Two function algebras defining functions in NC k boolean circuits
We describe the functions computed by boolean circuits in NCk by means of func- tions algebra for k ≥ 1 in the spirit of implicit computational complexity. The whole hierarchy defines NC. In other words, we give a recursion-theoretic charac- terization of the complexity classes NCk for k ≥ 1 without...
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| Vydáno v: | Information and computation Ročník 248; s. 82 - 103 |
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| Jazyk: | angličtina |
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01.06.2016
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| ISSN: | 0890-5401, 1090-2651 |
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| Abstract | We describe the functions computed by boolean circuits in NCk by means of func- tions algebra for k ≥ 1 in the spirit of implicit computational complexity. The whole hierarchy defines NC. In other words, we give a recursion-theoretic charac- terization of the complexity classes NCk for k ≥ 1 without reference to a machine model, nor explicit bounds in the recursion schema. Actually, we give two equiv- alent description of the classes NCk, f ≥ 1. One is based on a tree structure a` la Leivant, the other is based on words. This latter puts into light the role of computation of pointers in circuit complexity. We show that transducers are a key concept for pointer evaluation. |
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| AbstractList | We describe the functions computed by boolean circuits in NCk by means of func- tions algebra for k ≥ 1 in the spirit of implicit computational complexity. The whole hierarchy defines NC. In other words, we give a recursion-theoretic charac- terization of the complexity classes NCk for k ≥ 1 without reference to a machine model, nor explicit bounds in the recursion schema. Actually, we give two equiv- alent description of the classes NCk, f ≥ 1. One is based on a tree structure a` la Leivant, the other is based on words. This latter puts into light the role of computation of pointers in circuit complexity. We show that transducers are a key concept for pointer evaluation. |
| Author | Bonfante, Guillaume Marion, Jean-Yves Kahle, Reinhard Oitavem, Isabel |
| Author_xml | – sequence: 1 givenname: Guillaume surname: Bonfante fullname: Bonfante, Guillaume – sequence: 2 givenname: Reinhard surname: Kahle fullname: Kahle, Reinhard – sequence: 3 givenname: Jean-Yves surname: Marion fullname: Marion, Jean-Yves – sequence: 4 givenname: Isabel surname: Oitavem fullname: Oitavem, Isabel |
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| Cites_doi | 10.1147/rd.91.0047 10.1007/BF01620765 10.1145/322234.322243 10.2168/LMCS-5(1:7)2009 10.1007/BF01202288 10.4153/CJM-1965-045-4 10.1007/BF01201998 10.1006/inco.1998.2700 10.1016/0022-0000(81)90038-6 |
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| Keywords | parallel computation class transducers Boolean circuits NCk |
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