This paper serves two purposes. Firstly, it is an elementary introduction to the theory of P-completeness--- the branch of complexity theory that focuses on identifying the problems in the class P that are "hardest, " in the sense that they appear to lack highly parallel solutions. That is, they do not have parallel solutions using time polynomial in the logarithm of the problem size and a polynomial number of processors unless all problem in P have such solutions, or equivalently, unless P = NC. Secondly, this paper is a reference work of P-complete problems. We present a compilation of the known P-complete problems, including several unpublished or new P-completeness results, and many open problems. This is a preliminary version, mainly containing the problem list. The latest version of this document is available in electronic form by anonymous ftp from thorhild.cs.ualberta.ca (129.128.4.53) as either a compressed dvi file (TR91-11.dvi.Z) or as a compressed postscript file (TR91-11.ps.Z), or from cs.washington.edu (128.95.1.4) as a compressed postscript file
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7703
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