相关论文: Exploring mazes at random

Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…

The paper evaluates the power of best-first search over AND/OR search spaces for solving the Most Probable Explanation (MPE) task in Bayesian networks. The main virtue of the AND/OR representation of the search space is its sensitivity to…

Exploration has been a crucial part of reinforcement learning, yet several important questions concerning exploration efficiency are still not answered satisfactorily by existing analytical frameworks. These questions include exploration…

The mathematical runtime analysis of evolutionary algorithms traditionally regards the time an algorithm needs to find a solution of a certain quality when initialized with a random population. In practical applications it may be possible…

In this paper, the idea of applying Computational Intelligence in the process of creation board games, in particular mazes, is presented. For two different algorithms the proposed idea has been examined. The results of the experiments are…

Search algorithms are often categorized by their node expansion strategy. One option is the depth-first strategy, a simple backtracking strategy that traverses the search space in the order in which successor nodes are generated. An…

We give a series of combinatorial results that can be obtained from any two collections (both indexed by $\Z\times \N$) of left and right pointing arrows that satisfy some natural relationship. When applied to certain self-interacting…

We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…

A layerwise search in a split-by-edges tree (as defined by Br{\ae}ndeland, 2015) of agiven graph produces a maximum independent set in exponential time. A depth-first search produces an independent set, which may or may not be a maximum, in…

We announce a tool for mapping derivations of the E theorem prover to Mizar proofs. Our mapping complements earlier work that generates problems for automated theorem provers from Mizar inference checking problems. We describe the tool,…

In pure strategy meta-heuristics, only one search strategy is applied for all time. In mixed strategy meta-heuristics, each time one search strategy is chosen from a strategy pool with a probability and then is applied. An example is…

We study a simple model of algorithmic collusion in which Q-learning algorithms are designed in a strategic fashion. We let players (\textit{designers}) choose their exploration policy simultaneously prior to letting their algorithms…

We present a polynomial-time algorithm that determines, given some choice rule, whether there exists an obviously strategy-proof mechanism for that choice rule.

Let $S=(S_n)$ be an oscillatory random walk on the integer lattice $\mathbb{Z}$ with i.i.d. increments. Let $V_{{\rm d}}(x)$ be the renewal function of the strictly descending ladder height process for $S$. We obtain several sufficient…

In this short note we report on results on a computational search for a counterexample to the strong coincidence conjecture. In particular, we discuss the method used so that further searches can be conducted.

We introduce an approximate search algorithm for fast maximum a posteriori probability estimation in probabilistic programs, which we call Bayesian ascent Monte Carlo (BaMC). Probabilistic programs represent probabilistic models with…

There is no closed form analytical equation or quick method to calculate probabilities based only on the entropy of a signal or process. Except in the cases where there are constraints on the state probabilities, one must typically derive…

Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time.…

We show that the Minesweeper game is PP-hard, when the object is to locate all mines with the highest probability. When the probability of locating all mines may be infinitesimal, the Minesweeper game is even PSPACE-complete. In our…

Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…