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nexus/sreweekly/articles/223/04-who-s-afraid-of-serializability.html
2026-09-12 17:23:01 +08:00

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<meta name="description" content="https://twitter.com/jepsen_io/status/1271427955525185536?s=20 Kyle Kingsbury&#039;s Jepsen recently did an analysis of PostgreSQL 12.3 and found that under certain conditions it violated guarantees it makes about transactions, including violations of the serializability transaction isolation level. I thought it would be fun to use one of his counterexamples to illustrate what serializable means. Here&#039;s one of the counterexamples that&hellip;" />
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<h1 class="entry-title">Who&#8217;s afraid of serializability?</h1> </header><!-- .entry-header --> <div class="entry-meta">
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<a href="https://surfingcomplexity.blog/author/lorinh/" rel="author">Lorin Hochstein</a> </span>
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<time class="entry-date published" datetime="2020-06-13T23:05:05-07:00">June 13, 2020</time><time class="updated" datetime="2020-06-14T17:54:34-07:00">June 14, 2020</time> </span>
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<div class="embed-twitter"><blockquote class="twitter-tweet" data-width="550" data-dnt="true"><p lang="en" dir="ltr">A new Jepsen report! It turns out that PostgreSQL&#39;s &quot;serializable&quot; isolation was not, in fact, serializable: it exhibited G2-item. A patch is coming in the next minor release. 🙂 <a href="https://t.co/GjFyRhAJIh">https://t.co/GjFyRhAJIh</a></p>&mdash; Jepsen (@jepsen_io) <a href="https://twitter.com/jepsen_io/status/1271427955525185536?ref_src=twsrc%5Etfw">June 12, 2020</a></blockquote><script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script></div>
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<div class="wp-block-jetpack-markdown"><p>Kyle Kingsbury&#8217;s <em>Jepsen</em> recently did <a href="http://jepsen.io/analyses/postgresql-12.3">an analysis of PostgreSQL
12.3</a> and found that under certain
conditions it violated guarantees it makes about transactions, including
violations of the <a href="https://jepsen.io/consistency/models/serializable">serializability</a> transaction
isolation level.</p>
<p>I thought it would be fun to use one of his counterexamples to illustrate what serializable means.</p>
<p>Here&#8217;s one of the counterexamples that Jepsen&#8217;s tool, <a href="https://github.com/jepsen-io/elle">Elle</a>, found:</p>
</div>
<figure class="wp-block-image size-large"><img data-attachment-id="1325" data-permalink="https://surfingcomplexity.blog/counterexample/" data-orig-file="https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample.png" data-orig-size="769,330" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="counterexample" data-image-description="" data-image-caption="" data-large-file="https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample.png?w=769" width="769" height="330" src="https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample.png?w=769" alt="" class="wp-image-1325" srcset="https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample.png 769w, https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample.png?w=150 150w, https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample.png?w=300 300w" sizes="(max-width: 769px) 100vw, 769px" /></figure>
<div class="wp-block-jetpack-markdown"><p>In this counterexample, there are two list objects, here named 1799 and 1798, which I&#8217;m going to call <em>x</em> and <em>y</em>. The examples use two list operations, append (denoted &quot;a&quot;) and read (denoted &quot;r&quot;).</p>
<p>Here&#8217;s my redrawing of the example. I&#8217;ve drawn all operations against <em>x</em> in blue and against <em>y</em> in red. Note that I&#8217;m using empty list (<code>[]</code>) instead of <em>nil</em>.</p>
</div>
<figure class="wp-block-image size-large"><img data-attachment-id="1327" data-permalink="https://surfingcomplexity.blog/counterexample-redrawn/" data-orig-file="https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample-redrawn.jpg" data-orig-size="1193,745" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}" data-image-title="counterexample-redrawn" data-image-description="" data-image-caption="" data-large-file="https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample-redrawn.jpg?w=1024" width="1024" height="639" src="https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample-redrawn.jpg?w=1024" alt="" class="wp-image-1327" srcset="https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample-redrawn.jpg?w=1024 1024w, https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample-redrawn.jpg?w=150 150w, https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample-redrawn.jpg?w=300 300w, https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample-redrawn.jpg?w=768 768w, https://surfingcomplexity.blog/wp-content/uploads/2020/06/counterexample-redrawn.jpg 1193w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>
<div class="wp-block-jetpack-markdown"><p>There are two transactions, which I&#8217;ve denoted T1 and T2, and each one involves operations on two list objects, denoted <em>x</em> and <em>y</em>. The lists are initially empty.</p>
<p>For transactions that use the <em>serializability</em> isolation model, all of the operations in all of the
transactions have to be consistent with some sequential ordering of the transactions. In this particular
example, that means that all of the operations have to make sense assuming either:</p>
<ul>
<li>all of the operations in T1 happened before all of the operations in T2</li>
<li>all of the operations in T2 happened before all of the operations in T1</li>
</ul>
<h1>Assume order: T1, T2</h1>
<p>If we assume T1 happened before T2, then the operations for <em>x</em> are:</p>
<pre><code> x = []
T1: x.append(2)
T2: x.read() → []
</code></pre>
<p>This history violates the contract of a list: we&#8217;ve appended an element to a list but then read an empty list. It&#8217;s
as if the append didn&#8217;t happen!</p>
<h1>Assume order: T2, T1</h1>
<p>If we assume T2 happened before T1, then the operations for <em>y</em> are:</p>
<pre><code> y = []
T2: y.append(4)
y.append(5)
y.read() → [4, 5]
T1: y.read() → []
</code></pre>
<p>This history violates the contract of a list as well: we read <code>[4, 5]</code> and then <code>[ ]</code>: it&#8217;s as if the values disappeared!</p>
<p>Kingsbury indicates that this pair of transactions are illegal by annotating the operations with arrows that show required orderings. The &quot;rw&quot;
arrow means that the read operation that happened in the tail must be ordered before the write operation at the head of the arrow. If the arrows form a cycle, then the example violates serializability: there&#8217;s no possible ordering that can satisfy all of the arrows.</p>
<h1>Serializability, linearizability, locality</h1>
<p>This example is a good illustration of how serializability differs from <a href="https://jepsen.io/consistency/models/linearizable">linearizability</a>.
Lineraizability is a consistency model that also requires that operations must be consistent with sequential ordering.
However, linearizability is only about individual objects, where transactions refer to collections of objects.</p>
<p>(Linearizability also requires that if operation <em>A</em> happens before operation
<em>B</em> in time, then operation <em>A</em> must take effect before operation <em>B</em>, and
serializability doesn&#8217;t require that, but let&#8217;s put that aside for now).</p>
<p>This counterexample above is a <em>linearizable</em> history: we can order the operations such that they are consistent with the contracts of x and y. Here&#8217;s an example of a valid history, which is called a <em>linearization</em>:</p>
<pre><code>x = []
y = []
x.read() → []
x.append(2)
y.read() → []
y.append(4)
y.append(5)
y.read() → [4, 5]
</code></pre>
<p>Note how the operations between the two transactions are interleaved. This is forbidden by transactional isolation, but the definition of linearizability does not take into account transactions.</p>
<p>This example demonstrates how it&#8217;s possible to have histories that are linearizable but not serializable.</p>
<p>We say that lineariazibility is a <em>local</em> property where serializability is not: by the definition of linearizability, we can identify if a history is linearizable by looking at the histories of the individual objects (x, y). However, we can&#8217;t do that for serializability.</p>
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