1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
|
<!DOCTYPE HTML>
<html lang="en" class="sidebar-visible no-js light">
<head>
<!-- Book generated using mdBook -->
<meta charset="UTF-8">
<title>Room DAG concepts - Synapse</title>
<!-- Custom HTML head -->
<meta content="text/html; charset=utf-8" http-equiv="Content-Type">
<meta name="description" content="">
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="theme-color" content="#ffffff" />
<link rel="icon" href="../favicon.svg">
<link rel="shortcut icon" href="../favicon.png">
<link rel="stylesheet" href="../css/variables.css">
<link rel="stylesheet" href="../css/general.css">
<link rel="stylesheet" href="../css/chrome.css">
<link rel="stylesheet" href="../css/print.css" media="print">
<!-- Fonts -->
<link rel="stylesheet" href="../FontAwesome/css/font-awesome.css">
<link rel="stylesheet" href="../fonts/fonts.css">
<!-- Highlight.js Stylesheets -->
<link rel="stylesheet" href="../highlight.css">
<link rel="stylesheet" href="../tomorrow-night.css">
<link rel="stylesheet" href="../ayu-highlight.css">
<!-- Custom theme stylesheets -->
<link rel="stylesheet" href="../docs/website_files/table-of-contents.css">
<link rel="stylesheet" href="../docs/website_files/remove-nav-buttons.css">
<link rel="stylesheet" href="../docs/website_files/indent-section-headers.css">
</head>
<body>
<!-- Provide site root to javascript -->
<script type="text/javascript">
var path_to_root = "../";
var default_theme = window.matchMedia("(prefers-color-scheme: dark)").matches ? "navy" : "light";
</script>
<!-- Work around some values being stored in localStorage wrapped in quotes -->
<script type="text/javascript">
try {
var theme = localStorage.getItem('mdbook-theme');
var sidebar = localStorage.getItem('mdbook-sidebar');
if (theme.startsWith('"') && theme.endsWith('"')) {
localStorage.setItem('mdbook-theme', theme.slice(1, theme.length - 1));
}
if (sidebar.startsWith('"') && sidebar.endsWith('"')) {
localStorage.setItem('mdbook-sidebar', sidebar.slice(1, sidebar.length - 1));
}
} catch (e) { }
</script>
<!-- Set the theme before any content is loaded, prevents flash -->
<script type="text/javascript">
var theme;
try { theme = localStorage.getItem('mdbook-theme'); } catch(e) { }
if (theme === null || theme === undefined) { theme = default_theme; }
var html = document.querySelector('html');
html.classList.remove('no-js')
html.classList.remove('light')
html.classList.add(theme);
html.classList.add('js');
</script>
<!-- Hide / unhide sidebar before it is displayed -->
<script type="text/javascript">
var html = document.querySelector('html');
var sidebar = 'hidden';
if (document.body.clientWidth >= 1080) {
try { sidebar = localStorage.getItem('mdbook-sidebar'); } catch(e) { }
sidebar = sidebar || 'visible';
}
html.classList.remove('sidebar-visible');
html.classList.add("sidebar-" + sidebar);
</script>
<nav id="sidebar" class="sidebar" aria-label="Table of contents">
<div class="sidebar-scrollbox">
<ol class="chapter"><li class="chapter-item expanded affix "><li class="part-title">Introduction</li><li class="chapter-item expanded "><a href="../welcome_and_overview.html">Welcome and Overview</a></li><li class="chapter-item expanded affix "><li class="part-title">Setup</li><li class="chapter-item expanded "><a href="../setup/installation.html">Installation</a></li><li class="chapter-item expanded "><a href="../postgres.html">Using Postgres</a></li><li class="chapter-item expanded "><a href="../reverse_proxy.html">Configuring a Reverse Proxy</a></li><li class="chapter-item expanded "><a href="../setup/forward_proxy.html">Configuring a Forward/Outbound Proxy</a></li><li class="chapter-item expanded "><a href="../turn-howto.html">Configuring a Turn Server</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../setup/turn/coturn.html">coturn TURN server</a></li><li class="chapter-item expanded "><a href="../setup/turn/eturnal.html">eturnal TURN server</a></li></ol></li><li class="chapter-item expanded "><a href="../delegate.html">Delegation</a></li><li class="chapter-item expanded affix "><li class="part-title">Upgrading</li><li class="chapter-item expanded "><a href="../upgrade.html">Upgrading between Synapse Versions</a></li><li class="chapter-item expanded affix "><li class="part-title">Usage</li><li class="chapter-item expanded "><a href="../federate.html">Federation</a></li><li class="chapter-item expanded "><a href="../usage/configuration/index.html">Configuration</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../usage/configuration/config_documentation.html">Configuration Manual</a></li><li class="chapter-item expanded "><a href="../usage/configuration/homeserver_sample_config.html">Homeserver Sample Config File</a></li><li class="chapter-item expanded "><a href="../usage/configuration/logging_sample_config.html">Logging Sample Config File</a></li><li class="chapter-item expanded "><a href="../structured_logging.html">Structured Logging</a></li><li class="chapter-item expanded "><a href="../templates.html">Templates</a></li><li class="chapter-item expanded "><a href="../usage/configuration/user_authentication/index.html">User Authentication</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../usage/configuration/user_authentication/single_sign_on/index.html">Single-Sign On</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../openid.html">OpenID Connect</a></li><li class="chapter-item expanded "><a href="../usage/configuration/user_authentication/single_sign_on/saml.html">SAML</a></li><li class="chapter-item expanded "><a href="../usage/configuration/user_authentication/single_sign_on/cas.html">CAS</a></li><li class="chapter-item expanded "><a href="../sso_mapping_providers.html">SSO Mapping Providers</a></li></ol></li><li class="chapter-item expanded "><a href="../password_auth_providers.html">Password Auth Providers</a></li><li class="chapter-item expanded "><a href="../jwt.html">JSON Web Tokens</a></li><li class="chapter-item expanded "><a href="../usage/configuration/user_authentication/refresh_tokens.html">Refresh Tokens</a></li></ol></li><li class="chapter-item expanded "><a href="../CAPTCHA_SETUP.html">Registration Captcha</a></li><li class="chapter-item expanded "><a href="../application_services.html">Application Services</a></li><li class="chapter-item expanded "><a href="../server_notices.html">Server Notices</a></li><li class="chapter-item expanded "><a href="../consent_tracking.html">Consent Tracking</a></li><li class="chapter-item expanded "><a href="../user_directory.html">User Directory</a></li><li class="chapter-item expanded "><a href="../message_retention_policies.html">Message Retention Policies</a></li><li class="chapter-item expanded "><a href="../modules/index.html">Pluggable Modules</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../modules/writing_a_module.html">Writing a module</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../modules/spam_checker_callbacks.html">Spam checker callbacks</a></li><li class="chapter-item expanded "><a href="../modules/third_party_rules_callbacks.html">Third-party rules callbacks</a></li><li class="chapter-item expanded "><a href="../modules/presence_router_callbacks.html">Presence router callbacks</a></li><li class="chapter-item expanded "><a href="../modules/account_validity_callbacks.html">Account validity callbacks</a></li><li class="chapter-item expanded "><a href="../modules/password_auth_provider_callbacks.html">Password auth provider callbacks</a></li><li class="chapter-item expanded "><a href="../modules/background_update_controller_callbacks.html">Background update controller callbacks</a></li><li class="chapter-item expanded "><a href="../modules/account_data_callbacks.html">Account data callbacks</a></li><li class="chapter-item expanded "><a href="../modules/porting_legacy_module.html">Porting a legacy module to the new interface</a></li></ol></li></ol></li><li class="chapter-item expanded "><a href="../workers.html">Workers</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../synctl_workers.html">Using synctl with Workers</a></li><li class="chapter-item expanded "><a href="../systemd-with-workers/index.html">Systemd</a></li></ol></li></ol></li><li class="chapter-item expanded "><a href="../usage/administration/index.html">Administration</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../usage/administration/admin_api/index.html">Admin API</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../admin_api/account_validity.html">Account Validity</a></li><li class="chapter-item expanded "><a href="../usage/administration/admin_api/background_updates.html">Background Updates</a></li><li class="chapter-item expanded "><a href="../admin_api/event_reports.html">Event Reports</a></li><li class="chapter-item expanded "><a href="../admin_api/experimental_features.html">Experimental Features</a></li><li class="chapter-item expanded "><a href="../admin_api/media_admin_api.html">Media</a></li><li class="chapter-item expanded "><a href="../admin_api/purge_history_api.html">Purge History</a></li><li class="chapter-item expanded "><a href="../admin_api/register_api.html">Register Users</a></li><li class="chapter-item expanded "><a href="../usage/administration/admin_api/registration_tokens.html">Registration Tokens</a></li><li class="chapter-item expanded "><a href="../admin_api/room_membership.html">Manipulate Room Membership</a></li><li class="chapter-item expanded "><a href="../admin_api/rooms.html">Rooms</a></li><li class="chapter-item expanded "><a href="../admin_api/server_notices.html">Server Notices</a></li><li class="chapter-item expanded "><a href="../admin_api/statistics.html">Statistics</a></li><li class="chapter-item expanded "><a href="../admin_api/user_admin_api.html">Users</a></li><li class="chapter-item expanded "><a href="../admin_api/version_api.html">Server Version</a></li><li class="chapter-item expanded "><a href="../usage/administration/admin_api/federation.html">Federation</a></li></ol></li><li class="chapter-item expanded "><a href="../manhole.html">Manhole</a></li><li class="chapter-item expanded "><a href="../metrics-howto.html">Monitoring</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../usage/administration/monitoring/reporting_homeserver_usage_statistics.html">Reporting Homeserver Usage Statistics</a></li></ol></li><li class="chapter-item expanded "><a href="../usage/administration/monthly_active_users.html">Monthly Active Users</a></li><li class="chapter-item expanded "><a href="../usage/administration/understanding_synapse_through_grafana_graphs.html">Understanding Synapse Through Grafana Graphs</a></li><li class="chapter-item expanded "><a href="../usage/administration/useful_sql_for_admins.html">Useful SQL for Admins</a></li><li class="chapter-item expanded "><a href="../usage/administration/database_maintenance_tools.html">Database Maintenance Tools</a></li><li class="chapter-item expanded "><a href="../usage/administration/state_groups.html">State Groups</a></li><li class="chapter-item expanded "><a href="../usage/administration/request_log.html">Request log format</a></li><li class="chapter-item expanded "><a href="../usage/administration/admin_faq.html">Admin FAQ</a></li><li class="chapter-item expanded "><div>Scripts</div></li></ol></li><li class="chapter-item expanded "><li class="part-title">Development</li><li class="chapter-item expanded "><a href="../development/contributing_guide.html">Contributing Guide</a></li><li class="chapter-item expanded "><a href="../code_style.html">Code Style</a></li><li class="chapter-item expanded "><a href="../development/reviews.html">Reviewing Code</a></li><li class="chapter-item expanded "><a href="../development/releases.html">Release Cycle</a></li><li class="chapter-item expanded "><a href="../development/git.html">Git Usage</a></li><li class="chapter-item expanded "><div>Testing</div></li><li><ol class="section"><li class="chapter-item expanded "><a href="../development/demo.html">Demo scripts</a></li></ol></li><li class="chapter-item expanded "><a href="../opentracing.html">OpenTracing</a></li><li class="chapter-item expanded "><a href="../development/database_schema.html">Database Schemas</a></li><li class="chapter-item expanded "><a href="../development/experimental_features.html">Experimental features</a></li><li class="chapter-item expanded "><a href="../development/dependencies.html">Dependency management</a></li><li class="chapter-item expanded "><div>Synapse Architecture</div></li><li><ol class="section"><li class="chapter-item expanded "><a href="../development/synapse_architecture/cancellation.html">Cancellation</a></li><li class="chapter-item expanded "><a href="../log_contexts.html">Log Contexts</a></li><li class="chapter-item expanded "><a href="../replication.html">Replication</a></li><li class="chapter-item expanded "><a href="../tcp_replication.html">TCP Replication</a></li><li class="chapter-item expanded "><a href="../development/synapse_architecture/faster_joins.html">Faster remote joins</a></li></ol></li><li class="chapter-item expanded "><a href="../development/internal_documentation/index.html">Internal Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><div>Single Sign-On</div></li><li><ol class="section"><li class="chapter-item expanded "><a href="../development/saml.html">SAML</a></li><li class="chapter-item expanded "><a href="../development/cas.html">CAS</a></li></ol></li><li class="chapter-item expanded "><a href="../development/room-dag-concepts.html" class="active">Room DAG concepts</a></li><li class="chapter-item expanded "><div>State Resolution</div></li><li><ol class="section"><li class="chapter-item expanded "><a href="../auth_chain_difference_algorithm.html">The Auth Chain Difference Algorithm</a></li></ol></li><li class="chapter-item expanded "><a href="../media_repository.html">Media Repository</a></li><li class="chapter-item expanded "><a href="../room_and_user_statistics.html">Room and User Statistics</a></li></ol></li><li class="chapter-item expanded "><div>Scripts</div></li><li class="chapter-item expanded affix "><li class="part-title">Other</li><li class="chapter-item expanded "><a href="../deprecation_policy.html">Dependency Deprecation Policy</a></li><li class="chapter-item expanded "><a href="../other/running_synapse_on_single_board_computers.html">Running Synapse on a Single-Board Computer</a></li></ol>
</div>
<div id="sidebar-resize-handle" class="sidebar-resize-handle"></div>
</nav>
<div id="page-wrapper" class="page-wrapper">
<div class="page">
<div id="menu-bar-hover-placeholder"></div>
<div id="menu-bar" class="menu-bar sticky bordered">
<div class="left-buttons">
<button id="sidebar-toggle" class="icon-button" type="button" title="Toggle Table of Contents" aria-label="Toggle Table of Contents" aria-controls="sidebar">
<i class="fa fa-bars"></i>
</button>
<button id="theme-toggle" class="icon-button" type="button" title="Change theme" aria-label="Change theme" aria-haspopup="true" aria-expanded="false" aria-controls="theme-list">
<i class="fa fa-paint-brush"></i>
</button>
<ul id="theme-list" class="theme-popup" aria-label="Themes" role="menu">
<li role="none"><button role="menuitem" class="theme" id="light">Light (default)</button></li>
<li role="none"><button role="menuitem" class="theme" id="rust">Rust</button></li>
<li role="none"><button role="menuitem" class="theme" id="coal">Coal</button></li>
<li role="none"><button role="menuitem" class="theme" id="navy">Navy</button></li>
<li role="none"><button role="menuitem" class="theme" id="ayu">Ayu</button></li>
</ul>
<button id="search-toggle" class="icon-button" type="button" title="Search. (Shortkey: s)" aria-label="Toggle Searchbar" aria-expanded="false" aria-keyshortcuts="S" aria-controls="searchbar">
<i class="fa fa-search"></i>
</button>
</div>
<h1 class="menu-title">Synapse</h1>
<div class="right-buttons">
<a href="../print.html" title="Print this book" aria-label="Print this book">
<i id="print-button" class="fa fa-print"></i>
</a>
<a href="https://github.com/matrix-org/synapse" title="Git repository" aria-label="Git repository">
<i id="git-repository-button" class="fa fa-github"></i>
</a>
<a href="https://github.com/matrix-org/synapse/edit/develop/docs/development/room-dag-concepts.md" title="Suggest an edit" aria-label="Suggest an edit">
<i id="git-edit-button" class="fa fa-edit"></i>
</a>
</div>
</div>
<div id="search-wrapper" class="hidden">
<form id="searchbar-outer" class="searchbar-outer">
<input type="search" id="searchbar" name="searchbar" placeholder="Search this book ..." aria-controls="searchresults-outer" aria-describedby="searchresults-header">
</form>
<div id="searchresults-outer" class="searchresults-outer hidden">
<div id="searchresults-header" class="searchresults-header"></div>
<ul id="searchresults">
</ul>
</div>
</div>
<!-- Apply ARIA attributes after the sidebar and the sidebar toggle button are added to the DOM -->
<script type="text/javascript">
document.getElementById('sidebar-toggle').setAttribute('aria-expanded', sidebar === 'visible');
document.getElementById('sidebar').setAttribute('aria-hidden', sidebar !== 'visible');
Array.from(document.querySelectorAll('#sidebar a')).forEach(function(link) {
link.setAttribute('tabIndex', sidebar === 'visible' ? 0 : -1);
});
</script>
<div id="content" class="content">
<main>
<!-- Page table of contents -->
<div class="sidetoc">
<nav class="pagetoc"></nav>
</div>
<h1 id="room-dag-concepts"><a class="header" href="#room-dag-concepts">Room DAG concepts</a></h1>
<h2 id="edges"><a class="header" href="#edges">Edges</a></h2>
<p>The word "edge" comes from graph theory lingo. An edge is just a connection
between two events. In Synapse, we connect events by specifying their
<code>prev_events</code>. A subsequent event points back at a previous event.</p>
<pre><code>A (oldest) <---- B <---- C (most recent)
</code></pre>
<h2 id="depth-and-stream-ordering"><a class="header" href="#depth-and-stream-ordering">Depth and stream ordering</a></h2>
<p>Events are normally sorted by <code>(topological_ordering, stream_ordering)</code> where
<code>topological_ordering</code> is just <code>depth</code>. In other words, we first sort by <code>depth</code>
and then tie-break based on <code>stream_ordering</code>. <code>depth</code> is incremented as new
messages are added to the DAG. Normally, <code>stream_ordering</code> is an auto
incrementing integer, but backfilled events start with <code>stream_ordering=-1</code> and decrement.</p>
<hr />
<ul>
<li><code>/sync</code> returns things in the order they arrive at the server (<code>stream_ordering</code>).</li>
<li><code>/messages</code> (and <code>/backfill</code> in the federation API) return them in the order determined by the event graph <code>(topological_ordering, stream_ordering)</code>.</li>
</ul>
<p>The general idea is that, if you're following a room in real-time (i.e.
<code>/sync</code>), you probably want to see the messages as they arrive at your server,
rather than skipping any that arrived late; whereas if you're looking at a
historical section of timeline (i.e. <code>/messages</code>), you want to see the best
representation of the state of the room as others were seeing it at the time.</p>
<h2 id="outliers"><a class="header" href="#outliers">Outliers</a></h2>
<p>We mark an event as an <code>outlier</code> when we haven't figured out the state for the
room at that point in the DAG yet. They are "floating" events that we haven't
yet correlated to the DAG.</p>
<p>Outliers typically arise when we fetch the auth chain or state for a given
event. When that happens, we just grab the events in the state/auth chain,
without calculating the state at those events, or backfilling their
<code>prev_events</code>. Since we don't have the state at any events fetched in that
way, we mark them as outliers.</p>
<p>So, typically, we won't have the <code>prev_events</code> of an <code>outlier</code> in the database,
(though it's entirely possible that we <em>might</em> have them for some other
reason). Other things that make outliers different from regular events:</p>
<ul>
<li>
<p>We don't have state for them, so there should be no entry in
<code>event_to_state_groups</code> for an outlier. (In practice this isn't always
the case, though I'm not sure why: see https://github.com/matrix-org/synapse/issues/12201).</p>
</li>
<li>
<p>We don't record entries for them in the <code>event_edges</code>,
<code>event_forward_extremeties</code> or <code>event_backward_extremities</code> tables.</p>
</li>
</ul>
<p>Since outliers are not tied into the DAG, they do not normally form part of the
timeline sent down to clients via <code>/sync</code> or <code>/messages</code>; however there is an
exception:</p>
<h3 id="out-of-band-membership-events"><a class="header" href="#out-of-band-membership-events">Out-of-band membership events</a></h3>
<p>A special case of outlier events are some membership events for federated rooms
that we aren't full members of. For example:</p>
<ul>
<li>invites received over federation, before we join the room</li>
<li><em>rejections</em> for said invites</li>
<li>knock events for rooms that we would like to join but have not yet joined.</li>
</ul>
<p>In all the above cases, we don't have the state for the room, which is why they
are treated as outliers. They are a bit special though, in that they are
proactively sent to clients via <code>/sync</code>.</p>
<h2 id="forward-extremity"><a class="header" href="#forward-extremity">Forward extremity</a></h2>
<p>Most-recent-in-time events in the DAG which are not referenced by any other
events' <code>prev_events</code> yet. (In this definition, outliers, rejected events, and
soft-failed events don't count.)</p>
<p>The forward extremities of a room (or at least, a subset of them, if there are
more than ten) are used as the <code>prev_events</code> when the next event is sent.</p>
<p>The "current state" of a room (ie: the state which would be used if we
generated a new event) is, therefore, the resolution of the room states
at each of the forward extremities.</p>
<h2 id="backward-extremity"><a class="header" href="#backward-extremity">Backward extremity</a></h2>
<p>The current marker of where we have backfilled up to and will generally be the
<code>prev_events</code> of the oldest-in-time events we have in the DAG. This gives a starting point when
backfilling history.</p>
<p>Note that, unlike forward extremities, we typically don't have any backward
extremity events themselves in the database - or, if we do, they will be "outliers" (see
above). Either way, we don't expect to have the room state at a backward extremity.</p>
<p>When we persist a non-outlier event, if it was previously a backward extremity,
we clear it as a backward extremity and set all of its <code>prev_events</code> as the new
backward extremities if they aren't already persisted as non-outliers. This
therefore keeps the backward extremities up-to-date.</p>
<h2 id="state-groups"><a class="header" href="#state-groups">State groups</a></h2>
<p>For every non-outlier event we need to know the state at that event. Instead of
storing the full state for each event in the DB (i.e. a <code>event_id -> state</code>
mapping), which is <em>very</em> space inefficient when state doesn't change, we
instead assign each different set of state a "state group" and then have
mappings of <code>event_id -> state_group</code> and <code>state_group -> state</code>.</p>
<h3 id="stage-group-edges"><a class="header" href="#stage-group-edges">Stage group edges</a></h3>
<p>TODO: <code>state_group_edges</code> is a further optimization...
notes from @Azrenbeth, https://pastebin.com/seUGVGeT</p>
</main>
<nav class="nav-wrapper" aria-label="Page navigation">
<!-- Mobile navigation buttons -->
<a rel="prev" href="../development/cas.html" class="mobile-nav-chapters previous" title="Previous chapter" aria-label="Previous chapter" aria-keyshortcuts="Left">
<i class="fa fa-angle-left"></i>
</a>
<a rel="next" href="../auth_chain_difference_algorithm.html" class="mobile-nav-chapters next" title="Next chapter" aria-label="Next chapter" aria-keyshortcuts="Right">
<i class="fa fa-angle-right"></i>
</a>
<div style="clear: both"></div>
</nav>
</div>
</div>
<nav class="nav-wide-wrapper" aria-label="Page navigation">
<a rel="prev" href="../development/cas.html" class="nav-chapters previous" title="Previous chapter" aria-label="Previous chapter" aria-keyshortcuts="Left">
<i class="fa fa-angle-left"></i>
</a>
<a rel="next" href="../auth_chain_difference_algorithm.html" class="nav-chapters next" title="Next chapter" aria-label="Next chapter" aria-keyshortcuts="Right">
<i class="fa fa-angle-right"></i>
</a>
</nav>
</div>
<script type="text/javascript">
window.playground_copyable = true;
</script>
<script src="../elasticlunr.min.js" type="text/javascript" charset="utf-8"></script>
<script src="../mark.min.js" type="text/javascript" charset="utf-8"></script>
<script src="../searcher.js" type="text/javascript" charset="utf-8"></script>
<script src="../clipboard.min.js" type="text/javascript" charset="utf-8"></script>
<script src="../highlight.js" type="text/javascript" charset="utf-8"></script>
<script src="../book.js" type="text/javascript" charset="utf-8"></script>
<!-- Custom JS scripts -->
<script type="text/javascript" src="../docs/website_files/table-of-contents.js"></script>
</body>
</html>
|
