Digging input-driven pushdown automata

Input-driven pushdown automata (IDPDA) are where the next action on store (push, pop, nothing) is solely governed by input symbol. Nowadays such devices usually defined that popping from empty does not block computation but continues it with pushdown. Here, we consider IDPDAs have a more balanced behavior concerning pushing and popping. Digging input-driven (DIDPDA) basically that, when forced to pop pushdown, dig hole of shape popped symbol in bottom Popping further symbols having at deepens current furthermore. The can only be filled up previously popped. We study impact new DIDPDAs their power compare capacities ordinary tinput-driven which whose may preprocessed length-preserving finite state transducers. It turns out capabilities incomparable. address determinization descriptional complexity, closure properties, decidability questions.