On the expressive power of first-order boolean functions in PCF

Authors:
Riccardo Pucella;Prakash Panangaden
Affiliations:
Cornell Univ., Ithaca, NY;McGill Univ., Montreal, Canada
Venue:
Theoretical Computer Science
Year:
2001

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Abstract

Recent results of Bucciarelli show that the semilattice of degrees of parallelism of first-order boolean functions in PCF has both infinite chains and infinite antichains. By considering a simple subclass of Sieber's sequentiality relations, we identify levels in the semilattice and derive inexpressibility results concerning functions on different levels. This allows us to further explore the structure of the semilattice of degrees of parallelism: we identify semilattices characterized by simple level properties, and show the existence of new infinite hierarchies which are in a certain sense natural with respect to the levels. Copyright 2001 Elsevier Science B.V.