Last 10 minutes of class on Wednesday, February 18, 2026.
Everyone takes the exam at the same time.
Automata Theory, including Turing Machines and Register Machines.
You will take the exam on Brightspace. There is 10 minute time limit, or 15 minutes for those with time-and-a-half accommodations.
Do each of the following to maximize your preparation:
Were you able to check off every box?
The fact that active recall is better for acquiring long-term knowledge does not mean that outlines and concept maps are not useful. Learners should use multiple techniques—think “both and” rather than “either or.”
Automata Theory
Concerned with how computations can be carried out
Definition of an automaton
Why finiteness matters
Finite description of machine
Finite input, finite alphabet (but memory unbounded)
Each step must take finite time (but unbounded number of steps)
Reasons to study this theory
A framework for studying computation in general
Understanding of real and abstract computers
Applications in compiler and interpreter construction
Examples of automata
Turing machine
Multitape Turing machine
Linear Bounded Automata
Pushdown Automata
Finite Automata
Queue Automata
Rewrite Machines
Register Machines
Stack Machines
Classification
Control: state transitions vs instructions vs rewrites
Memory: tape vs. register
Output: transducers vs. recognizers
Architecture: Harvard vs. von Neumann
Other dimensions
Connections to language theory
Automata as language recognizers
Recognizers vs deciders
Determinism
Classes of languages
Finite
recognized by FA without loops
S->a|b|c
Regular (Chomsky Type 3)
recognized by FA
LLG, RLG, Regular Grammar
Deterministic Context-free (a.k.a. LR)
recognized by DPDA
Context-free (Chomsky Type 2)
recognized by PDA
CFG
Context-sensitive (Chomsky Type 1)
recognized by LBA
ENCG or CSG
Recursive
recognized by Turing machine that halts on all inputs
also called Decidable
Recursively enumerable (Chomsky Type 0)
recognized by Turing machine
also called Turing-recognizable
abbreviated r.e.
what we think of as "computable"
(Finitely) Describable
Beyond Finitely Describable 🤯
Connections to complexity theory
Applications
Instruction-oriented languages
P''
Brainfuck
Turing Machines as languages
Turing Machines
Backstory
Basic idea
Examples
Tables
State Diagrams
Formal definition
Of transducing machine
Of recognizing machine
Encodings
Universal Turing Machines
Other variations
Moveless transitions
Moving without examining the current symbol
Multi-track tape
Multitape
Queue-based tape
Read-only input tape
Write-only output tape
Semi-infinite tape
LBAs
Bounded tape
PDAs
Read-only input
No backsies
Separate stack memory
Formal Definition
FAs
Read-only input
No backsies
No separate memory
Formal Definition
Random Access TMs
Determinism
Transition function instead of a relation
Halt-as-action vs. Halt-as-state
Alternate encoding
Has same power has nondeterministic TMs!
DFA and NFA have same power too
NPDA has more power than DPDA
For LBAs, we don't know if nondeterminism adds power
Register Machines
Definition
Counter Machines
RAMs
3AC
2AC
1AC
0AC (aka stack machines)
RASPs
This is a mini-quiz which tests for immediate understanding of topics and not your ability to work out problems over an extended duration of time. There is a strict time limit so that your immediate fluency is tested rather than your ability to search the web (or worse, ask a chatbot), since these things take time. There will be 5–10 questions, some will be multiple choice, some multi-select, and some matching. There are no free-form answers, so the exam will be autograded and you will see your score immediately after it is submitted.
All content on the assigned readings is fair game for questions, so do not neglect the readings, and by all means do the recall questions!