1-22-25 notes

Formal Lang.md

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+# 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