Elimination Transformations for Associative–Commutative Rewriting Systems
Abstract To simplify the task of proving termination and AC-termination of term rewriting systems, elimination transformations have been vigorously studied since the 1990s. Dummy elimination, distribution elimination, general dummy elimination, and improved general dummy elimination are examples of...
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| Autor*in: |
Keiichirou, Kusakari [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2006 |
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| Anmerkung: |
© Springer Science+Business Media, Inc. 2006 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of automated reasoning - Springer Netherlands, 1985, 37(2006), 3 vom: Okt., Seite 205-229 |
|---|---|
| Übergeordnetes Werk: |
volume:37 ; year:2006 ; number:3 ; month:10 ; pages:205-229 |
| Links: |
|---|
| DOI / URN: |
10.1007/s10817-006-9053-y |
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OLC2034708105 |
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| 520 | |a Abstract To simplify the task of proving termination and AC-termination of term rewriting systems, elimination transformations have been vigorously studied since the 1990s. Dummy elimination, distribution elimination, general dummy elimination, and improved general dummy elimination are examples of elimination transformations. In this paper we clarify the essence of elimination transformations based on the notion of dependency pairs. We first present a theorem that gives a general and essential property for elimination transformations, making them sound with AC-termination. Based on the theorem, we design an elimination transformation called the argument filtering transformation. Next, we clarify the relation among various elimination transformations by comparing them with a corresponding restricted argument filtering transformation. Finally, we compare the AC-dependency pair method with the argument filtering transformation. | ||
| 700 | 1 | |a Masaki, Nakamura |4 aut | |
| 700 | 1 | |a Yoshihito, Toyama |4 aut | |
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10.1007/s10817-006-9053-y doi (DE-627)OLC2034708105 (DE-He213)s10817-006-9053-y-p DE-627 ger DE-627 rakwb eng 400 004 VZ 7,11 17,1 ssgn LING DE-30 fid Keiichirou, Kusakari verfasserin aut Elimination Transformations for Associative–Commutative Rewriting Systems 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2006 Abstract To simplify the task of proving termination and AC-termination of term rewriting systems, elimination transformations have been vigorously studied since the 1990s. Dummy elimination, distribution elimination, general dummy elimination, and improved general dummy elimination are examples of elimination transformations. In this paper we clarify the essence of elimination transformations based on the notion of dependency pairs. We first present a theorem that gives a general and essential property for elimination transformations, making them sound with AC-termination. Based on the theorem, we design an elimination transformation called the argument filtering transformation. Next, we clarify the relation among various elimination transformations by comparing them with a corresponding restricted argument filtering transformation. Finally, we compare the AC-dependency pair method with the argument filtering transformation. Masaki, Nakamura aut Yoshihito, Toyama aut Enthalten in Journal of automated reasoning Springer Netherlands, 1985 37(2006), 3 vom: Okt., Seite 205-229 (DE-627)129175277 (DE-600)51516-4 (DE-576)01445551X 0168-7433 nnns volume:37 year:2006 number:3 month:10 pages:205-229 https://doi.org/10.1007/s10817-006-9053-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-LING SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_21 GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_285 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2021 GBV_ILN_2190 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4116 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4324 GBV_ILN_4700 AR 37 2006 3 10 205-229 |
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10.1007/s10817-006-9053-y doi (DE-627)OLC2034708105 (DE-He213)s10817-006-9053-y-p DE-627 ger DE-627 rakwb eng 400 004 VZ 7,11 17,1 ssgn LING DE-30 fid Keiichirou, Kusakari verfasserin aut Elimination Transformations for Associative–Commutative Rewriting Systems 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2006 Abstract To simplify the task of proving termination and AC-termination of term rewriting systems, elimination transformations have been vigorously studied since the 1990s. Dummy elimination, distribution elimination, general dummy elimination, and improved general dummy elimination are examples of elimination transformations. In this paper we clarify the essence of elimination transformations based on the notion of dependency pairs. We first present a theorem that gives a general and essential property for elimination transformations, making them sound with AC-termination. Based on the theorem, we design an elimination transformation called the argument filtering transformation. Next, we clarify the relation among various elimination transformations by comparing them with a corresponding restricted argument filtering transformation. Finally, we compare the AC-dependency pair method with the argument filtering transformation. Masaki, Nakamura aut Yoshihito, Toyama aut Enthalten in Journal of automated reasoning Springer Netherlands, 1985 37(2006), 3 vom: Okt., Seite 205-229 (DE-627)129175277 (DE-600)51516-4 (DE-576)01445551X 0168-7433 nnns volume:37 year:2006 number:3 month:10 pages:205-229 https://doi.org/10.1007/s10817-006-9053-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-LING SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_21 GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_285 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2021 GBV_ILN_2190 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4116 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4324 GBV_ILN_4700 AR 37 2006 3 10 205-229 |
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elimination transformations for associative–commutative rewriting systems |
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Elimination Transformations for Associative–Commutative Rewriting Systems |
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Abstract To simplify the task of proving termination and AC-termination of term rewriting systems, elimination transformations have been vigorously studied since the 1990s. Dummy elimination, distribution elimination, general dummy elimination, and improved general dummy elimination are examples of elimination transformations. In this paper we clarify the essence of elimination transformations based on the notion of dependency pairs. We first present a theorem that gives a general and essential property for elimination transformations, making them sound with AC-termination. Based on the theorem, we design an elimination transformation called the argument filtering transformation. Next, we clarify the relation among various elimination transformations by comparing them with a corresponding restricted argument filtering transformation. Finally, we compare the AC-dependency pair method with the argument filtering transformation. © Springer Science+Business Media, Inc. 2006 |
| abstractGer |
Abstract To simplify the task of proving termination and AC-termination of term rewriting systems, elimination transformations have been vigorously studied since the 1990s. Dummy elimination, distribution elimination, general dummy elimination, and improved general dummy elimination are examples of elimination transformations. In this paper we clarify the essence of elimination transformations based on the notion of dependency pairs. We first present a theorem that gives a general and essential property for elimination transformations, making them sound with AC-termination. Based on the theorem, we design an elimination transformation called the argument filtering transformation. Next, we clarify the relation among various elimination transformations by comparing them with a corresponding restricted argument filtering transformation. Finally, we compare the AC-dependency pair method with the argument filtering transformation. © Springer Science+Business Media, Inc. 2006 |
| abstract_unstemmed |
Abstract To simplify the task of proving termination and AC-termination of term rewriting systems, elimination transformations have been vigorously studied since the 1990s. Dummy elimination, distribution elimination, general dummy elimination, and improved general dummy elimination are examples of elimination transformations. In this paper we clarify the essence of elimination transformations based on the notion of dependency pairs. We first present a theorem that gives a general and essential property for elimination transformations, making them sound with AC-termination. Based on the theorem, we design an elimination transformation called the argument filtering transformation. Next, we clarify the relation among various elimination transformations by comparing them with a corresponding restricted argument filtering transformation. Finally, we compare the AC-dependency pair method with the argument filtering transformation. © Springer Science+Business Media, Inc. 2006 |
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