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- Stephen A. Cook, Pierre McKenzie
- J. Algorithms
- 1987

Abstract We exhibit several problems complete for deterministic logarithmic space under NC 1 (i.e., log depth) reducibility. The list includes breadth-first search and depth-first search of an… (More)

- Klaus-Jörn Lange, Pierre McKenzie, Alain Tapp
- Proceedings of Computational Complexity. Twelfth…
- 1997

This paper describes the simulation of an S(n) space-bounded deterministic Turing machine by a reversible Turing machine operating in space S(n). It thus answers a question posed by C. Bennett (1989)… (More)

- Ran Raz, Pierre McKenzie
- Combinatorica
- 1997

, for the monotone depth of functions in monotone-P. As a result we achieve the separation of the following classes.
1. monotone-NC ≠ monotone-P.
2. For every i≥1, monotone-≠ monotone-.
3. More… (More)

- Pierre McKenzie, Klaus W. Wagner
- computational complexity
- 2003

Abstract.The problem of testing membership in the subset of the natural numbers produced at the output gate of a {$$\bigcup, \bigcap, ^-, +, \times$$} combinational circuit is shown to capture a wide… (More)

- Béatrice Bérard, Michel Bidoit, +5 authors Pierre McKenzie
- Springer Berlin Heidelberg
- 2001

ion by state merging consists in viewing some states of an automaton as identical. We also speak of folding, or quotient. We can visualize state merging in a very concrete way: the merged states are… (More)

- Birgit Jenner, Johannes Köbler, Pierre McKenzie, Jacobo Torán
- J. Comput. Syst. Sci.
- 2003

We prove that the graph isomorphism problem restricted to trees and to colored graphs with color multiplicities 2 and 3 is many-one complete for several complexity classes within NC2. In particular… (More)

- Hervé Caussinus, Pierre McKenzie, Denis Thérien, Heribert Vollmer
- J. Comput. Syst. Sci.
- 1996

We define the counting classes #NC1, GapNC1, PNC1 and C=NC1. We prove that boolean circuits, algebraic circuits, programs over nondeterministic finite automata, and programs over constant integer… (More)

We introduce the <i>tree evaluation problem</i>, show that it is in <b>LogDCFL</b> (and hence in <b>P</b>), and study its branching program complexity in the hope of eventually proving a… (More)

- Clemens Lautemann, Pierre McKenzie, Thomas Schwentick, Heribert Vollmer
- Electronic Colloquium on Computational Complexity
- 1998

Building upon the known generalized-quantifier-based first-order characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising… (More)

- Pierre McKenzie, Stephen A. Cook
- SIAM J. Comput.
- 1987

We classify Abelian permutation group problems with respect to their parallel complexity. For such groups specified by generating permutations we show that testing membership, computing order and… (More)