Related papers: The Power of Well-Structured Systems
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
Labelled Transition Systems (LTSs) are a fundamental semantic model in many areas of informatics, especially concurrency theory. Yet, reasoning on LTSs and relations between their states can be difficult and elusive: very simple process…
Stochastic orders are very useful tool to compare the lifetimes of two coherent systems. We show that, under certain conditions, a coherent system of used components performs better (worse) than a used coherent system with respect to…
We introduce the well structured problem as the question of whether a model (here a counter machine) is well structured (here for the usual ordering on integers). We show that it is undecidable for most of the (Presburger-defined) counter…
A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems,…
We investigate the mathematical structure of unit systems and the relations between them. Looking over the entire set of unit systems, we can find a mathematical structure that is called preorder (or quasi-order). For some pair of unit…
The well-quasi-orders (WQO) play an important role in various fields such as Computer Science, Logic or Graph Theory. Since the class of WQOs lacks closure under some important operations, the proof that a certain quasi-order is WQO…
We study the languages recognized by well-structured transition systems (WSTS) with upward and downward compatibility. Our first result shows that every pair of disjoint WSTS languages is regularly separable: there is a regular language…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…
Complex Systems were identified and studied in different fields, such as physics, biology, and economics. These systems exhibit exciting properties such as self-organization, robust order, and emergence. In recent years, software systems…
Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the…
In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…
This paper deals with strong structural controllability of structured networks. A structured network is a family of structured systems (called node systems) that are interconnected by means of a structured interconnection law. The node…
Decision-making in complex systems often relies on machine learning models, yet highly accurate models such as XGBoost and neural networks can obscure the reasoning behind their predictions. In operations research applications,…
By reformulating a learning process of a set system L as a game between Teacher (presenter of data) and Learner (updater of the abstract independent set), we define the order type dim L of L to be the order type of the game tree. The theory…
Steiner triple systems form one of the most studied classes of combinatorial designs. Configurations, including subsystems, play a central role in the investigation of Steiner triple systems. With sporadic instances of small systems, ad-hoc…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
The advanced data structure of the zero-suppressed binary decision diagram (ZDD) enables us to efficiently enumerate nonequivalent substitutional structures. Not only can the ZDD store a vast number of structures in a compressed manner, but…
In variable or graph selection problems, finding a right-sized model or controlling the number of false positives is notoriously difficult. Recently, a meta-algorithm called Stability Selection was proposed that can provide reliable…