Automata, Computability, and Complexity

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Automata, Computability, and Complexity

• Lecture 1
• Section 0.1
• Wed, Aug 22, 2007

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Basic Questions

• What are the fundamental capabilities and
  limitations of computers?
• What makes some problems computationally hard and
  others easy?
• What do we mean by hard?

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Automata Theory

• Mathematical models of computation.
• Finite automata
• Push-down automata
• Turing machines

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Computability Theory

• What does it mean to compute?
• Are there things that cannot be computed?

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Complexity Theory

• What makes a problem hard?
• Can a problems requirements be relaxed to make
  the solution easy?

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Computer Science as a Curriculum

• Computing Curricula 2005 The Overview Report

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Computing Curricula 2005 Overview Report

• You might be a computer scientist if
• You design and implement software.
• You devise new ways to use computers.
• You develop effective ways to solve computing
  problems.

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Computing Curricula 2005 Overview Report

• While other disciplines may produce graduates
  with more immediately relevant job-related
  skills, computer science offers a comprehensive
  foundation that permits graduates to adapt to new
  technologies and new ideas.

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Major Knowledge Areas

• Computing Topics
• Programming fundamentals
• Algorithms and complexity
• Operating Systems Principles Design
• Theory of Programming Languages
• Software Design

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Major Knowledge Areas

• Non-computing Topics
• Mathematical foundations
• A distant second
• Interpersonal communication

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Degree Expectations

• Computer scientists should be prepared to work
  in a broad range of positions involving tasks
  from theoretical work to software development.

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Degree Expectations Which is CS?

• Work effectively at planning, implementation,
  configuration, and maintenance of an
  organizations computing infrastructure.
• Work in a broad range of positions involving
  tasks from theoretical work to software
  development.
• Design and implement systems that involve the
  integration of software and hardware devices.
• Perform and manage activities at every stage of
  the life cycle of large-scale software systems.
• Analyze information requirements and business
  processes and be able specify and design systems.

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Degree Expectations Which is CS?

• Work effectively at planning, implementation,
  configuration, and maintenance of an
  organizations computing infrastructure.
• Work in a broad range of positions involving
  tasks from theoretical work to software
  development.
• Design and implement systems that involve the
  integration of software and hardware devices.
• Perform and manage activities at every stage of
  the life cycle of large-scale software systems.
• Analyze information requirements and business
  processes and be able specify and design systems.

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The CS Degree

• In general, a CS degree from a respected program
  is the most flexible of degrees and can open
  doors into the professional worlds of CS, SE, IT,
  and sometimes CE.
• In other words, you can do anything with a degree
  in CS.

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Computer Science

• Computer Science is no more about computers than
  astronomy is about telescopes.     -- E. W.
  Dijkstra

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Computer Science

• One more thing