Theory of Computation

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reading · we frame, you read MIT or the canonical taught · we author, no canonical fits ↺ spirals back to earlier lessons

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reading · 30 min + ~208 min canonical

Finite Automata and the Regex Engine

This course is where computer science stops asking "how do we build it?" and starts asking "what can be built at all?" — and it begins with the simplest possible model of computat…

primary MIT 18.404J Theory of Computation (OCW)

preview →

reading · 30 min + ~208 min canonical L1

The Limits of Regular Languages: The Pumping Lemma

The last lesson showed that regexes are exactly as powerful as finite automata. This lesson shows you the ceiling of that power — and it's lower than you'd think. There are dead-s…

primary MIT 18.404J Theory of Computation (OCW)

after L1 locked

reading · 30 min + ~208 min canonical L1

Context-Free Grammars and Parsing: Adding a Stack

Last lesson ended on a limit: finite automata can't handle nesting, so regexes can't parse HTML, arithmetic expressions, or any structure with arbitrary depth. This lesson is the …

primary MIT 18.404J Theory of Computation (OCW)

after L2 locked

reading · 35 min + ~208 min canonical L1

Turing Machines and Undecidability: The Halting Problem

Here is a result that will change how you think about problems forever: there are questions no computer can ever answer — not because we lack the hardware or haven't found the alg…

primary MIT 18.404J Theory of Computation (OCW)

after L3 locked

reading · 35 min + ~208 min canonical L1

Complexity Classes and NP-Completeness: When a Problem Is Provably Hard

The last lesson was about what computers can't do at all. This one is about what they can't do efficiently — and it's arguably even more practically useful, because you'll meet th…

primary MIT 18.404J Theory of Computation (OCW)

after L4 locked

exercise reading · 15 min L1

Exercises: Easy (Warm-up)

- [ ] Draw DFAs for: strings ending in "01", even number of 0s, divisible by 3 in binary — 3 DFA exercises - [ ] Convert an NFA to DFA using subset construction — Given a 4-state …

after L5 locked

exercise reading · 30 min L1

Exercises: Medium (Core)

- [ ] Prove a language is not regular using the Pumping Lemma — {a^n b^n | n >= 0} — Classic proof - [ ] Design a PDA for {a^n b^n | n >= 0} — Push a's, pop on b's, accept if stac…

after L6 locked

exercise reading · 45 min L1

Exercises: Hard (Stretch)

- [ ] Reduce Halting Problem to prove another language is undecidable — e.g., "does TM accept empty string?" - [ ] Prove 3-COLOR is NP-complete by reduction from 3-SAT — Polynomia…

after L7 locked

exercise reading · 60 min L1

Mini-Project

- [ ] Build a regex engine in Ruby from scratch — Parse regex to NFA (Thompson's construction), convert NFA to DFA (subset construction), simulate DFA on input strings; support .,…

after L8 locked

L10

project reading · 480 min L1

Project: Regex Engine in Ruby

Parse a regex pattern into an NFA (Thompson's construction), optionally convert to DFA (subset construction), and match input strings. Support ., , +, ?, |, and (). No Ruby Regexp…

after L9 locked

L11

project reading · 300 min L1

Project: Turing Machine Simulator

Build a Turing machine simulator in Ruby. Define machines with states, alphabet, transition function. Simulate execution step-by-step with tape visualization. Include 3 example ma…

after L10 locked

L12

project reading · 300 min L1

Project: Write-Ahead Log in Ruby

Implement a WAL that logs every write operation to a sequential file before applying it. On crash recovery (simulate by killing the process), replay the log to restore state. This…

after L11 locked

L13

assessment reading · 63 min L1

Self-Assessment: Theory of Computation

- [ ] What is a DFA? How does it differ from an NFA? Are they equivalent in power? - [ ] What is the Pumping Lemma for regular languages? How do you use it to prove a language is …

after L12 locked

L14

assessment reading · 60 min L1

Quarter 8 Gate Check: Databases and Theory of Computation

- [ ] Course 8.1 knowledge check passed - [ ] Course 8.2 knowledge check passed - [ ] Mini Database Engine capstone completed

after L13 locked

L15

assessment reading · 120 min L1

Year 2 Assessment: Systems

Complete all of the following:

after L14 locked

15 lessons. Read in order; spiral back when you need to. By the end you'll have used the core ideas twice — once on the abstract, once on something you'll meet at work next week.