diff --git a/document.pdf b/document.pdf index 5667997..ec699b2 100644 Binary files a/document.pdf and b/document.pdf differ diff --git a/document.tex b/document.tex index a6a87c7..1725a44 100644 --- a/document.tex +++ b/document.tex @@ -164,6 +164,15 @@ \Phi(T, P) &\define \Bigl( \Gamma(T, P), \Gamma(P, T) \Bigr) \end{align*} + Without stable revision where $(T, P) = (\{ a, b \}, \{ a, b \})$ + \begin{align*} + \Phi(T, P) = (\{ a, b \}, \{ a, b \}) \textrm{ (fixpoint reached)} + \end{align*} + With stable revision + \begin{align*} + S(T, P) = (\emptyset, \emptyset) \textrm{ (fixpoint reached)} + \end{align*} + \section{The Polynomial Heirarchy} Intuitive definitions of ${\sf NP}$