  We obtain a combinatorial formula for the Miller-Morita-Mumford classes for
the mapping class group of punctured surfaces and prove Witten's conjecture
that they are proportional to the dual to the Witten cycles. The
proportionality constant is shown to be exactly as conjectured by Arbarello and
Cornalba [J. Alg. Geom. 5 (1996) 705-749]. We also verify their conjectured
formula for the leading coefficient of the polynomial expressing the Kontsevich
cycles in terms of the Miller-Morita-Mumford classes.
