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+title = "Dominance relations"
+author = "Yann Herklotz"
+tags = []
+categories = []
+backlinks = ["1a2"]
+forwardlinks = ["1a4", "1a3a"]
+zettelid = "1a3"
++++
+
+Dominance analysis is important to figure out the control flow in a
+program an analyse it, so that it can be optimised. For example, it can
+be used to generate phi functions correctly for a minimal SSA form \[1\]
+or it can also be used to generate the data dependency graph to then
+perform modulo scheduling on \[2\].
+
+Dominance relations are present in a control-flow graph (CFG) ([\#1a4]).
+A node $i$ dominates another node $j$ if every path from the entry point
+of the CFG to $j$ contains $i$. In addition to that, the relation is
+strict if $i \ne j$.
+
+<div id="refs" class="references csl-bib-body" markdown="1">
+
+<div id="ref-barthe14_formal_verif_ssa_based_middl_end_compc"
+class="csl-entry" markdown="1">
+
+<span class="csl-left-margin">\[1\]
+</span><span class="csl-right-inline">G. Barthe, D. Demange, and D.
+Pichardie, “Formal verification of an SSA-based middle-end for
+CompCert,” *ACM Trans. Program. Lang. Syst.*, vol. 36, no. 1, Mar. 2014,
+doi: [10.1145/2579080].</span>
+
+</div>
+
+<div id="ref-tristan10_simpl_verif_valid_softw_pipel" class="csl-entry"
+markdown="1">
+
+<span class="csl-left-margin">\[2\]
+</span><span class="csl-right-inline">J.-B. Tristan and X. Leroy, “A
+simple, verified validator for software pipelining,” in *Proceedings of
+the 37th annual ACM SIGPLAN-SIGACT symposium on principles of
+programming languages*, in POPL ’10. Madrid, Spain: Association for
+Computing Machinery, 2010, pp. 83–92. doi:
+[10.1145/1706299.1706311].</span>
+
+</div>
+
+</div>
+
+  [\#1a4]: /zettel/1a4
+  [10.1145/2579080]: https://doi.org/10.1145/2579080
+  [10.1145/1706299.1706311]: https://doi.org/10.1145/1706299.1706311