Multihead Finite-State Compression
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909858410790912 |
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| author | Lutz, Neil |
| author_facet | Lutz, Neil |
| contents | This paper develops multihead finite-state compression, a generalization of finite-state compression, complementary to the multihead finite-state dimensions of Huang, Li, Lutz, and Lutz (2025). In this model, an infinite sequence of symbols is compressed by a compressor that produces outputs according to finite-state rules, based on the symbols read by a constant number of finite-state read heads moving forward obliviously through the sequence. The main theorem of this work establishes that for every sequence and every positive integer $h$, the infimum of the compression ratios achieved by $h$-head finite-state information-lossless compressors equals the $h$-head finite-state predimension of the sequence. As an immediate corollary, the infimum of these ratios over all $h$ is the multihead finite-state dimension of the sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17544 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multihead Finite-State Compression Lutz, Neil Information Theory Formal Languages and Automata Theory This paper develops multihead finite-state compression, a generalization of finite-state compression, complementary to the multihead finite-state dimensions of Huang, Li, Lutz, and Lutz (2025). In this model, an infinite sequence of symbols is compressed by a compressor that produces outputs according to finite-state rules, based on the symbols read by a constant number of finite-state read heads moving forward obliviously through the sequence. The main theorem of this work establishes that for every sequence and every positive integer $h$, the infimum of the compression ratios achieved by $h$-head finite-state information-lossless compressors equals the $h$-head finite-state predimension of the sequence. As an immediate corollary, the infimum of these ratios over all $h$ is the multihead finite-state dimension of the sequence. |
| title | Multihead Finite-State Compression |
| topic | Information Theory Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2510.17544 |