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<li><a href="#requires-and-conflicts">Requires and Conflicts</a></li>
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<li><a href="#provides">Provides</a></li>
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<li><a href="#references">References</a></li>
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<h1>CSP, SAT && RL</h1>
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<div class="lead">How Luet turns Image resolution into CSP</div>
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<header class="article-meta">
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<p>Under the hood, Luet uses boolean satisfiability problem (<a href="https://en.wikipedia.org/wiki/Boolean_satisfiability_problem">SAT</a>) <a href="https://en.wikipedia.org/wiki/Reinforcement_learning">reinforcement learning</a> techniques to solve package constraints.</p>
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<p>Luet allows you to specify 3 types of set of contraints on a <a href="/docs/concepts/packages/">package</a> definition:</p>
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<ul>
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<li>Requires</li>
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<li>Conflicts</li>
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<li>Provides</li>
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</ul>
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<p>The package definition in your tree definition, along with its Requires and Conflicts, are turned into Boolean formulas that are consumed by the solver to compute a solution. The solution represent the state of your system after a particular query is asked to the solver (Install, Uninstall, Upgrade).</p>
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<h2 id="requires-and-conflicts">Requires and Conflicts</h2>
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<p>A list of requires and conflicts, composed of one or more <a href="/docs/concepts/packages/">packages</a>, becomes a SAT formula. The formula is then given to the SAT solver to compute a finite state set of packages which must be installed in the system in order to met the requirements.</p>
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<p>As Luet allows to express constraints with selectors ( e.g. <code>A depends on >=B-1.0</code>) it generates additional constraints to guarantee that at least one package and at most one is picked as dependency (<em>ALO</em> and <em>AMO</em>).</p>
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<h2 id="provides">Provides</h2>
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<p>Provides constraints are not encoded in a SAT formula. Instead, they are <code>expanded</code> into an in-place substitution of the packages that they have to be replaced with.
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They share the same SAT logic of expansion, allowing to swap entire version ranges (e.g. <code>>=1.0</code>), allowing to handle package rename, removals, and virtuals.</p>
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<h2 id="references">References</h2>
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<ul>
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<li>OPIUM (Luet is inspired by it): <a href="https://ranjitjhala.github.io/static/opium.pdf">https://ranjitjhala.github.io/static/opium.pdf</a></li>
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<li>FROM TRACTABLE CSP TO TRACTABLE SAT: <a href="https://www.cs.ox.ac.uk/files/4014/maxclosed_orderencoding_v16_TR.pdf">https://www.cs.ox.ac.uk/files/4014/maxclosed_orderencoding_v16_TR.pdf</a></li>
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<li>Solver concepts applied to packages (<code>zypper</code>): <a href="https://en.opensuse.org/openSUSE:Libzypp_satsolver_basics">https://en.opensuse.org/openSUSE:Libzypp_satsolver_basics</a></li>
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Last modified April 22, 2025: <a href="https://github.com/mudler/luet/commit/383f62db8ba8408b9e8caef5d8251e91f6837cf2">Run `go mod tidy` and fix casing (#377) (383f62d)</a>
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