Bounded Counter Languages
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.
KeywordsTuring Machine Kolmogorov Complexity Input String Input Symbol Input Length
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