Related papers: Differential Tree Automata
The main objective of this paper is to introduce an algorithm for solving fractional and classical differential equations based on a new generalized fractional power series. The algorithm relies on expanding the solution of an FDE or an ODE…
In the first paper (part I) of this series of two, we introduce four novel definitions of the ODT problems: three for size-constrained trees and one for depth-constrained trees. These definitions are stated unambiguously through executable…
Graph-Rewriting Automata (GRA) are an extension of Cellular Automata to a dynamic structure using local graph-rewriting rules. This work introduces linear algebra based tools that allow for a practical investigation of their behavior in…
Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…
The lack of interpretability remains a barrier to the adoption of deep neural networks. Recently, tree regularization has been proposed to encourage deep neural networks to resemble compact, axis-aligned decision trees without significant…
In recent years, deep reinforcement learning (DRL) algorithms have gained traction in home energy management systems. However, their adoption by energy management companies remains limited due to the black-box nature of DRL, which fails to…
In this paper we propose a novel approach to identify dynamical systems. The method estimates the model structure and the parameters of the model simultaneously, automating the critical decisions involved in identification such as model…
Neither the classical nor intuitionistic logic traditions are perfectly-aligned with the purpose of reasoning about computation, in that neither tradition can permit unconstrained recursive definitions without inconsistency: recursive…
Lifted (family-based) static analysis by abstract interpretation is capable of analyzing all variants of a program family simultaneously, in a single run without generating any of the variants explicitly. The elements of the underlying…
We prove that if $y=\sum_{n=0}^\infty{\bf a}(n)x^n\in\mathbb{F}_q[[x]]$ is an algebraic power series of degree $d$, height $h$, and genus $g$, then the sequence ${\bf a}$ is generated by an automaton with at most $q^{h+d+g-1}$ states, up to…
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…
The successes of deep learning, variational inference, and many other fields have been aided by specialized implementations of reverse-mode automatic differentiation (AD) to compute gradients of mega-dimensional objectives. The AD…
Automatic differentiation (AD) has been a topic of interest for researchers in many disciplines, with increased popularity since its application to machine learning and neural networks. Although many researchers appreciate and know how to…
Discounting the influence of future events is a key paradigm in economics and it is widely used in computer-science models, such as games, Markov decision processes (MDPs), reinforcement learning, and automata. While a single game or MDP…
We present a general framework for balancing expressions (terms) in form of so called tree straight-line programs. The latter can be seen as circuits over the free term algebra extended by contexts (terms with a hole) and the operations…
We study varieties that contain unranked tree languages over all alphabets. Trees are labeled with symbols from two alphabets, an unranked operator alphabet and an alphabet used for leaves only. Syntactic algebras of unranked tree languages…
Let $T$ be a weighted tree. The weight of a subtree $T_1$ of $T$ is defined as the product of weights of vertices and edges of $T_1$. We obtain a linear-time algorithm to count the sum of weights of subtrees of $T$. As applications, we…
To obtain the Dirichlet series for complex powers of the Riemann zeta function, we define and study the basic properties of a sequence of polynomials that, used as coefficients of the respective terms of the Dirichlet series of the Riemann…
Decision trees are ubiquitous in machine learning for their ease of use and interpretability. Yet, these models are not typically employed in reinforcement learning as they cannot be updated online via stochastic gradient descent. We…
Bayesian Additive Regression Trees (BART) are a powerful ensemble learning technique for modeling nonlinear regression functions. Although initially BART was proposed for predicting only continuous and binary response variables, over the…