Changes

A more fine combing of the second Table brings to mind a rule that partly covers the remaining cases, that is, <math>\texttt{du~=~v}, ~\texttt{dv~=~(u)}.</math>  This much information about Orbit&nbsp;2 is also encapsulated by the extended proposition, <math>\texttt{(uv)((du, v))(dv, u)},</math> which says that <math>u\!</math> and <math>v\!</math> are not both true at the same time, while <math>du\!</math> is equal in value to <math>v\!</math> and <math>dv\!</math> is opposite in value to <math>u.\!</math>

A more fine combing of the second Table brings to mind a rule that partly covers the remaining cases, that is, <math>\texttt{du~=~v}, ~\texttt{dv~=~(u)}.</math>  This much information about Orbit&nbsp;2 is also encapsulated by the extended proposition, <math>\texttt{(uv)((du, v))(dv, u)},</math> which says that <math>u\!</math> and <math>v\!</math> are not both true at the same time, while <math>du\!</math> is equal in value to <math>v\!</math> and <math>dv\!</math> is opposite in value to <math>u.\!</math>

==Note 21==

==Turing Machine Example==

By way of providing a simple illustration of Cook's Theorem, namely, that "Propositional Satisfiability is NP-Complete", I will describe one way to translate finite approximations of turing machines into propositional expressions, using the cactus language syntax for propositional calculus that I will describe in more detail as we proceed.

By way of providing a simple illustration of Cook's Theorem, namely, that "Propositional Satisfiability is NP-Complete", I will describe one way to translate finite approximations of turing machines into propositional expressions, using the cactus language syntax for propositional calculus that I will describe in more detail as we proceed.