cancellation.tex

Paper VIII: Packet Operator Algorithms, Exact Compilation, and GPU Realization

cancellation.tex

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \node[font=\small,align=center,font=\small] at (2.3,4.3) {$K$};
4 \path[draw=black!30,fill=white] (0.7,2.8) rectangle (1.5,3.6);
5 \node[font=\small,align=center,font=\small] at (1.1,3.2) {$0$};
6 \path[draw=black!30,fill=white] (1.5,2.8) rectangle (2.3,3.6);
7 \node[font=\small,align=center,font=\small] at (1.9,3.2) {$0$};
8 \path[draw=black!30,fill=white] (2.3,2.8) rectangle (3.1,3.6);
9 \node[font=\small,align=center,font=\small] at (2.7,3.2) {$0$};
10 \path[draw=black!30,fill=white] (3.1,2.8) rectangle (3.9,3.6);
11 \node[font=\small,align=center,font=\small] at (3.5,3.2) {$0$};
12 \path[draw=black!30,fill=black!8] (0.7,2) rectangle (1.5,2.8);
13 \node[font=\small,align=center,font=\small] at (1.1,2.4) {$1$};
14 \path[draw=black!30,fill=white] (1.5,2) rectangle (2.3,2.8);
15 \node[font=\small,align=center,font=\small] at (1.9,2.4) {$0$};
16 \path[draw=black!30,fill=white] (2.3,2) rectangle (3.1,2.8);
17 \node[font=\small,align=center,font=\small] at (2.7,2.4) {$0$};
18 \path[draw=black!30,fill=white] (3.1,2) rectangle (3.9,2.8);
19 \node[font=\small,align=center,font=\small] at (3.5,2.4) {$0$};
20 \path[draw=black!30,fill=black!8] (0.7,1.2) rectangle (1.5,2);
21 \node[font=\small,align=center,font=\small] at (1.1,1.6) {$1$};
22 \path[draw=black!30,fill=white] (1.5,1.2) rectangle (2.3,2);
23 \node[font=\small,align=center,font=\small] at (1.9,1.6) {$0$};
24 \path[draw=black!30,fill=white] (2.3,1.2) rectangle (3.1,2);
25 \node[font=\small,align=center,font=\small] at (2.7,1.6) {$0$};
26 \path[draw=black!30,fill=white] (3.1,1.2) rectangle (3.9,2);
27 \node[font=\small,align=center,font=\small] at (3.5,1.6) {$0$};
28 \path[draw=black!30,fill=white] (0.7,0.4) rectangle (1.5,1.2);
29 \node[font=\small,align=center,font=\small] at (1.1,0.8) {$0$};
30 \path[draw=black!30,fill=black!8] (1.5,0.4) rectangle (2.3,1.2);
31 \node[font=\small,align=center,font=\small] at (1.9,0.8) {$1$};
32 \path[draw=black!30,fill=black!8] (2.3,0.4) rectangle (3.1,1.2);
33 \node[font=\small,align=center,font=\small] at (2.7,0.8) {$-1$};
34 \path[draw=black!30,fill=white] (3.1,0.4) rectangle (3.9,1.2);
35 \node[font=\small,align=center,font=\small] at (3.5,0.8) {$0$};
36 \node[font=\small,align=center,font=\small] at (7.2,4.3) {path counts at length two};
37 \path[draw=black!30,fill=white] (5.6,2.8) rectangle (6.4,3.6);
38 \node[font=\small,align=center,font=\small] at (6,3.2) {$0$};
39 \path[draw=black!30,fill=white] (6.4,2.8) rectangle (7.2,3.6);
40 \node[font=\small,align=center,font=\small] at (6.8,3.2) {$0$};
41 \path[draw=black!30,fill=white] (7.2,2.8) rectangle (8,3.6);
42 \node[font=\small,align=center,font=\small] at (7.6,3.2) {$0$};
43 \path[draw=black!30,fill=white] (8,2.8) rectangle (8.8,3.6);
44 \node[font=\small,align=center,font=\small] at (8.4,3.2) {$0$};
45 \path[draw=black!30,fill=white] (5.6,2) rectangle (6.4,2.8);
46 \node[font=\small,align=center,font=\small] at (6,2.4) {$0$};
47 \path[draw=black!30,fill=white] (6.4,2) rectangle (7.2,2.8);
48 \node[font=\small,align=center,font=\small] at (6.8,2.4) {$0$};
49 \path[draw=black!30,fill=white] (7.2,2) rectangle (8,2.8);
50 \node[font=\small,align=center,font=\small] at (7.6,2.4) {$0$};
51 \path[draw=black!30,fill=white] (8,2) rectangle (8.8,2.8);
52 \node[font=\small,align=center,font=\small] at (8.4,2.4) {$0$};
53 \path[draw=black!30,fill=white] (5.6,1.2) rectangle (6.4,2);
54 \node[font=\small,align=center,font=\small] at (6,1.6) {$0$};
55 \path[draw=black!30,fill=white] (6.4,1.2) rectangle (7.2,2);
56 \node[font=\small,align=center,font=\small] at (6.8,1.6) {$0$};
57 \path[draw=black!30,fill=white] (7.2,1.2) rectangle (8,2);
58 \node[font=\small,align=center,font=\small] at (7.6,1.6) {$0$};
59 \path[draw=black!30,fill=white] (8,1.2) rectangle (8.8,2);
60 \node[font=\small,align=center,font=\small] at (8.4,1.6) {$0$};
61 \path[draw=black!30,fill=black!8] (5.6,0.4) rectangle (6.4,1.2);
62 \node[font=\small,align=center,font=\small] at (6,0.8) {$2$};
63 \path[draw=black!30,fill=white] (6.4,0.4) rectangle (7.2,1.2);
64 \node[font=\small,align=center,font=\small] at (6.8,0.8) {$0$};
65 \path[draw=black!30,fill=white] (7.2,0.4) rectangle (8,1.2);
66 \node[font=\small,align=center,font=\small] at (7.6,0.8) {$0$};
67 \path[draw=black!30,fill=white] (8,0.4) rectangle (8.8,1.2);
68 \node[font=\small,align=center,font=\small] at (8.4,0.8) {$0$};
69 \node[font=\small,align=center] at (11.85,3) {$1+(-1)=0$};
70 \node[font=\small,align=center] at (11.85,1.65) {$K^2=0$};
71 \node[font=\small,align=center,font=\scriptsize] at (7,0.1) {Structural support is an upper bound. It does not encode destructive cancellation.};
72 \end{tikzpicture}

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