Foundations of Computing
Foundations of Computing
An Accessible Introduction to Formal Languages
About the Book
A textbook for upper-division Computer Science majors covering formal languages and automata with an introduction to computability. Intended to give CS majors a solid foundation in the Theory of Computation without being overly formal mathematically, while retaining the rigor of the material. It has been classroom tested since 2016 with good success.
About the Author
Table of Contents
- Foreword
- Preface
- 1.Introduction
- 1.1Formal Languages
- 1.2Finite State Machines
- 1.2.1Exercises
- 1.2.2Chapter Summary
- 2.Finite Automata
- 2.0.1Where Are We?
- 2.0.2Chapter Objectives
- 2.1Deterministic Finite Automata
- 2.1.1Exercises
- 2.2Non-Deterministic Finite Automata
- 2.2.1Equivalence of NFAs and DFAs
- 2.2.2NFAs and Complements
- 2.2.3Exercises
- 2.3Minimal Automata
- 2.3.1Exercises
- 2.4Machines with Output
- 2.4.1Computer Arithmetic
- 2.4.2Lexical Analysis
- 2.4.3Minimal Mealy Machines
- 2.4.4Exercises
- 2.4.5Chapter Summary
- 3.Regular Expressions and Grammars
- 3.0.1Where Are We?
- 3.0.2Chapter Objectives
- 3.1Regular Expressions
- 3.1.1Exercises
- 3.2Equivalence of Regular Expressions and Regular Languages
- 3.2.1From Regular Expression to NFA
- 3.2.2From NFA to Regular Expression
- 3.2.3Exercises
- 3.3Regular Grammars
- 3.3.1Left-Linear Grammars
- 3.3.2Exercises
- 3.3.3Chapter Summary
- 4.Properties of Regular Languages
- 4.0.1Where Are We?
- 4.0.2Chapter Objectives
- 4.1Closure Properties
- 4.1.1Computing Set Operations
- 4.1.2Exercises
- 4.2Decision Algorithms
- 4.2.1Exercises
- 4.3Infinite Regular Languages and a “Pumping Theorem”
- 4.3.1Exercises
- 4.3.2Chapter Summary
- 5.Pushdown Automata
- 5.0.1Where Are We?
- 5.0.2Chapter Objectives
- 5.1Adding a Stack to Finite Automata
- 5.1.1Exercises
- 5.2Pushdown Automata and Determinism
- 5.2.1Exercise
- 5.2.2Chapter Summary
- 6.Context-Free Grammars
- 6.0.1Where Are We?
- 6.0.2Chapter Objectives
- 6.1Context-Free Grammars and Derivations
- 6.1.1Simplifying Grammars
- 6.1.2Exercises
- 6.2Derivation Trees and Ambiguous Grammars
- 6.2.1Operator Precedence
- 6.2.2Operator Associativity
- 6.2.3Expression Trees
- 6.2.4Exercises
- 6.3Equivalence of PDAs and CFGs
- 6.3.1From CFG to PDA
- 6.3.2From PDA to CFG (Special Case)
- 6.3.3From PDA to CFG (General Case)
- 6.3.4Exercises
- 6.3.5Chapter Summary
- 7.Properties of Context-Free Languages
- 7.0.1Where Are We?
- 7.0.2Chapter Objectives
- 7.1Chomsky Normal Form
- 7.1.1Removing Lambda
- 7.1.2Removing Unit Productions
- 7.1.3Chomsky Normal Form Rules
- 7.1.4Exercises
- 7.2Closure Properties
- 7.2.1Closure Properties of DCFLs
- 7.2.2Exercises
- 7.3Decision Algorithms
- 7.3.1Is a CFL Empty or Infinite?
- 7.3.2Exercises
- 7.4Infinite CFLs and Another Pumping Theorem
- 7.4.1Exercises
- 7.4.2Chapter Summary
- 8.Turing Machines
- 8.0.1Where Are We?
- 8.0.2Chapter Objectives
- 8.1Prelude
- 8.1.1Queue Machines
- 8.1.2Exercise
- 8.2The Standard Turing Machine
- 8.2.1Subroutines
- 8.2.2Halting
- 8.2.3Exercises
- 8.2.4Programming Exercise
- 8.3Variations on Turing Machines
- 8.3.1The Universal Turing Machine
- 8.3.2Non-Deterministic TM = Deterministic TM
- 8.3.3Programming Exercise
- 8.3.4Chapter Summary
- 9.The Landscape of Formal Languages
- 9.0.1Where Are We?
- 9.0.2Chapter Objectives
- 9.1Recursively Enumerable Languages
- 9.1.1A Non-Recursive, RE Language
- 9.1.2Context-Sensitive Languages
- 9.1.3Properties of Recursively Enumerable Languages
- 9.1.4Exercises
- 9.2Unrestricted Grammars
- 9.2.1Context-Sensitive Grammars
- 9.2.2Equivalence of Unrestricted Grammars and Turing Machines
- 9.2.3Exercises
- 9.3The Chomsky Hierarchy
- 9.3.1Countable Sets
- 9.3.2Uncountable Sets
- 9.3.3Chapter Summary
- 10.Computability
- 10.0.1Chapter Objectives
- 10.1The Halting Problem
- 10.2Reductions and Undecidability
- 10.2.1Exercises
- 10.2.2Chapter Summary
- Glossary
- Bibliography
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