Coinductive Properties of Causal Maps

Authors:
Jiho Kim
Affiliations:
Department of Mathematics, Indiana University, Bloomington, IN 47405
Venue:
AMAST 2008 Proceedings of the 12th international conference on Algebraic Methodology and Software Technology
Year:
2008

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Abstract

Variants of causal functions on streams are defined, and the interplay between them is studied from different perspectives with attention to coalgebraic considerations. We prove that the sets of causal and bicausal functions, respectively, are closed under a certain natural coinductive construction. This closure property paves the way to constructing new final stream coalgebras over finite alphabets. This result is used to show that the 2-adic version of the Collatz function yields a final bit-stream coalgebra.