Static analysis based on formal models and incremental computation in Go programming

Computer-Go programs have high computational costs for static analysis, even though most intersections of the board remain unchanged by one move. Therefore, incremental computation as well as theoretical models are essential features for static analysis. This paper describes some formal models for static analysis, and explores how incremental computation is applied to the static analysis in Go programs. The static analysis in this paper includes (1) recognizing blocks and groups of stones and evaluating their properties, (2) determining the life and death of a group by numerical features, (3) finding the numbers of regions enclosed by the groups based on Euler's formula, and (4) analysing capturing races (semeai) and sekis based on an abstract description called the semeai graph. Several operations on the sets of intersections on the board are used for defining the notions on Go boards as well as for describing the analysis methods.