Related papers: Exact Method for Generating Strategy-Solvable Sudo…
Elimination algorithms for bandit identification, which prune the plausible correct answers sequentially until only one remains, are computationally convenient since they reduce the problem size over time. However, existing elimination…
Active set method aims to find the correct active set of the optimal solution and it is a powerful method for solving strictly convex quadratic problem with bound constraints. To guarantee the finite step convergence, the existing active…
For very large values of $k$, we consider methods for fast $k$-means clustering of massive datasets with $10^7\sim10^9$ points in high-dimensions ($d\geq100$). All current practical methods for this problem have runtimes at least…
We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…
We study the problem of resilient strategies in the presence of uncertainty. Resilient strategies enable an agent to make decisions that are robust against disturbances. In particular, we are interested in those disturbances that are able…
Ultimate Tic-Tac-Toe is a variant of the popular Tic-Tac-Toe game. Two players compete to win three aligned "fields," with each field constituting its own miniature tic-tac-toe game. Each move determines which field the next player must…
Strategy Logic (SL, for short) has been recently introduced by Mogavero, Murano, and Vardi as a useful formalism for reasoning explicitly about strategies, as first-order objects, in multi-agent concurrent games. This logic turns to be very…
This work examines the problem to describe an efficient algorithm for obtaining $n^2 \times n^2$ Sudoku matrices. For this purpose, we define the concepts of $n\times n$ $\Pi_n$-matrix and disjoint $\Pi_n$-matrices. The article, using the…
We study a system of linear equations associated with Sudoku latin squares. The coefficient matrix $M$ of the normal system has various symmetries arising from Sudoku. From this, we find the eigenvalues and eigenvectors of $M$, and compute…
We propose discrete diffusion guidance for constraint satisfaction problems (CSPs) and demonstrate its ability to solve Sudoku puzzles without supervision.
For any odd integer $n\geq3$ a board (of size $n$) is a square array of $n\times n$ positions with a simple rule of how to move between positions. The goal of the game we introduce is to find a path from the upper left corner of a board to…
The clustering problem has many applications in Machine Learning, Operations Research, and Statistics. We propose three algorithms to create starting solutions for improvement algorithms for this problem. We test the algorithms on 72…
We address the problem of clustering a set of points in $\mathbb{R}^d$ with axis-parallel clusters. Previous exact approaches to this problem are mostly based on integer programming formulations and can only solve to optimality instances of…
Humans excel in solving complex reasoning tasks through a mental process of moving from one idea to a related one. Inspired by this, we propose Subgoal Search (kSubS) method. Its key component is a learned subgoal generator that produces a…
Challenges for physical solitaire puzzle games are typically designed in advance by humans and limited in number. Alternatively, some games incorporate rules for stochastic setup, where the human solver randomly sets up the game board…
We consider a card guessing game with complete feedback. An ordered deck of $n$ cards labeled $1$ up to $n$ is riffle-shuffled exactly one time. Given a value $p\in(0{,}1)\setminus\{\frac12\}$, the riffle shuffle is assumed to be…
Neural networks have long been used to model human intelligence, capturing elements of behavior and cognition, and their neural basis. Recent advancements in deep learning have enabled neural network models to reach and even surpass human…
Biological neural systems must be fast but are energy-constrained. Evolution's solution: act on the first signal. Winner-take-all circuits and time-to-first-spike coding implicitly treat when a neuron fires as an expression of confidence.…
Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random…
How many moves does it take to solve Rubik's Cube? Positions are known that require 20 moves, and it has already been shown that there are no positions that require 27 or more moves; this is a surprisingly large gap. This paper describes a…