License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2021.48
URN: urn:nbn:de:0030-drops-136933
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Koechlin, Florent ; Rotondo, Pablo

Absorbing Patterns in BST-Like Expression-Trees

LIPIcs-STACS-2021-48.pdf (1 MB)


In this article we study the effect of simple semantic reductions on random BST-like expression-trees. Such random unary-binary expression-trees are often used in benchmarks for model-checking tools. We consider the reduction induced by an absorbing pattern for some given operator ⊛, which we apply bottom-up, producing an equivalent (and smaller) tree-expression. Our main result concerns the expected size of a random tree, of given input size n → ∞, after reduction. We show that there are two different thresholds, leading to a total of five regimes, ranging from no significant reduction at all, to almost complete reduction. These regimes are completely characterized according to the probability of the absorbing operator. Our results prove that random BST-like trees have to be considered with care, and that they offer a richer range of behaviours than uniform random trees.

BibTeX - Entry

  author =	{Koechlin, Florent and Rotondo, Pablo},
  title =	{{Absorbing Patterns in BST-Like Expression-Trees}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{48:1--48:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-136933},
  doi =		{10.4230/LIPIcs.STACS.2021.48},
  annote =	{Keywords: BST trees, absorbing pattern, reduction, analytic combinatorics}

Keywords: BST trees, absorbing pattern, reduction, analytic combinatorics
Collection: 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)
Issue Date: 2021
Date of publication: 10.03.2021

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