Efficient algorithms for isomorphisms of simple types

• Autores: Joseph Gil, Yoab Zibin
• Localización: Mathematical structures in computer science, ISSN 0960-1295, Vol. 15, Nº 5, 2005, págs. 917-957
• Idioma: inglés
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• Resumen

  • The first-order isomorphism problem is to decide whether two non-recursive types using product- and function-type constructors are isomorphic under the axioms of commutative and associative products, and currying and distributivity of functions over products. We show that this problem can be solved in $O(n \log^2 n)$ time and $O(n)$ space, where $n$ is the input size. This result improves upon the $O(n^2 \log n)$ time and $O(n^2)$ space bounds of the best previous algorithm. We also describe an $O(n)$ time algorithm for the linear isomorphism problem, which does not include the distributive axiom, thereby improving upon the $O(n \log n)$ time of the best previous algorithm for this problem.