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\@writefile{toc}{\contentsline {section}{\numberline {1}Monotone Circuit Depth Lower Bounds}{1}{section.1}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Block sensitivity, Critical Block Sensitivity, Decision Tree Depth}{1}{section.2}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Defining the Gadget}{2}{section.3}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Communication Complexity Lower Bound for Lifted Tseitin via Set Disjointness}{2}{section.4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}The Reduction}{3}{subsection.4.1}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The reduction mapping $(a,b)$ to a distribution $(x,y)$. In this example $bs=2$ and $n=7$. The critical input is $\alpha =1011010$ and the two sensitive blocks are $B_1=\{2,3,4\}$ and $B_2=\{6,7\}$. The input pair $(a_i,b_i)$, $i=1,2$, is plugged in for the block $B_i$.}}{4}{figure.1}}
\newlabel{fig:reduction}{{1}{4}{The reduction mapping $(a,b)$ to a distribution $(x,y)$. In this example $bs=2$ and $n=7$. The critical input is $\alpha =1011010$ and the two sensitive blocks are $B_1=\{2,3,4\}$ and $B_2=\{6,7\}$. The input pair $(a_i,b_i)$, $i=1,2$, is plugged in for the block $B_i$}{figure.1}{}}