Integer octagonal constraints (a.k.a. Unit Two Variables Per Inequality or UTVPI integer constraints) constitute an interesting class of constraints for the representation and solution of integer problems in the fields of constraint programming and formal analysis and verification of software and hardware systems, since they couple algorithms having polynomial complexity with a relatively good expressive power. The main algorithms required for the manipulation of such constraints are the satisfiability check and the computation of the inferential closure of a set of constraints. The latter is called tight closure to mark the difference with the (incomplete) closure algorithm that does not exploit the integrality of the variables. In this paper we present and fully justify an O(n^3) algorithm to compute the tight closure of a set of UTVPI integer constraints.
An Improved Tight Closure Algorithm for Integer Octagonal Constraints / Bagnara, Roberto; Hill, P. M.; Zaffanella, Enea. - 4905 of LNCS:(2008), pp. 8-21. (Intervento presentato al convegno 9th International Conference on Verification, Model Checking and Abstract Interpretation tenutosi a San Francisco, CA, USA nel January 7-9, 2008) [10.1007/978-3-540-78163-9_6].
An Improved Tight Closure Algorithm for Integer Octagonal Constraints
BAGNARA, Roberto;ZAFFANELLA, Enea
2008-01-01
Abstract
Integer octagonal constraints (a.k.a. Unit Two Variables Per Inequality or UTVPI integer constraints) constitute an interesting class of constraints for the representation and solution of integer problems in the fields of constraint programming and formal analysis and verification of software and hardware systems, since they couple algorithms having polynomial complexity with a relatively good expressive power. The main algorithms required for the manipulation of such constraints are the satisfiability check and the computation of the inferential closure of a set of constraints. The latter is called tight closure to mark the difference with the (incomplete) closure algorithm that does not exploit the integrality of the variables. In this paper we present and fully justify an O(n^3) algorithm to compute the tight closure of a set of UTVPI integer constraints.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
