Simulation of Two-Way Pushdown Automata Revisited

Robert Glück

The linear-time simulation of 2-way deterministic pushdown automata (2DPDA) by the Cook and Jones constructions is revisited. Following the semantics-based approach by Jones, an interpreter is given which, when extended with random-access memory, performs a linear-time simulation of 2DPDA. The recursive interpreter works without the dump list of the original constructions, which makes Cook's insight into linear-time simulation of exponential-time automata more intuitive and the complexity argument clearer. The simulation is then extended to 2-way nondeterministic pushdown automata (2NPDA) to provide for a cubic-time recognition of context-free languages. The time required to run the final construction depends on the degree of nondeterminism. The key mechanism that enables the polynomial-time simulations is the sharing of computations by memoization.

In Anindya Banerjee, Olivier Danvy, Kyung-Goo Doh and John Hatcliff: Semantics, Abstract Interpretation, and Reasoning about Programs: Essays Dedicated to David A. Schmidt on the Occasion of his Sixtieth Birthday (Festschrift for Dave Schmidt), Manhattan, Kansas, USA, 19-20th September 2013, Electronic Proceedings in Theoretical Computer Science 129, pp. 250–258.
Published: 19th September 2013.

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