diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 50c85a2..01ae2cb 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -13,7 +13,7 @@ "state": { "type": "markdown", "state": { - "file": "UNB/Year 4/Semester 2/CS3873/2024-01-24.md", + "file": "UNB/Year 4/Semester 2/CS2333/2024-01-24.md", "mode": "source", "source": false } @@ -85,7 +85,7 @@ "state": { "type": "backlink", "state": { - "file": "UNB/Year 4/Semester 2/CS3873/2024-01-24.md", + "file": "UNB/Year 4/Semester 2/CS2333/2024-01-24.md", "collapseAll": false, "extraContext": false, "sortOrder": "alphabetical", @@ -102,7 +102,7 @@ "state": { "type": "outgoing-link", "state": { - "file": "UNB/Year 4/Semester 2/CS3873/2024-01-24.md", + "file": "UNB/Year 4/Semester 2/CS2333/2024-01-24.md", "linksCollapsed": false, "unlinkedCollapsed": true } @@ -125,7 +125,7 @@ "state": { "type": "outline", "state": { - "file": "UNB/Year 4/Semester 2/CS3873/2024-01-24.md" + "file": "UNB/Year 4/Semester 2/CS2333/2024-01-24.md" } } }, @@ -158,8 +158,9 @@ }, "active": "81e5aff710e811bc", "lastOpenFiles": [ - "UNB/Year 4/Semester 2/CS3873/2024-01-22.md", "UNB/Year 4/Semester 2/CS3873/2024-01-24.md", + "UNB/Year 4/Semester 2/CS2333/2024-01-24.md", + "UNB/Year 4/Semester 2/CS3873/2024-01-22.md", "UNB/Year 4/Semester 2/STAT2593/2024-01-24.md", "UNB/Year 4/Semester 2/CS2333/2024-01-22.md", "UNB/Year 4/Semester 2/CS2333/2024-01-19.md", @@ -190,7 +191,6 @@ "Semester 1/CS3418/11-15-2023.md", "Semester 1/CS3418/11-13-2023.md", "Semester 1/CS3418/11-1-2023.md", - "Semester 1/CS2418/10-27-2023.md", "Semester 1/CS2418", "Semester 1/CS3418" ] diff --git a/UNB/Year 4/Semester 2/CS2333/2024-01-24.md b/UNB/Year 4/Semester 2/CS2333/2024-01-24.md new file mode 100644 index 0000000..e286f20 --- /dev/null +++ b/UNB/Year 4/Semester 2/CS2333/2024-01-24.md @@ -0,0 +1,49 @@ +Lecture Topic: + +# Equivalence Classes +You can represent equivalence classes by writing each one as a set: +$$C_0 = \{..., -10, -5, 0, 5, 10, 15, ...\} \text{ or } \{5p | p \in \mathbb{Z}\}$$ +$$C_0 = \{..., -9, -4, 1, 6, 11, 16, ...\} \text{ or } \{5p + 1| p \in \mathbb{Z}\}$$ +$$\text{and so on...}$$ +# Graphs +Definitions: +- For each *vertex* v, the **degree** of v is the number of edges incident on v +- A *path* is a **sequence** of vertices connected by edges +- A *cycle* is a path that **starts and ends** at the same vertex +- A *simple path* is a path that has **no repeated** vertices +- A *connected graph* contains a path between **every pair** of vertices +- A *disconnected graph* is the opposite (look at slides for real def) + +# Regular Languages +A class of languages that can be processed by simple computers called **finite automata** + +## Simple Example of a finite automaton +Vending machine/toll booth gate +Requires 25 cents or more to be deposited (gives no change) + +Takes as input, 5 cent, 10 cent, 25 cent coins +Uses **states** to remember how much has been deposited so far + +States: +- q_0 : 0 cents deposited (START STATE) +- q_5 : 5 cents +- q_10 : 10 cents +- q_15 : 15 cents +- q_20 : 20 cents +- q_25 : 25 cents (ACCEPT STATE) + +We represent the input as a **string** of symbols. +- n = nickel +- d = dime +- q = quarter +Examples: +- ddn +- ndd +- dnd +- q +Not accepted examples: +- nd +- d +- $\epsilon$ +## State Diagram +(not really possible without an image in obsidian) \ No newline at end of file