# MPI-I-94-216

## Linear 0-1 inequalities and extended clauses

### Barth, Peter

**MPI-I-94-216**. April** **1994, 53 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

Extended clauses are the basic formulas of the 0-1 constraint solver for the constraint logic programming language CLP(PB). We present a method for transforming an arbitrary linear 0-1 inequality into a set of extended clauses, such that the solution space remains invariant. After applying well-known linearization techniques on non-linear 0-1 constraints followed by the presented transformation method, we are able to handle arbitrary 0-1 constraints in CLP(PB).

The transformation method presented relies on cutting planes techniques known from 0-1 integer programming. We develop specialized redundancy criteria and so produce the minimal number of extended clauses needed for preserving equivalence. The method is enhanced by using a compact representation of linear 0-1 inequalities and extended clauses. Unit resolution for classical clauses is generalized to pseudo-Boolean unit resolution for arbitrary linear 0-1 inequalities. We extend the transformation method to constrained transformation when the inequality to be transformed is part of a larger set of linear 0-1 inequalities. Furthermore the method can be used to obtain all strongest extended cover inequalities of a knapsack inequality.

Acknowledgement:** **

Categories / Keywords:** **constraint logic programming, pseudo-Boolean constraints, 0-1 integer programming, extended clauses, extended cover inequalities

Computing Reviews Classification:** **D.1.6 Software - Programming Techniques - Logic Programming

F.4.1 Theory of Computation - Mathematical Logic And Formal Languages - Mathematical Logic - Logic programming

G.1.6 Mathematics of Computing - Numerical Analysis - Optimization - Integer programming

I.2.3 Computing Methodologies - Artificial Intelligence - Deduction and Theorem Proving - Logic programming

References to related material:

**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1994-216

**BibTeX**
`@TECHREPORT{``Barth-94-mpii216``,`

` AUTHOR = {Barth, Peter},`

` TITLE = {Linear 0-1 inequalities and extended clauses},`

` TYPE = {Research Report},`

` INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},`

` ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},`

` NUMBER = {MPI-I-94-216},`

` MONTH = {April},`

` YEAR = {1994},`

` ISSN = {0946-011X},`

`}`