Declarative Representation of Algorithms of Completion by Critical Pairs
A declarative representation of critical pairs for completion algorithms is described. The representation can be considered as a generic program that, after parametrization of some of its functions, realizes the Knuth-Bendix algorithm for solving the word problem in universal algebras or Buchberger...
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| Vydáno v: | Cybernetics and systems analysis Ročník 37; číslo 6; s. 795 - 799 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer Nature B.V
01.11.2001
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| Témata: | |
| ISSN: | 1060-0396, 1573-8337 |
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| Abstract | A declarative representation of critical pairs for completion algorithms is described. The representation can be considered as a generic program that, after parametrization of some of its functions, realizes the Knuth-Bendix algorithm for solving the word problem in universal algebras or Buchberger algorithm for constructing Grobner bases of polynomial ideals. The properties of termination and correction are considered. A realization of the representation in the APS algebraic system is described. [PUBLICATION ABSTRACT] |
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| AbstractList | A declarative representation of critical pairs for completion algorithms is described. The representation can be considered as a generic program that, after parametrization of some of its functions, realizes the Knuth-Bendix algorithm for solving the word problem in universal algebras or Buchberger algorithm for constructing Grobner bases of polynomial ideals. The properties of termination and correction are considered. A realization of the representation in the APS algebraic system is described. [PUBLICATION ABSTRACT] |
| Author | Volkov, V. A. |
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| Cites_doi | 10.1145/174652.174655 10.2307/1968867 10.1007/BF02366919 10.1145/321250.321253 10.1016/0304-3975(93)90343-R 10.1145/1089389.1089396 10.1016/S0747-7171(87)80020-2 |
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| Copyright | Copyright Kluwer Academic Publishers Nov/Dec 2001 |
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| DOI | 10.1023/A:1014569528986 |
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| References | D. E. Knuth (372855_CR4) 1970 372855_CR8 B. Buchberger (372855_CR1) 1987; 3 372855_CR5 372855_CR7 L. Bachmair (372855_CR6) 1994; 41 M. H. A. Newman (372855_CR10) 1942; 43 A.A. Letichevskii (372855_CR9) 1993; 119 J. A. Robinson (372855_CR2) 1965; 12 B. Buchberger (372855_CR3) 1985 |
| References_xml | – ident: 372855_CR7 – volume: 41 start-page: 132 issue: 2 year: 1994 ident: 372855_CR6 publication-title: J. ACM. doi: 10.1145/174652.174655 – volume: 43 start-page: 223 issue: 2 year: 1942 ident: 372855_CR10 publication-title: Ann. Math. doi: 10.2307/1968867 – ident: 372855_CR8 doi: 10.1007/BF02366919 – volume: 12 start-page: 54 issue: 1 year: 1965 ident: 372855_CR2 publication-title: J. ACM doi: 10.1145/321250.321253 – volume: 119 start-page: 145 year: 1993 ident: 372855_CR9 publication-title: Theor. Comp. Sci. doi: 10.1016/0304-3975(93)90343-R – start-page: 80 volume-title: Multidimensional Systems Theory year: 1985 ident: 372855_CR3 – start-page: 17 volume-title: Computational Problems in Abstract Algebra year: 1970 ident: 372855_CR4 – ident: 372855_CR5 doi: 10.1145/1089389.1089396 – volume: 3 start-page: 3 issue: 12 year: 1987 ident: 372855_CR1 publication-title: J. Symb. Comp. doi: 10.1016/S0747-7171(87)80020-2 |
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| Title | Declarative Representation of Algorithms of Completion by Critical Pairs |
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