-topics, and details, students can divide large amounts of data into smaller, more orderly sections. The Formal Outline helps students organize their thoughts, stay on topic, and follow a logical order. It also provides students with the opportunity to show a progression of thought and direction, and can highlight specific areas of the Research Project that may need more or less attention. The following article is helpful in structuring the paper: http://explorable.com/research-paper-outlineexamples Write a three to four (3-4) page paper in which you: 1. Provide an Introduction, Body, and Conclusion. 2. Identify the main points and sections of the Research Project. 3. Identify the sub-topics and details consistent with the main points and sections. More Details hidden... Activity mode aims to provide quality study notes and tutorials to the students of CRJ 105 WK 4 Assignment 2 Formal Outline in order to ace their studies. CRJ 105 WK 4 ASSIGNMENT 2 FORMAL OUTLINE To purchase this visit here: http://www.activitymode.com/product/crj-105-wk-4-assignment-2-formal-outline/ Contact us at: SUPPORT@ACTIVITYMODE.COM CRJ 105 WK 4 ASSIGNMENT 2 FORMAL OUTLINE CRJ 105 WK 4 Assignment 2 - Formal Outline The purpose of the Formal Outline is for students to organize their research and...
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...Strategic Alternative Implementation-Action Items and Action Plan After selecting the most appropriate strategy (that is, the strategy with the highest probability of enhancing a firm's strategic competitiveness), you must consider effective implementation. Effective synthesis is important to ensure that you have considered and evaluated all critical implementation issues. Issues you might consider include the structural changes necessary to implement the new strategy. In addition, leadership changes and new controls or incentives may be necessary to implement strategic actions. The implementation actions you recommend should be explicit and thoroughly explained. Occasionally, careful evaluation of implementation actions may show the strategy to be less favorable than you thought originally. A strategy is only as good as the firm's ability to implement it effectively. Therefore, effort to determine effective implementation is important. Process Issues You should ensure that your presentation (either oral or written) has logical consistency throughout. For example, if your presentation identifies one purpose, but your analysis focuses on issues that differ from the stated purpose, the logical inconsistency will be apparent. Likewise, your alternatives should flow from the configuration of strengths, weaknesses, opportunities, and threats you identified by the internal and external analyses. Thoroughness and clarity also are critical to an effective presentation. Thoroughness...
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...Grouping, Sequencing, and Documenting Information The following systems will help keep you organized: a system for noting sources on bibliography cards a system for organizing material according to its relative importance a system for taking notes Writing an Outline and a Prospectus for Yourself Consider the following questions: What is the topic? Why is it significant? What background material is relevant? What is my thesis or purpose statement? What organizational plan will best support my purpose? top Writing the Introduction In the introduction you will need to do the following things: present relevant background or contextual material define terms or concepts when necessary explain the focus of the paper and your specific purpose reveal your plan of organization Writing the Body Use your outline and prospectus as flexible guides Build your essay around points you want to make (i.e., don't let your sources organize your paper) Integrate your sources into your discussion Summarize, analyze, explain, and evaluate published work rather than merely reporting it Move up and down the "ladder of abstraction" from generalization to varying levels of detail back to generalization top Writing the Conclusion If the argument or point of your paper is complex, you may need to summarize the argument for your reader. If prior to your conclusion you have not yet explained the significance of your findings or if you are proceeding inductively, use the...
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...Predicate Calculus Examples : Ex1 : It rained on Tuesday . weather(tuesday , rain) Ex2 : It rained every days. weather(X , rain) ( day(X) Ex3 : mother(layla, adel) mother(layla, suha) father(adam, adel) father(adam, suha) (X(Y father(X,Y) ( mother(X,Y) ( parent(X,Y) (X(Y(Z parent(X,Y) ( parent(X,Z) ( brother(Y,Z) In this example we use the predicate mother and father to define a set of other relationships such as parent and brother. Predicate calculus semantics : provide a formal basis for determining the truth value of Well Formed Formula (WFF) . The truth of expressions depends on the mapping of constants, variables and functions into objects and relation in the domain of discourse. First order predicate Calculus : It is a language allows quantified variables to refer to objects in the domain of discourse and not to predicates or functions. Ex3 : if it doesn't rain tomorrow . Tom will go to the mountains. ~weather(rain, tomorrow) ( go (tom, mountains) Ex4 : All person play football are tall (X(Y (person(X) ^ play(X,Y) ^ football(Y) ( tall(X) Ex5 : some person like anchovies. (X (person(X) ^ like (X, anchovies)). Ex6 : No body likes taxes. ~ (X likes(X, taxes) or (X ~likes(X, taxes). Ex7 : Suppose we want to model the blocks world of figure below to design a control algorithm for a robot arm : on (c, a). on (b, d). on-table ( a ) on-table ( d ) clear ( b ) ...
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...Trucks Cols VIN MakeModelID LastMaintenanceID NextScheduledMaintenanceID Type Varchar(20) Int Int Int Key Type PK FK FK FK Allows Nulls MakeModel Cols ID Year MakeID ModelID Type Int Int(4) Int Int Key Type PK FK FK Allows Nulls Makes Cols ID Make Type Int Text Key Type PK Allows Nulls Models Cols ID Model Type Int Text Key Type PK Allows Nulls TruckMaintenanceHistroy Cols ID PerformedOn PerformedBy MaintenanceSheetID Type Int DateTime Int Int Key Type PK FK FK Allows Nulls TruckMaintenanceSheets Cols ID Status Type Int Int Key Type PK FK Allows Nulls TractorUnitPerformed EngineCompartmentPerformed CabinPerformed AirDamPerformed AirTanksPerformed FuleTanksPerformed WheelsPerformed BrakesPerformed AxelPerformed Bool Bool Bool Bool Bool Bool Bool Bool Bool Trailers Cols VIN TypeID LastMaintenanceID NextScheduledMaintenance Type Varchar(20) Int Int Int Key Type PK FK FK FK Allows Nulls Yes Yes TrailerTypes Cols ID Name TypeSpecID Type Int Text Int Key Type PK FK Allows Nulls TypeSpecs Cols ID Dimension_L Dimension_W Dimension_H LoadCapacity Weight Type Int Varchar(6) Varchar(6) Varchar(6) Varchar(6) Varchar(6) Key Type PK Allows Nulls TrailerMaintenanceHistroy Cols ID PerformedOn Type Int DateTime Key Type PK Allows Nulls PerformedBy MaintenanceSheetID Int Int FK FK TrailerMaintenanceSheets Cols ID Status FifthWheelCouplingPerformed CargoSpacePerformed LoadingDoorPerformed LandingGearPerformed WheelsPerformed BrakesPerformed...
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...TITLE: 4 type of sentences PURPOSE: To introduce the class to four kinds of sentences, and how understanding and using different types of sentences allows writers to control the tone of their sentences. GOAL: Students will be able to both name and write the four different types of sentences. OBJECTIVES: Students will be able to differentiate between the four different types of sentences. MATERIALS: PowerPoint, overhead projector, notebooks, pencils/pens, 4 types of sentences worksheets (8), Jeopardy Game PROCEDURES AND METHODS: Tell students that they will be learning about the four different types of sentences today. Ask the class for volunteers to name the different types of sentences. Once students have made educated guesses, begin the PowerPoint presentation. At the end of the PowerPoint there are several examples. Have each student take a turn identifying the type of sentence displayed and have them give an explanation. Students will then be given a worksheet covering the different sentence types, for which they will work on independently as I walk around answering any questions. Once the worksheet is complete, if time allows, the class will participate in a Jeopardy review game over the 4 types of sentences, which I have prepared to display on the projector. The winning team will receive Crown Jewel Bucks, which can be spent at the school Academic Bookstore. EVALUATION: Ask students to complete the Sentence Types worksheet. This should take approximately 15 minutes...
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...HTML & CSS The content and its presentation Using two websites http://www.bbc.com/ and http://www.basf.com/group/corporate/en/, I am able observe that both sites present their content in a very good way although differently from one another given the nature of their businesses. Both sites have the ability to present their content in more than one language. The content and its presentation on the BBC websites leaves no doubt that it is a news portal. The homepage is displayed distinctively with a unique color from the rest of the pages. The other pages are also displayed with different but consistent colors throughout each particular page. Take for example the Sports page, its dominant and consistent color is yellow throughout the various sports like football, cricket, rugby, formula one and all the rest that are covered in the sports section of the BBC website. The weather page is blue in color. Likewise, the content on the BASF website also leave no doubt that it is a website for a chemical company dealing in various goods and service. The http://www.basf.com/group/corporate/en/ is displayed in a different but consistent color throughout the page every time it is accessed while still maintains the same look. This is a unique property of this page because no matter the change in the dominant color of the page, I was still able to know that I am visiting the BASF website each time the color changed. I think this is because of the consistency of the other properties of the...
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...Ayman Abdeldayem CMIS 320 A piano manufacturer wants to track all pianos it makes. Each piano has a unique serial number and a manufacturing completion date. Each instrument represents exactly one piano model, all of which have an identification number and model. The company produces thousands of pianos of a certain model, and the design is specified before any single piano exists. 1. Identify the degree and cardinalities of the relationship. The degree is the number of attributes in a relation. For this company, the attributes to distinguish between the products would be serial number, completion date, piano model, and identification number. This company makes thousands of pianos per model, and makes many different models. “Cardinality is the number of tuples in a relation,” in this case, a tuple would be a single piano model. So depending on the number of different piano models they produce will be the cardinality. 2. Express the relationships graphically with an E-R diagram. A vendor builds multiple types of tablet computers. Each has a type, identification number, and a name. The key specifications for each type include amount of storage and display type. The company uses multiple processor types, exactly one of which is used for a specific tablet type. The same processor can be used in multiple types of tablets. Each processor has a manufacturer and a manufacturer's unique code that identifies it. 1. Identify the degree and cardinalities of the relationship...
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