Fatal Attractors in Parity Games: Building Blocks for Partial Solvers

Attractors in parity games are a technical device for solving "alternating" reachability of given node sets. A well known solver of parity games - Zielonka's algorithm - uses such attractor computations recursively. We here propose new forms of attractors that are monotone in that they are aware of specific static patterns of colors encountered in reaching a given node set in alternating fashion. Then we demonstrate how these new forms of attractors can be embedded within greatest fixed-point computations to design solvers of parity games that run in polynomial time but are partial in that they may not decide the winning status of all nodes in the input game. Experimental results show that our partial solvers completely solve benchmarks that were constructed to challenge existing full solvers. Our partial solvers also have encouraging run times in practice. For one partial solver we prove that its run-time is at most cubic in the number of nodes in the parity game, that its output game is independent of the order in which monotone attractors are computed, and that it solves all Buechi games and weak games. We then define and study a transformation that converts partial solvers into more precise partial solvers, and we prove that this transformation is sound under very reasonable conditions on the input partial solvers. Noting that one of our partial solvers meets these conditions, we apply its transformation on 1.6 million randomly generated games and so experimentally validate that the transformation can be very effective in increasing the precision of partial solvers

Distance-uniform graphs with large diameter

An ϵ-distance-uniform graph is one with a critical distance d such that from every vertex, all but at most an ϵ-fraction of the remaining vertices are at distance exactly d. Motivated by the theory of network creation games, Alon, Demaine, Hajiaghayi, and Leighton made the follow- ing conjecture of independent interest: that every ϵ-distance-uniform graph (and, in fact, a broader class of ϵ-distance-almost-uniform graphs) has critical distance at most logarithmic in the number of vertices n. We disprove this conjecture and characterize the asymptotics of this extremal prob- lem. Speci-cally, for 1/n ≤ ϵ ≤ 1 /log n , we construct ϵ-distance-uniform graphs with critical distance 2ω(log n/log ϵ-1). We also prove an upper bound on the critical distance of the form 2O(log n/log ϵ-1) for all ϵ and n. Our lower bound construction introduces a novel method inspired by the Tower of Hanoi puzzle and may itself be of independent interest.Peer ReviewedPostprint (author's final draft

The Impact of Individual Expertise and Public Information on Group Decision-Making

In this open-access-book the author concludes that expertise could be the key factor for global and interconnected problems. Experimental results have shown that expertise was a stronger predictor than public information regarding change in behavior and strategy adaption. Identifying non-routine problem-solving experts by efficient online assessments could lead to less volatile system performance, from which all decision-makers could potentially profit

Board Game Focused on Educational Support for Gaming Algorithms

Tato práce se zabývá oblastí umělé inteligence zvané jako ''Metody pro hraní her''. Cílem této bakalářské práce je navrhnout a implementovat software, který umožní uživateli snadněji pochopit principy herních algoritmů Minimax a Alfa-beta prořezávání. Typickými uživateli tohoto softwaru mohou být například studenti oboru umělá inteligence. Práci lze rozdělit do dvou hlavních částí. První, teoretická část, se snaží vysvělit koncept ''Metoda pro hraní her'', dále obsahuje popis návrhu softwaru a popis výukových přínosů aplikace. Druhá část práce je věnována popisu implementace softwaru, testování a diskuzi dosažených výsledků.This work deals with the part of field of artificial intelligence known as ''Methods of playing games''. The goal of this bachelor's thesis is to design and implement software that allows the user to more easily understand the principles of game algorithms Minimax and Alpha-beta pruning. Typical users of this software can be, for example, students of artificial intelligence. This work is divided into two main parts. The first theoretical part tries to explain the ''Method of playing games'' concept and subsequently contains detailed descriptions of software design and educational benefits. The second part of this work is devoted to a description of software implementation, testing and discussion of the achieved results.