62 lines
997 B
Markdown
62 lines
997 B
Markdown
# Chapter 0
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dont do np hard problems
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# Define
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## Computability Theory
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1930s - 1950s
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What can be computed?
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## Automata Theory
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1930s - 1950s
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How does making changes o the underlying model effect computational power?
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## Complexity Theory
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1960s - Present
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What is computable in practice?
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P vs. NP
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# Graph Theory?
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## Define
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### Subgraph
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Let $G = \{V_G, E_G\}$ and $H = \{V_H, E_H\}$
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$G$ is a subgraph of $H$ if
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1. $V_A = V_H$
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2. $E_G \subset E_H + \forall(v_1, v_2)$
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### Path
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Hits vertices in a graph
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Simple Graph: only hits vertices once
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Cycle: There's some sort of loop in the graph
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Simple Cycle: Only repeated node is the first and last one
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Tree
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Directed Graph: a graph that is made up of a set of vertices connected by directed edges
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Strongly Connected: A directed graph is strongly connected if a directed path connects every two nodes.
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# Strings & Languages
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Alphabet: Non-empty finite set
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Symbol: Member of alphabet
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String: Sequence of symbols
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Language: Set of strings |