Grammar of zones with admissible trajectories of arbitrary degrees

Abstract

Stilman's linguistic geometry (LG) is a theory describing how to find strategies intending to win in multi-player abstract board games with concurrent moves. The areas of applicability of LG are such problems as scheduling problems, construction of combat strategies for military applications, robot control, security of computer networks, safety for multi-agent systems in the presence of cooperating and non-cooperating agents, etc. One of the major tools of LG is the notion of "zones". A zone represents a possible skirmish between a player and its opponents. LG also provides means to evaluate for the player a cost of reaching the goal within a zone. The LG grammar of zones would allow the player to generate a number of possible zones. Then the player can choose a zone with the most favorable cost and proceed along the respective trajectory. We generalized the LG grammar of zones developed by Stilman by permitting admissible trajectories of arbitrary degrees. Previously, the LG grammar of zones utilized only admissible trajectories of second degree. We also simplified the way such grammars are represented.