Comparing the Power of Monadic NP Games

The descriptive complexity of a problem is the complexity of describing the problem in some logical formalism. One of the few techniques for proving separation results in descriptive complexity is to make use of games on graphs played between two players, called the spoiler and the duplicator. There are two types of these games, which differ in the order in which the spoiler and duplicator make various moves. In one of these games, the rules seem to be tilted towards favoring the duplicator. These seemingly more favorable rules make it easier to prove separation results, since separation results are proven by showing that the duplicator has a winning strategy. In this paper, the relationship between these games is investigated. It is shown that in one sense, the two games are equivalent. Specifically, each family of graphs used in one game (the game with the seemingly more favorable rules for the duplicator) to prove a separation result can in principle be used in the other game to pro...

• Type: Conference
• Year: 1994
• Where: LCC
• Authors: Ronald Fagin
• Keywords: Algorithms, Descriptive Complexity, Favorable Rules, LCC 1994, Logical Formalism