Complexity of terms, composition, and hypersubstitution
We consider four useful measures of the complexity of a term: the maximum depth (usually called the depth), the minimum depth, the variable count, and the operation count. For each of these, we produce a formula for the complexity of the composition Smn(s,t1,…,tn) in terms of the complexity of the i...
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Hindawi Limited
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203202118 |
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doaj-0a7eb33ad54d4f3bbff91447099be90f2020-11-25T00:06:33ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-0120031595996910.1155/S0161171203202118Complexity of terms, composition, and hypersubstitutionKlaus Denecke0Shelly L. Wismath1Institut für Mathematik, Universität Potsdam, Am Neuen Palais, Potsdam 14415, GermanyDepartment of Mathematics and Computer Science, University of Lethbridge, Alberta, Lethbridge, T1K 3M4, CanadaWe consider four useful measures of the complexity of a term: the maximum depth (usually called the depth), the minimum depth, the variable count, and the operation count. For each of these, we produce a formula for the complexity of the composition Smn(s,t1,…,tn) in terms of the complexity of the inputs s, t1,…, tn. As a corollary, we also obtain formulas for the complexity of σˆ[t] in terms of the complexity of t when t is a compound term and σ is a hypersubstitution. We then apply these formulas to the theory of M-solid varieties, examining the k-normalization chains of a variety with respect to the four complexity measures.http://dx.doi.org/10.1155/S0161171203202118 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Klaus Denecke Shelly L. Wismath |
| spellingShingle |
Klaus Denecke Shelly L. Wismath Complexity of terms, composition, and hypersubstitution International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Klaus Denecke Shelly L. Wismath |
| author_sort |
Klaus Denecke |
| title |
Complexity of terms, composition, and hypersubstitution |
| title_short |
Complexity of terms, composition, and hypersubstitution |
| title_full |
Complexity of terms, composition, and hypersubstitution |
| title_fullStr |
Complexity of terms, composition, and hypersubstitution |
| title_full_unstemmed |
Complexity of terms, composition, and hypersubstitution |
| title_sort |
complexity of terms, composition, and hypersubstitution |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2003-01-01 |
| description |
We consider four useful measures of the complexity of a term: the maximum depth (usually called the depth), the minimum depth, the
variable count, and the operation count. For each of these, we produce a formula for the complexity of the composition Smn(s,t1,…,tn) in terms of the complexity
of the inputs s, t1,…, tn. As a corollary, we also obtain formulas for the complexity of
σˆ[t] in terms of the complexity of t when t is a compound term and σ is a hypersubstitution. We then apply these formulas to the theory of M-solid varieties, examining the k-normalization chains of a variety with respect to the four complexity measures. |
| url |
http://dx.doi.org/10.1155/S0161171203202118 |
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AT klausdenecke complexityoftermscompositionandhypersubstitution AT shellylwismath complexityoftermscompositionandhypersubstitution |
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