Interconvertibility of a class of set constraints and context-free-language reachability

AbstractWe show the interconvertibility of context-free-language reachability problems and a class of set-constraint problems: given a context-free-language reachability problem, we show how to construct a set-constraint problem whose answer gives a solution to the reachability problem; given a set-constraint problem, we show how to construct a context-free-language reachability problem whose answer gives a solution to the set-constraint problem. The interconvertibility of these two formalisms offers a conceptual advantage akin to the advantage gained from the interconvertibility of finite-state automata and regular expressions in formal language theory, namely, a problem can be formulated in whichever formalism is most natural. It also offers some insight into the “O(n3) bottleneck” for different types of program-analysis problems and allows results previously obtained for context-free-language reachability problems to be applied to set-constraint problems and vice versa