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On the Expressive Power of First-Order Boolean Functions in PCF

Programming Languages 2007-05-23 v1

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.

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Cite

@article{arxiv.cs/0405085,
  title  = {On the Expressive Power of First-Order Boolean Functions in PCF},
  author = {Riccardo Pucella and Prakash Panangaden},
  journal= {arXiv preprint arXiv:cs/0405085},
  year   = {2007}
}

Comments

23 pages

R2 v1 2026-07-22T12:22:08.091Z