formal-notes/Formal Lang.md
2025-01-22 15:05:47 -06:00

997 B

Chapter 0

dont do np hard problems

Define

Computability Theory

1930s - 1950s

What can be computed?

Automata Theory

1930s - 1950s

How does making changes o the underlying model effect computational power?

Complexity Theory

1960s - Present

What is computable in practice?

P vs. NP

Graph Theory?

Define

Subgraph

Let G = \{V_G, E_G\} and H = \{V_H, E_H\}

G is a subgraph of H if

  1. V_A = V_H
  2. E_G \subset E_H + \forall(v_1, v_2)

Path

Hits vertices in a graph

Simple Graph: only hits vertices once

Cycle: There's some sort of loop in the graph

Simple Cycle: Only repeated node is the first and last one

Tree

Directed Graph: a graph that is made up of a set of vertices connected by directed edges

Strongly Connected: A directed graph is strongly connected if a directed path connects every two nodes.

Strings & Languages

Alphabet: Non-empty finite set

Symbol: Member of alphabet

String: Sequence of symbols

Language: Set of strings