Complex Algebras of Arithmetic
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2009
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| _version_ | 1866917647773335552 |
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| author | Düntsch, Ivo Pratt-Hartmann, Ian |
| author_facet | Düntsch, Ivo Pratt-Hartmann, Ian |
| contents | An 'arithmetic circuit' is a labeled, acyclic directed graph specifying a sequence of arithmetic and logical operations to be performed on sets of natural numbers. Arithmetic circuits can also be viewed as the elements of the smallest subalgebra of the complex algebra of the semiring of natural numbers. In the present paper, we investigate the algebraic structure of complex algebras of natural numbers, and make some observations regarding the complexity of various theories of such algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0911_5246 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | Complex Algebras of Arithmetic Düntsch, Ivo Pratt-Hartmann, Ian Logic in Computer Science F.1.1 An 'arithmetic circuit' is a labeled, acyclic directed graph specifying a sequence of arithmetic and logical operations to be performed on sets of natural numbers. Arithmetic circuits can also be viewed as the elements of the smallest subalgebra of the complex algebra of the semiring of natural numbers. In the present paper, we investigate the algebraic structure of complex algebras of natural numbers, and make some observations regarding the complexity of various theories of such algebras. |
| title | Complex Algebras of Arithmetic |
| topic | Logic in Computer Science F.1.1 |
| url | https://arxiv.org/abs/0911.5246 |