Foundations of Computing
Course Info
This course includes 1 attempt.
The course is based on 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.
Course Material
- 1. Introduction
- 1.1 Formal Languages
- Example 1–1
- Example 1–2
- 1.2 Finite State Machines
- Example 1–3
- Example 1–4
- Example 1–5
- Example 1–6
- Example 1–7
- Paper Exercises
- Chapter Summary
- I Regular Languages
- 2. Finite Automata
- Where Are We?
- Chapter Objectives
- 2.1 Deterministic Finite Automata
- Example 2–1
- Example 2–2
- Example 2–3
- Example 2–4
- Example 2–5
- Example 2–6
- Example 2–7
- Example 2–8
- Paper Exercises
- Programming Exercise
- Exercise 1
- 2.2 Non-Deterministic Finite Automata
- Example 2–9
- Example 2–10
- Example 2–11
- Example 2–12
- Example 2–13
- Equivalence of NFAs and DFAs
- Example 2–14
- NFAs and Complements
- Example 2–15
- Example 2–16
- Paper Exercises
- Exercise 2
- 2.3 Minimal Automata
- Example 2–17
- Example 2–18
- Example 2–19
- Example 2–20
- Paper Exercises
- Exercise 3
- 2.4 Machines with Output
- Example 2–1
- Example 2–22
- Example 2–23
- Example 2–24
- Computer Arithmetic
- Example 2–25
- Example 2–26
- Example 2–27
- Lexical Analysis
- Example 2–28
- Example 2–29
- Minimal Mealy Machines
- Example 2–30
- Paper Exercises
- Programming Exercises
- Chapter Summary
- Exercise 4
- Quiz 11 attempt allowed
- 3. Regular Expressions and Grammars
- Where Are We?
- Chapter Objectives
- 3.1 Regular Expressions
- Paper Exercises
- 3.2 Equivalence of Regular Expressions and Regular Languages
- From Regular Expression to NFA
- From NFA to Regular Expression
- Example 3–1
- Example 3–2
- Paper Exercises
- 3.3 Regular Grammars
- Example 3–3
- Left-Linear Grammars
- Example 3–4
- Example 3–5
- Example 3–6
- Paper Exercises
- Chapter Summary
- Exercise 5
- Quiz 21 attempt allowed
- 4. Properties of Regular Languages
- Where Are We?
- Chapter Objectives
- 4.1 Closure Properties
- Example 4–1
- Computing Set Operations
- Example 4–2
- Example 4–3
- Paper Exercises
- Exercise 6
- 4.2 Decision Algorithms
- Example 4–4
- Example 4–5
- Example 4–6
- Paper Exercises
- 4.3 Infinite Regular Languages and a “Pumping Theorem”
- A “Pumping Theorem” for Infinite Regular Languages
- Example 4–7
- The Pumping Theorem for Regular Languages
- Example 4–8
- Example 4–9
- Example 4–10
- Example 4–11
- Example 4–12
- Example 4–13
- Example 4–14
- Using Closure Properties to Show Non-Regularity
- Example 4–15
- Paper Exercises
- Chapter Summary
- Exercise 7
- Quiz 31 attempt allowed
- II Context-Free Languages
- 5. Pushdown Automata
- Where Are We?
- Chapter Objectives
- 5.1 Adding a Stack to Finite Automata
- Example 5–1
- Example 5–2
- Example 5–3
- Example 5–4
- Example 5–5
- Example 5–6
- Example 5–7
- Paper Exercises
- Exercise 8
- 5.2 Pushdown Automata and Determinism
- Example 5–8
- Paper Exercise
- Chapter Summary
- Quiz 41 attempt allowed
- 6. Context-Free Grammars
- Where Are We?
- Chapter Objectives
- 6.1 Context-Free Grammars and Derivations
- Example 6–1
- Example 6–2
- Example 6–3
- Example 6–4
- Example 6–5
- Example 6–6
- Example 6–7
- Example 6–8
- Example 6–9
- Simplifying Grammars
- Example 6–10
- Example 6–11
- Paper Exercises
- Programming Exercise
- Exercise 9
- 6.2 Derivation Trees and Ambiguous Grammars
- Example 6–12
- Operator Precedence
- Operator Associativity
- Example 6–13
- Expression Trees
- Paper Exercises
- Exercise 10
- 6.3 Equivalence of PDAs and CFGs
- From CFG to PDA
- Example 6–14
- From PDA to CFG (Special Case)
- Example 6–15
- From PDA to CFG (General Case)
- Example 6–16
- Example 6–17
- Example 6–18
- Paper Exercises
- Chapter Summary
- Exercise 11
- Quiz 51 attempt allowed
- 7. Properties of Context-Free Languages
- Where Are We?
- Chapter Objectives
- 7.1 Chomsky Normal Form
- Removing Lambda
- Example 7–1
- Removing Unit Productions
- Example 7–2
- Chomsky Normal Form Rules
- Example 7–3
- Example 7–4
- Paper Exercises
- Exercise 12
- 7.2 Closure Properties
- Closure Properties of DCFLs
- Paper Exercises
- Exercise 13
- 7.3 Decision Algorithms
- Stage 1
- Stage 2
- Stage 3
- Stage 4
- Diagonal (Stage) 1
- Diagonal (Stage) 2
- Diagonal 3
- Diagonal 4
- Example 7–5
- Is a CFL Empty or Infinite?
- Example 7–6
- Example 7–7
- Paper Exercises
- Exercise 14
- 7.4 Infinite CFLs and Another Pumping Theorem
- The Pumping Theorem for Context Free Languages
- Example 7–8
- Example 7–9
- Example 7–10
- Example 7–11
- Example 7–12
- Paper Exercises
- Chapter Summary
- Exercise 15
- Quiz 61 attempt allowed
- III Recursively Enumerable Languages
- 8. Turing Machines
- Where Are We?
- Chapter Objectives
- 8.1 Prelude
- Queue Machines
- Exercise
- 8.2 The Standard Turing Machine
- Example 8–1
- Example 8–2
- Example 8–3
- Example 8–4
- Example 8–5
- Subroutines
- Example 8–6
- Halting
- Paper Exercises
- Exercise 16
- 8.3 Variations on Turing Machines
- The Universal Turing Machine
- Non-Deterministic TM = Deterministic TM
- Programming Exercise
- Chapter Summary
- Exercise 17
- Quiz 71 attempt allowed
- 9. The Landscape of Formal Languages
- Where Are We?
- Chapter Objectives
- 9.1 Recursively Enumerable Languages
- A Non-Recursive, RE Language
- Context-Sensitive Languages
- Properties of Recursively Enumerable Languages
- Paper Exercises
- 9.2 Unrestricted Grammars
- Example 9–1
- Example 9–2
- Example 9–3
- Example 9–4
- Context-Sensitive Grammars
- Equivalence of Unrestricted Grammars and Turing Machines
- Example 9–5
- Example 9–6
- Paper Exercises
- Exercise 18
- 9.3 The Chomsky Hierarchy
- Countable Sets
- Uncountable Sets
- Chapter Summary
- Exercise 19
- Quiz 81 attempt allowed
- 10. Computability
- Chapter Objectives
- 10.1 The Halting Problem
- Exercise 20
- 10.2 Reductions and Undecidability
- Example 10–1
- Example 10–2
- Example 10–3
- Paper Exercises
- Chapter Summary
- Exercise 21
- Quiz 91 attempt allowed
Instructors
Professional software developer for 20 years until 2001. Professor of Computer Science at Utah Valley University 2001–2022. Former contributing member of the C++ Standards Committee and Senior Editor of the C/C++ Users Journal. Author of C & C++ Code Capsules (Prentice-Hall, 1998) and co-author of Thinking in C++, Volume 2 (Prentice-Hall, 2004, with Bruce Eckel).
The Leanpub 60 Day 100% Happiness Guarantee
Within 60 days of purchase you can get a 100% refund on any Leanpub purchase, in two clicks.
Now, this is technically risky for us, since you'll have the book or course files either way. But we're so confident in our products and services, and in our authors and readers, that we're happy to offer a full money back guarantee for everything we sell.
You can only find out how good something is by trying it, and because of our 100% money back guarantee there's literally no risk to do so!
So, there's no reason not to click the Add to Cart button, is there?
See full terms...
Earn $8 on a $10 Purchase, and $16 on a $20 Purchase
We pay 80% royalties on purchases of $7.99 or more, and 80% royalties minus a 50 cent flat fee on purchases between $0.99 and $7.98. You earn $8 on a $10 sale, and $16 on a $20 sale. So, if we sell 5000 non-refunded copies of your book for $20, you'll earn $80,000.
(Yes, some authors have already earned much more than that on Leanpub.)
In fact, authors have earnedover $14 millionwriting, publishing and selling on Leanpub.
Learn more about writing on Leanpub
Free Updates. DRM Free.
If you buy a Leanpub book, you get free updates for as long as the author updates the book! Many authors use Leanpub to publish their books in-progress, while they are writing them. All readers get free updates, regardless of when they bought the book or how much they paid (including free).
Most Leanpub books are available in PDF (for computers) and EPUB (for phones, tablets and Kindle). The formats that a book includes are shown at the top right corner of this page.
Finally, Leanpub books don't have any DRM copy-protection nonsense, so you can easily read them on any supported device.
Learn more about Leanpub's ebook formats and where to read them
