Equality of streams is a Π0 over 2-complete problem

Authors:
Grigore Roşu
Affiliations:
University of Illinois at Urbana-Champaign
Venue:
Proceedings of the eleventh ACM SIGPLAN international conference on Functional programming
Year:
2006

Citing 8
Cited 8

Theory of recursive functions and effective computability

Theory of recursive functions and effective computability
Types as theories

Topology and category theory in computer science
Transfinite reductions in orthogonal term rewriting systems

Information and Computation
Equational specifications, complete term rewriting systems, and computable and semicomputable algebras

Journal of the ACM (JACM)
Term rewriting and all that

Term rewriting and all that
A hidden agenda

Theoretical Computer Science
Observational logic, constructor-based logic, and their duality

Theoretical Computer Science - Foundations of software science and computation structures
A tutorial on coinductive stream calculus and signal flow graphs

Theoretical Computer Science - Formal methods for components and objects

Regular Strategies as Proof Tactics for CIRC

Electronic Notes in Theoretical Computer Science (ENTCS)
Well-Definedness of Streams by Termination

RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
The $\Pi^0_2$-Completeness of Most of the Properties of Rewriting Systems You Care About (and Productivity)

RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Circular Coinduction with Special Contexts

ICFEM '09 Proceedings of the 11th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
CIRC: a circular coinductive prover

CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
Circular coinduction: a proof theoretical foundation

CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Levels of undecidability in rewriting

Information and Computation
On the complexity of equivalence of specifications of infinite objects

Proceedings of the 17th ACM SIGPLAN international conference on Functional programming

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper gives a precise characterization for the complexity of the problem of proving equal two streams defined with a finite number of equations: Π0 over 2. Since the Π 0 over 2 class includes properly both the reursively enumerable and the corecursively enumerable classes, this result implies that neither the set of pairs of equal streams nor the set of pairs of unequal streams is recursively enumerable. Consequently, one can find no algorithm for determining equality of streams, as well as no algorithm for determining inequality of streams. In particular, there is no complete proof system for equality of streams and no complete system for inequality of streams.