Pebbling with an auxiliary pushdown

A pebble game on graphs is introduced which bears the same relationship to the ordinary pebble game as auxiliary pushdown machines bear to ordinary machines. The worst-case time-space trade-off for pebbling with an auxiliary pushdown is shown to be T = N exp e( N S) (where T denotes time, S denotes space and N denotes the size of the graph), which contrasts with T = N exp exp e( N S) for ordinary pebbling. The significance of this result to various questions concerning relations among complexity classes is discussed. © 1981.