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 We present a compilation of the known P-complete problems, including several unpublished or new P-completeness results, and many open problems.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 fi...

Properties of probabilistic as well as "probabilistic plus nondeterministic" pushdown automata and auxiliary pushdown automata are studied. These models are analogous to their counterparts with nondeterministic and alternating states. Complete characterizations in terms of well-known complexity classes are given for the classes of languages recognized by polynomial time-bounded, logarithmic space-bounded auxiliary pushdown automata with probabilistic states and with "probabilistic plus nondeterministic" states. Also, complexity lower bounds are given for the classes of languages recognized by these automata with unlimited running time. It follows that, by fixing an appropriate mode of computation, the difference between classes of languages such as P and PSPACE, NL and SAC 1 , PL and Diff ?(#SAC 1 ) is characterized as the difference between the number of stack symbols; that is, whether the stack alphabet contains one versus two distinct symbols. 1 Introduction The notion of det...

Simpler proofs that DAuxPDA-TIME(polynomial) equals LOGDCFL and that SAC 1 equals LOGCFL are given which avoid Sudborough's multi-head automata [Sud78]. The first characterization of LOGDCFL in terms of polynomial proof-tree-size is obtained, using circuits built from the multiplex select gates of [FLR96]. The classes L and NC 1 are also characterized by polynomial size such circuits: "self-similar" logarithmic depth captures L, and bounded width captures NC 1 . 1 Introduction The class LOGCFL occupies a central place in the landscape of parallel complexity classes. LOGCFL sits between two interesting classes, NL and AC 1 : NL is often viewed as the space analog of NP, and AC 1 characterizes the problems solvable on a PRAM in O(log n) time using a polynomial number of processors. As a class, LOGCFL has attracted a lot of attention due to its seemingly "richer structure" than that of NL. The initial papers by Sudburough [Sud78] and Ruzzo [Ruz80] characterized LOGCFL using mul...