A computing machinery using a continuous memory tape
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917558976774144 |
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| author | Oktar, Yigit |
| author_facet | Oktar, Yigit |
| contents | By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study, using shifts and element-wise summations. This machinery can be extended symbolically to continuous case by thinking each possible sum as a single frequency impulse on the frequency band. Multiplication with a cosine in this case corresponds to the shifting operation as modulation in communication systems. Preliminary experimentation suggests that signal generation thus solution space calculation can be done in polynomial time. However, reading the value at a specific frequency (sum value) is problematic, namely cannot be simulated in polynomial time currently. Dedicated hardware implementation might be a solution, where both circuit-based and wireless versions might be tried out. A polynomial representation is also given that is claimed to be analogous to a tape of a Turing machine. Both rational and real number versions of the subset sum problem are also discussed, where the rational version of the problem is mapped to 0-1 range with specific patterns of True values. Although this machinery may not be totally equivalent to a non-deterministic Turing machine, it may be helpful for non-deterministic universal Turing machine actualization. It may pave way to both theoretical and practical considerations that can help computing machinery, information processing, and pattern recognition domains in various ways. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02420 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A computing machinery using a continuous memory tape Oktar, Yigit Computational Complexity By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study, using shifts and element-wise summations. This machinery can be extended symbolically to continuous case by thinking each possible sum as a single frequency impulse on the frequency band. Multiplication with a cosine in this case corresponds to the shifting operation as modulation in communication systems. Preliminary experimentation suggests that signal generation thus solution space calculation can be done in polynomial time. However, reading the value at a specific frequency (sum value) is problematic, namely cannot be simulated in polynomial time currently. Dedicated hardware implementation might be a solution, where both circuit-based and wireless versions might be tried out. A polynomial representation is also given that is claimed to be analogous to a tape of a Turing machine. Both rational and real number versions of the subset sum problem are also discussed, where the rational version of the problem is mapped to 0-1 range with specific patterns of True values. Although this machinery may not be totally equivalent to a non-deterministic Turing machine, it may be helpful for non-deterministic universal Turing machine actualization. It may pave way to both theoretical and practical considerations that can help computing machinery, information processing, and pattern recognition domains in various ways. |
| title | A computing machinery using a continuous memory tape |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2401.02420 |