Abstract
We show that deterministic finite automata equipped with k two-way heads are equivalent to deterministic machines with a single two-way input head and k − 1 linearly bounded counters if the accepted language is strictly bounded, i.e., a subset of \(a_1^*a_2^*\cdots a_m^*\) for a fixed sequence of symbols a 1, a 2,…, a m . Then we investigate linear speed-up for counter machines. Lower and upper time bounds for concrete recognition problems are shown, implying that in general linear speed-up does not hold for counter machines. For bounded languages we develop a technique for speeding up computations by any constant factor at the expense of adding a fixed number of counters.
Research partially supported by “Deutsche Akademie der Naturforscher Leopoldina”, grant number BMBF-LPD 9901/8-1 of “Bundesministerium für Bildung und Forschung”.
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Petersen, H. (2012). Bounded Counter Languages. In: Kutrib, M., Moreira, N., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2012. Lecture Notes in Computer Science, vol 7386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31623-4_21
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DOI: https://doi.org/10.1007/978-3-642-31623-4_21
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