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ajsutton committed Apr 16, 2024
1 parent 2b17d6e commit 113333f
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2 changes: 1 addition & 1 deletion experimental/fault-proof/stage-one/fault-dispute-game.html
Original file line number Diff line number Diff line change
Expand Up @@ -298,7 +298,7 @@ <h3 id="game-tree"><a class="header" href="#game-tree">Game Tree</a></h3>
The Game Tree has a split depth and maximum depth, <code>SPLIT_DEPTH</code> and <code>MAX_GAME_DEPTH</code> respectively, that are both
preset to an FDG implementation. The split depth defines the maximum depth at which claims about
<a href="../../../glossary.html#L2-output-root">output roots</a> can occur, and below it, execution trace bisection occurs. Thus, the Game Tree contains
<span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8491em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">d</span><span class="mbin mtight"></span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span> positions, where <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">d</span></span></span></span> is the <code>MAX_GAME_DEPTH</code> (unless <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span>, in which case there's only 1 position).</p>
<span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9324em;vertical-align:-0.0833em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">d</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin"></span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> positions, where <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">d</span></span></span></span> is the <code>MAX_GAME_DEPTH</code> (unless <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span>, in which case there's only 1 position).</p>
<p>The full game tree, with a layer of the tree allocated to output bisection, and sub-trees after an arbitrary split
depth, looks like:</p>
<p><img src="../../../static/assets/ob-tree.png" alt="ob-tree" /></p>
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2 changes: 1 addition & 1 deletion print.html
Original file line number Diff line number Diff line change
Expand Up @@ -6231,7 +6231,7 @@ <h3 id="game-tree"><a class="header" href="#game-tree">Game Tree</a></h3>
The Game Tree has a split depth and maximum depth, <code>SPLIT_DEPTH</code> and <code>MAX_GAME_DEPTH</code> respectively, that are both
preset to an FDG implementation. The split depth defines the maximum depth at which claims about
<a href="experimental/fault-proof/stage-one/../../../glossary.html#L2-output-root">output roots</a> can occur, and below it, execution trace bisection occurs. Thus, the Game Tree contains
<span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8491em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">d</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span> positions, where <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">d</span></span></span></span> is the <code>MAX_GAME_DEPTH</code> (unless <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span>, in which case there's only 1 position).</p>
<span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9324em;vertical-align:-0.0833em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">d</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> positions, where <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">d</span></span></span></span> is the <code>MAX_GAME_DEPTH</code> (unless <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span>, in which case there's only 1 position).</p>
<p>The full game tree, with a layer of the tree allocated to output bisection, and sub-trees after an arbitrary split
depth, looks like:</p>
<p><img src="experimental/fault-proof/stage-one/../../../static/assets/ob-tree.png" alt="ob-tree" /></p>
Expand Down
2 changes: 1 addition & 1 deletion searchindex.js

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2 changes: 1 addition & 1 deletion searchindex.json

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