@InProceedings{Niehren_et_al:1999,
AUTHOR = {Niehren, Joachim and Müller, Martin and Talbot, JeanMarc},
TITLE = {Entailment of Atomic Set Constraints is PSPACEComplete},
YEAR = {1999},
BOOKTITLE = {14th Annual IEEE Symposium on Logic in Computer Science (LICS '99), July 25},
PAGES = {285294},
ADDRESS = {Trento, Italy},
PUBLISHER = {IEEE Press},
URL = {www.ps.unisb.de/Papers/abstracts/atomic:98.html ftp://ftp.ps.unisb.de/pub/papers/ProgrammingSysLab/atomiclics99.ps.gz},
ABSTRACT = {The complexity of set constraints has been extensively studied over the last years and was often found quite high. At the lower end of expressiveness, there are atomic set constraints which are conjunctions of inclusions t1 $subseteq$ t2 between firstorder terms without set operators. It is wellknown that satisfiability of atomic set constraints can be tested in cubic time. Also, entailment of atomic set constraints has been claimed decidable in polynomial time. We refute this claim. We show that entailment between atomic set constraints can express validity of quantified boolean formulas and is thus PSPACE hard. For infinite signatures, we also present a PSPACEalgorithm for solving atomic set constraints with negation. This proves that entailment of atomic set constraints is PSPACEcomplete for infinite signatures. In case of finite signatures, this problem is even DEXPTIMEhard.},
ANNOTE = {COLIURL : Niehren:1999:EAS.pdf Niehren:1999:EAS.ps} }
