# 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