Related papers: A Phase Transition in Minesweeper
Many problems in compositional synthesis and verification of multi-agent systems -- such as rational verification and assume-guarantee verification in probabilistic systems -- reduce to reasoning about two-player multi-objective stochastic…
Collective motion of dislocations is governed by the obstacles they encounter. In pure crystals, dislocations form complex structures as they become jammed by their anisotropic shear stress fields. On the other hand, introducing disorder to…
We investigate the dynamics of a conservative version of Conway's Game of Life, in which a pair consisting of a dead and a living cell can switch their states following Conway's rules but only by swapping their positions, irrespective of…
A matched formula is a CNF formula whose incidence graph admits a matching which matches a distinct variable to every clause. We study phase transition in a context of matched formulas and their generalization of biclique satisfiable…
We study the computational complexity of an important property of simple, regular and weighted games, which is decisiveness. We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness…
Alongside the effort underway to build quantum computers, it is important to better understand which classes of problems they will find easy and which others even they will find intractable. We study random ensembles of the QMA$_1$-complete…
In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…
Much of the recent work on random constraint satisfaction problems has been inspired by ingenious but non-rigorous approaches from physics. The physics predictions typically come in the form of distributional fixed point problems that are…
We study the complexity of problems related to subgame-perfect equilibria (SPEs) in infinite duration non zero-sum multiplayer games played on finite graphs with parity objectives. We present new complexity results that close gaps in the…
Petri games are a multi-player game model for the automatic synthesis of distributed systems, where the players are represented as tokens on a Petri net and are grouped into environment players and system players. As long as the players…
We study the computational complexity of the Buttons \& Scissors game and obtain sharp thresholds with respect to several parameters. Specifically we show that the game is NP-complete for $C = 2$ colors but polytime solvable for $C = 1$.…
We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…
Boolean games are a succinct representation of strategic games wherein a player seeks to satisfy a formula of propositional logic by selecting a truth assignment to a set of propositional variables under his control. The framework has…
Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We…
The stable cooperation ratio of spatial evolutionary games has been widely studied using simulations or approximate analysis methods. However, sometimes such ``stable'' cooperation ratios obtained via approximate methods might not be…
This work reports deep-learning-unique first-order and second-order phase transitions, whose phenomenology closely follows that in statistical physics. In particular, we prove that the competition between prediction error and model…
For an NP intersect coNP function g of the Nisan-Wigderson type and a string b outside its range we consider a two player game on a common input a to the function. One player, a computationally limited Student, tries to find a bit of g(a)…
The study of phase transition behaviour in SAT has led to deeper understanding and algorithmic improvements of modern SAT solvers. Motivated by these prior studies of phase transitions in SAT, we seek to study the behaviour of size and…
We study the optimization problem faced by a perfectly informed principal in a Bayesian game, who reveals information to the players about the state of nature to obtain a desirable equilibrium. This signaling problem is the natural design…
The metal-insulator transition (MIT) observed in two-dimensional (2D) systems is apparently contradictory to the well known scaling theory of localization. By investigating the conductance of disordered one-dimensional systems with a finite…