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A general paradigm for relating measures of succinctness of representation and complexity theory is presented. The measures are based on the new Private and Blindfold Alternation machines. These measures are used to indicate the inherent information (or "randomness") of a string, but with respect to time and space complexity classes. These measures are then used to show that the existence...
The computational power of 2-way pushdown automata with m additional counters (called mC-PDA) is investigated. It is shown that any multi-tape Turingmachine (with a two-way input tape) which accepts within time T(n), where n is the input length, can be simulated by a 3C-PDA whose counters are bounded by T(n) and that any such Turing machine can also be simulated by a 2C-PDA whose counters are bounded...
An n-dimensional iterative array of finitestate machines (abbreviated nD) is a special type of real-time tape acceptor. The principal results are as follows: 1. nD's have equivalent forms With simplified stencils and length k encodings of the input alphabet. 2. The set of palindromes and the set of tapes of the form ττ are accepted by 1D's. 3. The sets of tapes accepted by nD's are a Boolean algebra...
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