2014/08/26 by Constantin Enea, Peter Habermehl, Omar Inverso +1
Computer Science · #cs.LO #cs.CC #cs.FL
paper · pdf · doi:10.4204/eptcs.161.9
published as EPTCS 161, 2014, pp. 74-87 · In Proceedings GandALF 2014, arXiv:1408.5560
arxiv created 2014/08/26 · arxiv updated 2014/08/27
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.