We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FO-definable class of graphs. For each solution there may be many graphs representing it. However, one of these graphs is of path-width at most 2n, where n is the number of variables in the instance. Since FO is decidable on graphs of bounded path-width, we obtain an alternative decidability result for ILP. The technique we use underlines a common principle to prove decidability which has previously been employed for automata with auxiliary storage. We also show how this new result links to automata theory and program verification.
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1016/j.ic.2016.07.010|
|Codice identificativo ISI:||WOS:000397701700006|
|Codice identificativo Scopus:||2-s2.0-84998704735|
|Titolo:||On the path-width of integer linear programming|
|Appare nelle tipologie:||1.1 Articolo in rivista|