On the complexity of equivalence of specifications of infinite objects
Proceedings of the 17th ACM SIGPLAN international conference on Functional …, 2012•dl.acm.org
We study the complexity of deciding the equality of infinite objects specified by systems of
equations, and of infinite objects specified by λ-terms. For equational specifications there are
several natural notions of equality: equality in all models, equality of the sets of solutions,
and equality of normal forms for productive specifications. For λ-terms we investigate Böhm-
tree equality and various notions of observational equality. We pinpoint the complexity of
each of these notions in the arithmetical or analytical hierarchy. We show that the complexity …
equations, and of infinite objects specified by λ-terms. For equational specifications there are
several natural notions of equality: equality in all models, equality of the sets of solutions,
and equality of normal forms for productive specifications. For λ-terms we investigate Böhm-
tree equality and various notions of observational equality. We pinpoint the complexity of
each of these notions in the arithmetical or analytical hierarchy. We show that the complexity …
We study the complexity of deciding the equality of infinite objects specified by systems of equations, and of infinite objects specified by λ-terms. For equational specifications there are several natural notions of equality: equality in all models, equality of the sets of solutions, and equality of normal forms for productive specifications. For λ-terms we investigate Böhm-tree equality and various notions of observational equality. We pinpoint the complexity of each of these notions in the arithmetical or analytical hierarchy.
We show that the complexity of deciding equality in all models subsumes the entire analytical hierarchy. This holds already for the most simple infinite objects, viz. streams over {0,1}, and stands in sharp contrast to the low arithmetical ϖ02-completeness of equality of equationally specified streams derived in [17] employing a different notion of equality.
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