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mpote
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There are 5 letters in MPOTE ( E1M3O1P3T1 )
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In theoretical computer science, in particular in term rewriting, a path ordering is a well-founded strict total order (>) on the set of all terms such that * f(...) > g(s1,...,sn) if f .> g and f(...) > si for i=1,...,n,where (.>) is a user-given total precedence order on the set of all function symbols. * Intuitively, a term f(...) is bigger than any term g(...) built from terms si smaller than f(...) using a * lower-precedence root symbol g. * In particular, by structural induction, a term f(...) is bigger than any term containing only symbols smaller than f. * A path ordering is often used as reduction ordering in term rewriting, in particular in the Knuth–Bendix completion algorithm. * As an example, a term rewriting system for "multiplying out" mathematical expressions could contain a rule x*(y+z) → (x*y) + (x*z). In order to prove termination, a reduction ordering (>) must be found with respect to which the term x*(y+z) is greater than the term (x*y)+(x*z). This is not trivial, since the former term contains both fewer function symbols and fewer variables than the latter. However, setting the precedence (*) .> (+), a path ordering can be used, since both x*(y+z) > x*y and x*(y+z) > x*z is easy to achieve. * Given two terms s and t, with a root symbol f and g, respectively, to decide their relation their root symbols are compared first. * If f <. g, then s can dominate t only if one of s's subterms does. * If f .> g, then s dominates t if s dominates each of t's subterms. * If f = g, then the immediate subterms of s and t need to be compared recursively. Depending on the particular method, different variations of path orderings exist.The latter variations include: * the multiset path ordering (mpo), originally called recursive path ordering (rpo) * the lexicographic path ordering (lpo) * a combination of mpo and lpo, called recursive path ordering by Dershowitz, Jouannaud (1990)Dershowitz, Okada (1988) list more variants, and relate them to Ackermann's system of ordinals. |