Troll, a Language for specifying Dice-rolls

ABSTRACT Dice are used in many games, and often in fairly complex ways that make it difficult to unambiguously describe the dice-roll mechanism in plain language. Many role-playing games, such as Dungeons & Dragons, use a formalised notation for some instances of dice-rolls. This notation, once explained, make dice-roll descriptions concise and unambiguous. Furthermore, the notation has been used in automated tools for pseudo-random dice-rolling (typically used when playing over the Internet). This notation is, however, fairly limited in the types of dice-rolls it can describe, so most games still use natural language to describe rolls. Even Dungeons & Dragons use formal notation only for some of the dice-roll methods used in the game. Hence, a more complete notation is in this paper proposed, and a tool for pseudo-random rolls and (nearly) exact probability calculations is described. The notation is called "Troll", combining the initial of the Danish word for dice ("terninger") with the English word "roll". It is a development of the language Roll described in an earlier paper. The present paper describes the most important features of Troll and its implementation

Worm-2dpdas: An extension to 2dpdas that can be simulated in linear time

We extend 2-way deterministic push-down au-tomata (2DPDAs) with a write-once-read-many (WORM) store. We show that it allows linear time simulation by a variant of Cook’s construction. As an example we develop a linear time algorithm that recognizes the lan-guage {V V −1WW−1 | V,W ∈ (a | b)∗}, that by Aho, Hopcroft and Ullman is conjectured not to be recognizable by a 2DPDA. Thus we believe that the extension strictly increases the expressive power of 2DPDAs