Related papers: Phase transition in the Countdown problem

In the last 30 years it was found that many combinatorial systems undergo phase transitions. One of the most important examples of these can be found among the random k-satisfiability problems (often referred to as k-SAT), asking whether…

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random…

Number partitioning is an NP-complete problem of combinatorial optimization. A statistical mechanics analysis reveals the existence of a phase transition that separates the easy from the hard to solve instances and that reflects the…

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…

Phase transition is an important feature of SAT problem. For random k-SAT model, it is proved that as r (ratio of clauses to variables) increases, the structure of solutions will undergo a sudden change like satisfiability phase transition…

We introduce a prime number generator in the form of a stochastic algorithm. The character of such algorithm gives rise to a continuous phase transition which distinguishes a phase where the algorithm is able to reduce the whole system of…

The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed in our former work [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008], where we introduced the notion of…

Number partitioning is one of the classical NP-hard problems of combinatorial optimization. It has applications in areas like public key encryption and task scheduling. The random version of number partitioning has an "easy-hard" phase…

We introduce a stochastic algorithm that acts as a prime number generator. The dynamics of such algorithm gives rise to a continuous phase transition which separates a phase where the algorithm is able to reduce a whole set of integers into…

Random constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark instances for algorithms and they have been harnessed in probabilistic constructions of…

We introduce a voting model that is similar to a Keynesian beauty contest and analyze it from a mathematical point of view. There are two types of voters-copycat and independent-and two candidates. Our voting model is a binomial…

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 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 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…

Gibbs sampling is fundamental to a wide range of computer algorithms. Such algorithms are set to be replaced by physics based processors$-$be it quantum or stochastic annealing devices$-$which embed problem instances and evolve a physical…

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…

In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the…

We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase…

We present a study of the phase diagram of a random optimization problem in presence of quantum fluctuations. Our main result is the characterization of the nature of the phase transition, which we find to be a first-order quantum phase…

I present an analytic approach to establishing the presence of phase transitions in a large set of decision problems. This approach does not require extensive computational study of the problems considered. The set -- that of all paddable…