# Solving Systems of Set Constraints with Negated Subset Relationships

Abstract : We present a decision procedure, based on tree automata techniques, for satisfiability of systems of set constraints including negated subset relationships. This result extends all previous works on set constraints solving (Heintze et Jaffar; Aiken et Wimmers; Gilleron, Tison and Tommasi; Bachmair, Gantzinger and Waldmann) and solves a problem which was left open in Bachmair et al. We prove in a constructive way that a non empty set of solutions always contains a regular solution, that is a tuple of regular tree languages. Moreover, we think that the new class of tree automata describes here could be interesting in its own.
Document type :
Conference papers

https://hal.inria.fr/inria-00538879
Contributor : Rémi Gilleron <>
Submitted on : Tuesday, November 23, 2010 - 2:48:34 PM
Last modification on : Tuesday, April 28, 2020 - 11:52:08 AM

### Identifiers

• HAL Id : inria-00538879, version 1

### Citation

Rémi Gilleron, Sophie Tison, Marc Tommasi. Solving Systems of Set Constraints with Negated Subset Relationships. Proceedings of the $34^th$ Symposium on Foundations of Computer Science, FOCS'93, 1993, Palo Alto California, United States. pp.372--380. ⟨inria-00538879⟩

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