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Article Dans Une Revue Discrete Mathematics Année : 2024

The effects of semantic simplifications on random BST-like expression-trees

Résumé

In this article, we consider random expressions produced as BST-like trees (from the term BST, binary search trees), and study the effect of simple semantic reductions on them. These random trees are fast to produce and can be parametrized; that is why they are often used in benchmarks for model-checking tools. We assume the existence of an operator ⊛ that has an absorbing pattern and study the effect of the induced bottom-up reduction, which produces a semantically equivalent (and smaller) tree. 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. We characterize these regimes completely in terms of the probability of picking the absorbing operator. Our study shows that the parameters of random BST-like trees must be considered carefully, yet, contrarily to uniform random trees, they might offer a relevant way to sample interesting random expressions in practice.
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Dates et versions

hal-04484412 , version 1 (29-02-2024)

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Florent Koechlin, Pablo Rotondo. The effects of semantic simplifications on random BST-like expression-trees. Discrete Mathematics, 2024, 347 (5), pp.113906. ⟨10.1016/j.disc.2024.113906⟩. ⟨hal-04484412⟩
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