CS 390 Introduction to Theoretical Computer Science

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CS 390 Introduction to Theoretical Computer
Science
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Instructor

• Name Shunichi Toida
• Office ED 252-4
• Phone 683 - 3392
• e-mail toida_at_cs.odu.edu

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Textbook

• John Martin,
• Introduction to Languages and the Theory
  of Computation,
• 2nd edition,
• McGraw-Hill, New York, 1996.

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Grading

• Homework 20
• Projects 10
• Test x 2 35
• Final Exam 35

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Home Page for CS 390

• http//www.cs.odu.edu/toida
• /courses/CS390/390.html
• Homework questions and solutions, syllabus
  etc. are on this page.

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Office Hours

• Mondays Wednesdays
• 430 - 530 p.m.
• You can walk in any other time.

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Final Exam

• Thursday, August 3, 2000
• 300 - 600 p.m.
• ED 226

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Objectives and Outline
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Objectives

• Study the concept of computation, and limitations
  of computer and computation.
• Learn abstract languages called formal languages
  and devices to process them called automata.
• Train in reasoning and problem solving.
• Train in reading and writing technical articles.

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Solve problems with Computers
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To solve a problem by a computer

• a sequence of step by step
• instructions must be given to the
• computer.
• (Algorithm/Computer Program)

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• The instructions must be of finite
• length and executable by the
• computer.
• The computation must terminate
• after a finite amount of time.

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Hierarchy of Computational Problems

• Problems which can be solved by a fast algorithm
  ---- CS 361
• Problems which can NOT be solved by a fast
  algorithm ---- CS 361
• Problems which may or may not be solved by a fast
  algorithm --- CS 361, 483
• Problems which can not be solved by a computer --
  CS 390

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• Can such a sequence of instructions always be
  found for a given problem ?

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No, not always !
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• When can none be found ?

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Examples of unsolvable problem

• Halting problem
• Tiling problem

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Halting problem

• Does a given program stop after a finite
  amount of time for a given input ?

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Tiling problem

• Can a given finite area, of any size,
  be covered using only tiles of given types such
  that the colors on any touching edges are the
  same ?

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• It is known that no computer programs can be
  written to solve those problems.

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How do we know they are unsolvable ?
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• To answer the question we must know
• what we mean by computation and
  computer,
• independent of differences among computers,
  and languages.

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• We must know
• the essence of computation, and
• computer.

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• The essence of computer and computation is
  represented by
• Turing machine, and
• computation by Turing machine.
• Also problem solving is modeled as
  language recognition.

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Four Major Topics

• Regular languages and finite automata as a warm
  up for Turing machines --- also practically
  useful
• Turing machines
• Computation as processing by Turing machine
• Unsolvability of Halting Problem

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Course Outline

• (1) Review of mathematics
• (2) Languages --- abstract languages
• (3) Regular languages, regular expressions
• (4) Finite automata
• (5) Applications of finite automata

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Course Outline Continued

• (6) Context-free languages, and push down
  automata --- used for compilers
• (7) Turing machines
• (8) Turing acceptable, decidable, computable
• (9) Unsolvability of Halting Problem

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Objectives Revisited

• Study the concept of computation, and limitations
  of computer and computation.
• Learn abstract languages called formal languages
  and devices to process them called automata.
• Train in reasoning and problem solving.
• Train in reading and writing technical articles.

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Review of Mathematics