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ACM Transactions on Programming Languages and Systems (TOPLAS)
Infinite objects in type theory
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Nondeterminism vs. Underspecification
ISAS-SCI '01 Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics: Information Systems Development-Volume I - Volume I
Observational logic, constructor-based logic, and their duality
Theoretical Computer Science - Foundations of software science and computation structures
POPL '76 Proceedings of the 3rd ACM SIGACT-SIGPLAN symposium on Principles on programming languages
Behavioural differential equations: a coinductive calculus of streams, automata, and power series
Theoretical Computer Science
A tutorial on coinductive stream calculus and signal flow graphs
Theoretical Computer Science - Formal methods for components and objects
Equality of streams is a Π0 over 2-complete problem
Proceedings of the eleventh ACM SIGPLAN international conference on Functional programming
Data-Oblivious Stream Productivity
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Complexity of Fractran and Productivity
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Levels of undecidability in rewriting
Information and Computation
Advanced Topics in Bisimulation and Coinduction
Advanced Topics in Bisimulation and Coinduction
Automatic Sequences and Zip-Specifications
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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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.