Related papers: Explaining the Ubiquity of Phase Transitions in De…
In [A. Jackson, Explaining the ubiquity of phase transitions in decision problems (2025), arXiv:2501.14569], I established that phase transitions are always present in a large subset of decision problems over even-sized alphabets,…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
We discuss how phase-transitions may be detected in computationally hard problems in the context of Anytime Algorithms. Treating the computational time, value and utility functions involved in the search results in analogy with quantities…
We examine the phase transition phenomenon for the Knapsack problem from both a computational and a human perspective. We first provide, via an empirical and a theoretical analysis, a characterization of the phenomenon in terms of two…
We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
The identification and classification of phases in small systems, e.g. nuclei, social and financial networks, clusters, and biological systems, where the traditional definitions of phase transitions are not applicable, is important to…
The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their…
We review connections between phase transitions in high-dimensional combinatorial geometry and phase transitions occurring in modern high-dimensional data analysis and signal processing. In data analysis, such transitions arise as abrupt…
The problem of distributing the workload on a parallel computer to minimize the overall runtime is known as Multiprocessor Scheduling Problem. It is NP-hard, but like many other NP-hard problems, the average hardness of random instances…
The notion of (auto) catalytic networks has become a cornerstone in understanding the possibility of a sudden dramatic increase of diversity in biological evolution as well as in the evolution of social and economical systems. Here we study…
We propose the concept of adaptable processes as a way of overcoming the limitations that process calculi have for describing patterns of dynamic process evolution. Such patterns rely on direct ways of controlling the behavior and location…
We study the large-time behavior of a class of periodically driven macroscopic systems. We find, for a certain range of the parameters of either the system or the driving fields, the time-averaged asymptotic behavior effectively is that of…
A fundamental question in Computer Science is understanding when a specific class of problems go from being computationally easy to hard. Because of its generality and applications, the problem of Boolean Satisfiability (aka SAT) is often…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing theory provides a rather complete picture…
Statistical inference problems arising within signal processing, data mining, and machine learning naturally give rise to hard combinatorial optimization problems. These problems become intractable when the dimensionality of the data is…
Phase transitions in many complex combinational problems have been widely studied in the past decade. In this paper, we investigate phase transitions in the knowledge compilation empirically, where DFA, OBDD and d-DNNF are chosen as the…
Here we present a combinatorial decision problem, inspired by the celebrated quiz show called the countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic…
Although NP-Complete problems are the most difficult decisional problems, it is possible to discover in them polynomial (or easy) observables. We study the Graph Partitioning Problem showing that it is possible to recognize in it two…