One-reversal counter machines and multihead automata: Revisited

Authors:
Ehsan Chiniforooshan;Mark Daley;Oscar H. Ibarra;Lila Kari;Shinnosuke Seki
Affiliations:
Google, Canada;Department of Computer Science, University of Western Ontario, London, Ontario, N6A 5B7, Canada;Department of Computer Science, University of California, Santa Barbara, CA 93106, USA;Department of Computer Science, University of Western Ontario, London, Ontario, N6A 5B7, Canada;Department of Systems Bioscience for Drug Discovery, Kyoto University, 46-29, Yoshida-Shimo-Adachi-cho, Sakyo-ku, Kyoto, 606-8501, Japan
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

We investigate the power of (1-reversal) counter machines (finite automata with multiple counters, where each counter can ''reverse'' only once, i.e., once a counter decrements, it can no longer increment) and one-way multihead finite automata (finite automata with multiple one-way input heads) as a language acceptor. They can be non-deterministic as well as augmented with a pushdown stack. First, we prove that adding a pushdown stack properly strengthens the deterministic counter machines. Non-deterministic counter machines with a pushdown stack are then compared with multihead finite automata. The proof of their incomparability involves an interesting technique: an assumption that a language be accepted by a non-deterministic counter machine would bring a contradictory algorithm to decide an undecidable language. Furthermore, we will show that over bounded languages, these two kinds of machines have the same power, and neither non-determinism nor a pushdown stack makes them stronger.