Pebbling mountain ranges and its application to DCFL-recognition

Abstract

Recently, S.A. Cook showed that DCFL's can be recognized in O((log n)²) space and polynomial time simultaneously. We study the problem of pebbling mountain ranges (= the height of the pushdown-store as a function of time) and describe a family of pebbling strategies. One such pebbling strategy achieves a simultaneous O((log n)²/log log n) space and polynomial time bound for pebbling mountain ranges. We apply our results to DCFL recognition and show that the languages of input-driven DPDA's can be recognized in space O((log n)²/log log n). For general DCFL's we obtain a parameterized family of recognition algorithms realizing various simultaneous space and time bounds. In particular, DCFL's can be recognized in space O((log n)²) and time O(n^2.87) or space O(√n log n) and time O(n^1.5 log log n) or space O(n/log n) and time O(n(log n)³). More generally, our methods exhibit a general space-time tradeoff for manipulating pushdownstores (e.g. run time stack in block structured programming languages).

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