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We show that left-linear generalized semi-monadic TRSs effectively preserving recognizability of finite tree languages (are EPRF-TRSs). We show that reachability, joinability, and local confluence are decidable for EPRF-TRSs.
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
A recent work shows how we can optimize a tree based mode of operation for a rate 1 hash function. In particular, an algorithm and a theorem are presented for selecting a good tree topology in order to optimize both the running time and the…
Density Estimation Trees (DETs) are decision trees trained on a multivariate dataset to estimate its probability density function. While not competitive with kernel techniques in terms of accuracy, they are incredibly fast, embarrassingly…
Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources…
This paper explores the rich structure of peakon and pseudo-peakon solutions for a class of higher-order $b$-family equations, referred to as the $J$-th $b$-family ($J$-bF) equations. We propose several conjectures concerning the weak…
We introduce a recursive AlphaZero-style Monte--Carlo tree search algorithm, "RMCTS". The advantage of RMCTS over AlphaZero's MCTS-UCB is speed. In RMCTS, the search tree is explored in a breadth-first manner, so that network inferences…
Link-cut trees have been introduced by D.D. Sleator and R.E. Tarjan (Journal of Computer and System Sciences, 1983) with the aim of efficiently maintaining a forest of vertex-disjoint dynamic rooted trees under cut and link operations.…
With the prevalence of online platforms, today, data is being generated and accessed by users at a very high rate. Besides, applications such as stock trading or high frequency trading require guaranteed low delays for performing an…
Decision trees (DTs) epitomize the ideal of interpretability of machine learning (ML) models. The interpretability of decision trees motivates explainability approaches by so-called intrinsic interpretability, and it is at the core of…
It is proved that the family of tree languages recognized by nondeterministic tree-walking automata is not closed under complementation, solving a problem raised by Boja\'nczyk and Colcombet ("Tree-walking automata do not recognize all…
Large Language Models (LLMs) face significant inference latency challenges stemming from their autoregressive design and large size. To address this, speculative decoding emerges as a solution, enabling the simultaneous generation and…
The Binary Space Partitioning-Tree~(BSP-Tree) process was recently proposed as an efficient strategy for space partitioning tasks. Because it uses more than one dimension to partition the space, the BSP-Tree Process is more efficient and…
Interpreting three-leaf binary trees or {\em rooted triples} as constraints yields an entailment relation, whereby binary trees satisfying some rooted triples must also thus satisfy others, and thence a closure operator, which is known to…
The theme of this article is the algebraic combinatorics of leaf-labeled rooted binary trees and forests of such trees. The structure of a Hopf operad is defined on the vector spaces spanned by forests of leaf-labeled, rooted, binary trees.…
The working-set bound [Sleator and Tarjan, J. ACM, 1985] roughly states that searching for an element is fast if the element was accessed recently. Binary search trees, such as splay trees, can achieve this property in the amortized sense,…
The braids of $B\_\infty$ can be equipped with a selfdistributive operation $\mathbin{\triangleright}$ enjoying a number of deep properties. This text is a survey of known properties and open questions involving this structure, its…
In this paper we show that given a max-plus automaton (over trees, and with real weights) computing a function $f$ and a min-plus automaton (similar) computing a function $g$ such that $f\leqslant g$, there exists effectively an unambiguous…
The M-tree is a paged, dynamically balanced metric access method that responds gracefully to the insertion of new objects. To date, no algorithm has been published for the corresponding Delete operation. We believe this to be non-trivial…
In a recent paper we introduced a new framework for the study of call by need computations to normal form and root-stable form in term rewriting. Using elementary tree automata techniques and ground tree transducers we obtained simple…