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The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…

We axiomatize and generalize Markov's approach to the continuity problem for Type 1 computable functions, i.e. the problem of finding sufficient conditions on a computable topological space to obtain a theorem of the form "computable…

The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class $\Game (D\_n({\bf\Sigma}^0\_2))$ for some natural number $n\geq 1$, where $\Game$ is the game quantifier. We first give…

We show that in the class of solvable Lie algebras there exist algebras which admit local derivations which are not ordinary derivation and also algebras for which every local derivation is a derivation. We found necessary and sufficient…

This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…

A classification, according to invariant theory, of non-constant invariant Abel ODEs known as solvable and found in the literature is presented. A set of new integrable classes depending on one or no parameters, derived from the analysis of…

The Local Lemma is a fundamental tool of probabilistic combinatorics and theoretical computer science, yet there are hardly any natural problems known where it provides an asymptotically tight answer. The main theme of our paper is to…

Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…

Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root.…

We develop a finite-sample, design-based theory for random forests in which each tree is a randomized conditional predictor acting on fixed covariates and the forest is their Monte Carlo average. An exact variance identity separates Monte…

The cellular tree classifier model addresses a fundamental problem in the design of classifiers for a parallel or distributed computing world: Given a data set, is it sufficient to apply a majority rule for classification, or shall one…

Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…

I argue that questions of algorithmic decidability, computability and complexity should play a larger role in deciding the "ultimate" theoretical description of the Landscape of string vacua. More specifically, I examine the notion of the…

Milliken's tree theorem is a deep result in combinatorics that generalizes a vast number of other results in the subject, most notably Ramsey's theorem and its many variants and consequences. Motivated by a question of Dobrinen, we initiate…

The celebrated Time Hierarchy Theorem for Turing machines states, informally, that more problems can be solved given more time. The extent to which a time hierarchy-type theorem holds in the distributed LOCAL model has been open for many…

Can a deep neural network be approximated by a small decision tree based on simple features? This question and its variants are behind the growing demand for machine learning models that are *interpretable* by humans. In this work we study…

We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…

Model interpretability is an increasingly important component of practical machine learning. Some of the most common forms of interpretability systems are example-based, local, and global explanations. One of the main challenges in…

In this thesis we will present and discuss various results pertaining to tiling problems and mathematical logic, specifically computability theory. We focus on Wang prototiles, as defined in [32]. We begin by studying Domino Problems, and…

If a complex $X$ is a subcomplex of a diagrammatically reducible 2-complex $Y$ that has locally indicable fundamental group, then $X$ has locally indicable fundamental group. This is a consequence of the Corson-Trace characterization of…