On the faithful regular extensions of iterative algebras

Authors:
Francesco Parisi-Presicce
Affiliations:
-
Venue:
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Year:
1981

Citing 2
Cited 0

Initial Algebra Semantics and Continuous Algebras

Journal of the ACM (JACM)
Unique Fixed Points v. Least Fixed Points

Proceedings of the 6th Colloquium, on Automata, Languages and Programming

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Abstract

In ([6]), Tiuryn proved the existence of extensions of algebras with the unique fixed point property (iterative algebras) to ordered algebras with the least fixed point property (regular algebras), extensions preserving the fixed point solutions. The aim of this paper is to prove that whenever the extension is “faithful”, i.e. obtained without collapsing elements of the carrier, the new regular algebra is again iterative. In Section 1 we fix some notations and definitions and state Tiuryn's result. Section 2 contains the formulation of the problem and a sketch of the proof. Section 3 deals with the main construction.