Interconvertbility of set constraints and context-free language reachability

  • Authors:

  • David Melski;Thomas Reps

  • Affiliations:

  • Computer Sciences Department, University of Wisconsin, 1210 West Dayton Street, Madison, WI;Computer Sciences Department, University of Wisconsin, 1210 West Dayton Street, Madison, WI

  • Venue:
  • PEPM '97 Proceedings of the 1997 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
  • Year:
  • 1997

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Abstract

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 an 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.