Computer-based Problem Solving Process

Teodor Rus

• Publisher: WSPC
• Year: 2015
• eBook ISBN: 9789814663755
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

The author looks at the issues of how computing are used and taught, with a focus on embedding computers within problem solving process by making computer language part of natural language of the domain instead of embedding problem domain in the computer by programming. The book builds on previous editions of system software and software systems, concepts and methodology and develops a framework for software creation that supports domain-oriented problem solving process adapting Polya's four steps methodology for mathematical problem solving:

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• Formalize the problem;
• Develop an algorithm to solve the problem;
• Perform the algorithm on the data characterizing the problem;
• Validate the solution.

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to the computer use for problem solving in any domain, including computer programming.

Contents:

• Systems Methodology:
  • Introduction to System Software
  • Formal Systems
  • Ad Hoc Systems
  • Common Systems in Software Development
• Computer Architecture and Functionality:
  • Hardware System
  • Functional Behavior of Hardware Components
  • Algorithmic Expression of a Hardware System
  • Using Computers to Solve Problems
• Software Tools Supporting Program Execution:
  • Computer Process Manipulation by Programs
  • Memory Management System
  • I/O Device Management System
  • Computation Activity and Its Management Tools
• Software Tools Supporting Program Development:
  • Problem Solving by Software Tools
  • Web-Based Problem Solving Process
  • Software Tool Development Illustration
  • Software Tools for Correct Program Development
• Computer Operation by Problem Solving Process:
  • Using First Computers to Solve Problems
  • Batch Operating System
  • Problem of Protection
  • Timing Program Execution
  • Efficiency of Batch Operating Systems
  • Convenience of the BOS
  • Real-Time Systems

Readership: Student, general public and professional.
Key Features:

• This is one of the few books in the market that promote programming as a problem solving process following Polya for mathematical problem solving
• This book consolidates the concepts of system methodology, computer architecture, system tools program execution into workflow of the four steps Polya problem solving process
• This book insists to hold the hands of readers to walk through the internal working of a computer system from problem deposition to hardware state transitions, a view that has been lost in most computer science curricula currently taught in universities and colleges

 

 

 

 

PART 1

Systems Methodology

Chapter 1

Introduction to System Software

System software is a collection of software tools with the goal of making computers convenient and efficient by:

• allowing programmers to develop programs using a human logic;
• allowing hardware to execute programs using a machine logic.

After more that 50 years of computer use during problem solving process the question one may raise is: does the system software really make computers convenient to computer users?

Postponing the answer to the previous question, we say that today goal of system software should be: allow application domain experts so solve their problems by manipulating concepts and abstractions of their own problem domains using a computer platform.

This means move the computer process involved within problem solving from the computer environment within the application domain environment. For example, rather than developing a C or Fortran program to solve a second degree equation ax² + bx + x = 0 a high-school students should do by typing:

computer: solve equation ax² + bx + c = 0

Likewise, a mechanical engineer should be able to solve differential equations without writing (conventional) Fortran programs!

So, how do we develop (engineer) system software? Is this approach amenable to developing software tools that can be used by application domain experts independent of their computer education?

While developing software tools we should use the same approach as for any other engineering activity, that is:

• Define the artifacts (objects) handled by system software;
• Develop a methodology for handling system software artifacts;
• Develop tools to perform this activity.

We use systems methodology for system software development. The rationale for using systems methodology for software tool development are:

• Systems describe complex relationship among things and systems abound in computer industry;
• A system can be formally defined in the framework of universal algebra;
• Similarity of the objects manipulated by algebra and computer science, which are abstractions;
• Reuse of the theories developed by algebraic methodology in the framework provided by system software;
• Universality of algebraic methodology for science discovery.

1.1Abstraction Manipulation

Since software objects are abstractions the first thing we need is a mechanism for abstraction manipulation. This mechanism is provided by the algebraic methodology where:

• Abstract objects are manipulated by their representations. The representation of a concrete or abstract object is an item of information that stands for that object.
• Representations are characterized by the tuple 〈Value, Literal, Type〉:

• –The Value is an entity that measures the represented object thus allowing us to relate abstract objects to each other;
• –The Literal is a notation allowing us to refer to the object while manipulating it;
• –The Type indicates a set of operations we can use while manipulating the object.

Example abstract objects:

• Numbers: values are units of, literals are strings of digits, types are operations with numbers;
• Blue prints (what do blue-prints represent?): values are concrete object represented, literals are graphic designs used to represent the objects, types are operations used to manipulate the objects;
• C-language constructs (what do C language constructs represent?): values are computation entities represented by the C language construct, literals are string of terminal characters denoting C language constructs, types are operations used to combine C language constructs getting other C language constructs.

System software tools manipulate abstractions obtained by mapping real world objects into computation representations by the mechanism of abstraction manipulation that operates with:

• Mental representations, M;
• Computational representations, C;
• Explanatory representations, E.

That is, system software tools manipulate abstractions represented by the scheme

. Here we sketch properties Value, Literal, Type for each of M, C, and E. V alue(M) is a brain representation of the object represented; Literal(M) is the language representation of the object represented; Type(M) is the collection of operation brain can perform on the object represented. Similarly, V alue(C) is measured by the intellectual meaning of the object represented; Literal(C) is the language expression of the object represented, such as a natural language expression or a computational language expression, or a musical language expression, etc., depending upon what M is; Type(C) is the collection of operations allowed by the language used to represent C. The tuple 〈V alue, Literal, Type〉 applied to E can be defined within the framework of knowledge manipulation.

The generic approach for abstraction manipulation through system software tools consist of:

• Develop a semantic model for the object you want to represent (one world), W₁.
• Develop a syntactic model for the object you want to represent (another world), W₂.
• Put them together: R : W₁ → W₂.
• Manipulate W₂ as you would do with W₁.

Examples abstraction manipulation in everyday life are:

(1)Handling numbers: represent them, define operations on them i.e, develop the arithmetic as a tuple

Arithmetic = 〈Constants⊕ Variables⊕ Expressions;=, :=, +, −, etc〉

and study properties of expressions with numbers.

(2)Handling logical objects: define the logical values (true, false), constants, variables, and operations on them (∧, ∨, ¬, …) thus developing the propositional logic as the tuple

Logic = 〈{true, false} ⊕ Variables ⊕ Expressions; =, :=, ∧, ∨, ¬〉

and study the properties of logic expressions.

(3)Handling lists: define lists, define list notation, define operations for list creation and manipulation, study properties of list expressions.

Challenge: identify in each of the examples above the three elements involved in abstraction manipulation: W₁ (semantics), W₂ (syntax), and E : W₁ → W₂ their association mechanism.

1.2Systems Methodology

Informally a methodology is a collection of methods, principles and rules, as those of an art or science (see Webster). Example methodologies are a high school algebra methodology, high school geometry methodology, C language programming methodology, house building methodology, etc. Note that principles and rules of a methodology are determined by:

• the model of the problem to be solved;
• relations between agents manipulating principles and rules while solving problems.

Consequently we need to understand the concept of a problem.

1.2.1Problem solving

Following Polya [Polya (1957)] we say that to have a problem means to search consciously for some action (solution) appropriate to attain a given aim (purpose). Note that hidden in this phrase are three things that characterize a problem: unknown, action, purpose. To solve a problem means to find such an action. Example problem is C programming: unknown is the C program, action is the C program development, and the goal is solving problems by C programming. A problem is thus characterized by three elements :

(1)unknown, (what is a C program?);

(2)data, (what do we need to know in order to write C programs?);

(3)purpose, (what are conditions satisfied by unknown and data according to the goal of C program development) or (how do we or how does the C compiler recognize a valid C p...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Dedication
• Preface
• Contents
• Part 1 Systems Methodology
• 1. Introduction to System Software
• 2. Formal Systems
• 3. Ad Hoc Systems
• 4. Common Systems in Software Development
• Part 2 Computer Architecture and Functionality
• 5. Hardware System
• 6. Functional Behavior of Hardware Components
• 7. Algorithmic Expression of a Hardware System
• 8. Using Computers to Solve Problems
• Part 3 Software Tools Supporting Program Execution
• 9. Computer Process Manipulation by Programs
• 10. Memory Management System
• 11. I/O Device Management System
• 12. Computation Activity and Its Management Tools
• Part 4 Software Tools Supporting Program Development
• 13. Problem Solving by Software Tools
• 14. Web-Based Problem Solving Process
• 15. Software Tool Development Illustration
• 16. Software Tools for Correct Program Development
• Part 5 Computer Operation by Problem Solving Process
• 17. Using First Computers to Solve Problems
• 18. Batch Operating System
• 19. Problem of Protection
• 20. Timing Program Execution
• 21. Efficiency of Batch Operating Systems
• 22. Convenience of the BOS
• 23. Real-Time Systems
• Bibliography
• Index