Computational Complexity of One-Tape Turing Machine Computations
Journal of the ACM (JACM)
A Note Concerning Nondeterministic Tape Complexities
Journal of the ACM (JACM)
Reversal-Bounded Multicounter Machines and Their Decision Problems
Journal of the ACM (JACM)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Formal languages and their relation to automata
Formal languages and their relation to automata
Quantum computation with write-only memory
Natural Computing: an international journal
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It has long been known that deterministic 1-way counter machines recognize exactly all r.e. sets. Here we investigate counter machines with general recursive bounds on counter reversals. Our main result is that for bounds which are at least linear, counter reversal is polynomially related to Turing machine time, for both 1-way and 2-way counter machines and in both the deterministic and the nondeterministic cases. This leads to natural characterizations of the classes P and NP, and hence of the P &equil;? NP question, on the counter machine model. We also establish reversal complexity hierarchies for counter machines, using a variety of techniques which include translation of Turing machine time hierarchies, padding arguments as well as more ad hoc counting arguments.