997 B
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
V_A = V_HE_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