Related papers: Algorithmic Problems for Computation Trees
The decision tree is one of the most fundamental programming abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) ``less than'' versus ''greater than or equal to'' tests…
The satisfiability problem of hybrid logics with the downarrow binder is known to be undecidable. This initiated a research program on decidable and tractable fragments. In this paper, we investigate the effect of restricting the…
Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random…
We give an algorithm to enumerate the results on trees of monadic second-order (MSO) queries represented by nondeterministic tree automata. After linear time preprocessing (in the input tree), we can enumerate answers with linear delay (in…
We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of…
We initiate a formal study of reproducibility in optimization. We define a quantitative measure of reproducibility of optimization procedures in the face of noisy or error-prone operations such as inexact or stochastic gradient computations…
The field of algorithmic optimization has significantly advanced with the development of methods for the automatic configuration of algorithmic parameters. This article delves into the Algorithm Configuration Problem, focused on optimizing…
Optimization problems are crucial in artificial intelligence. Optimization algorithms are generally used to adjust the performance of artificial intelligence models to minimize the error of mapping inputs to outputs. Current evaluation…
Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, suffer from the curse of…
The Algorithm Selection Problem is concerned with selecting the best algorithm to solve a given problem on a case-by-case basis. It has become especially relevant in the last decade, as researchers are increasingly investigating how to…
In this work we study preprocessing for tractable problems when part of the input is unknown or uncertain. This comes up naturally if, e.g., the load of some machines or the congestion of some roads is not known far enough in advance, or if…
The election is a classical problem in distributed algorithmic. It aims to design and to analyze a distributed algorithm choosing a node in a graph, here, in a tree. In this paper, a class of randomized algorithms for the election is…
We study the problem of explainability-first clustering where explainability becomes a first-class citizen for clustering. Previous clustering approaches use decision trees for explanation, but only after the clustering is completed. In…
Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems…
We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Problem is undecidable by constructing a many-to-one reduction…
Can AI agents deal with hard choices -- cases where options are incommensurable because multiple objectives are pursued simultaneously? Adopting a technologically engaged approach distinct from existing philosophical literature, I submit…
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…
We study the decidability of the Skolem Problem, the Positivity Problem, and the Ultimate Positivity Problem for linear recurrences with real number initial values and real number coefficients in the bit-model of real computation. We show…