Set constraints with projections are in NEXPTIME

Systems of set constraints describe relations between sets of ground terms. They have been successfully used in program analysis and type inference. In this paper we prove that the problem of existence of a solution of a system of set constraints with projections is in NEXPTIME, and thus that it is NEXPTIME-complete. This extends the result of A. Aiken, D. Kozen, and E.L. Wimmers (1993) and R. Gilleron, S. Tison, and M. Tommasi (1990) on decidability of negated set constraints and solves a problem that was open for several years.<
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