**Interconvertibility of a Class of Set Constraints and
Context-Free-Language Reachability**

*David Melski and Thomas Reps*

University of Wisconsin

We 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(n**3) 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.

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