Tilings and patterns
Randomized algorithms
Reachability problems for sequential dynamical systems with threshold functions
Theoretical Computer Science - Mathematical foundations of computer science
Cellular Automata: A Discrete Universe
Cellular Automata: A Discrete Universe
Convergence of the Iterated Prisoner's Dilemma Game
Combinatorics, Probability and Computing
Survey propagation: An algorithm for satisfiability
Random Structures & Algorithms
An Introduction to Sequential Dynamical Systems
An Introduction to Sequential Dynamical Systems
Complexity of reachability problems for finite discrete dynamical systems
Journal of Computer and System Sciences
Slow emergence of cooperation for win-stay lose-shift on trees
Machine Learning
Some Recent Attempts to Simulate the Heider Balance Problem
Computing in Science and Engineering
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We study nondeterministic and probabilistic versions of a discrete dynamical system (due to T. Antal, P. L. Krapivsky, and S. Redner [3]) inspired by Heider's social balance theory. We investigate the convergence time of this dynamics on several classes of graphs. Our contributions include: 1. We point out the connection between the triad dynamics and a generalization of annihilating walks to hypergraphs. In particular, this connection allows us to completely characterize the recurrent states in graphs where each edge belongs to at most two triangles. 2. We also solve the case of hypergraphs that do not contain edges consisting of one or two vertices. 3. We show that on the so-called "triadic cycle" graph, the convergence time is linear. 4. We obtain a cubic upper bound on the convergence time on 2-regular triadic simplexes G. This bound can be further improved to a quantity that depends on the Cheeger constant of G. In particular this provides some rigorous counterparts to experimental observations in [25]. We also point out an application to the analysis of the random walk algorithm on certain instances of the 3-XOR-SAT problem.