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Electronic Colloquium on Computational Complexity

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All reports by Author Pierre McKenzie:

TR17-109 | 22nd June 2017
Russell Impagliazzo, Valentine Kabanets, Antonina Kolokolova, Pierre McKenzie, Shadab Romani

Does Looking Inside a Circuit Help?

The Black-Box Hypothesis, introduced by Barak et al. (JACM, 2012), states that any property of boolean functions decided efficiently (e.g., in BPP) with inputs represented by circuits can also be decided efficiently in the black-box setting, where an algorithm is given an oracle access to the input function and an ... more >>>

TR17-072 | 25th April 2017
Eric Allender, Andreas Krebs, Pierre McKenzie

Better Complexity Bounds for Cost Register Machines

Revisions: 1

Cost register automata (CRA) are one-way finite automata whose transitions have the side effect that a register is set to the result of applying a state-dependent semiring operation to a pair of registers. Here it is shown that CRAs over the semiring (N,min,+) can simulate polynomial time computation, proving along ... more >>>

TR13-040 | 11th March 2013
Michaƫl Cadilhac, Andreas Krebs, Pierre McKenzie

The Algebraic Theory of Parikh Automata

Revisions: 2

The Parikh automaton model equips a finite automaton with integer registers and imposes a semilinear constraint on the set of their final settings. Here the theory of typed monoids is used to characterize the language classes that arise algebraically. Complexity bounds are derived, such as containment of the unambiguous Parikh ... more >>>

TR12-090 | 2nd July 2012
Michael Blondin, Andreas Krebs, Pierre McKenzie

The Complexity of Intersecting Finite Automata Having Few Final States

The problem of determining whether several finite automata accept a word in common is closely related to the well-studied membership problem in transformation monoids. We raise the issue of limiting the number of final states in the automata intersection problem. For automata with two final states, we show the problem ... more >>>

TR11-095 | 22nd June 2011
Christoph Behle, Andreas Krebs, Klaus-Joern Lange, Pierre McKenzie

Low uniform versions of NC1

Revisions: 1

In the setting known as DLOGTIME-uniformity,
the fundamental complexity classes
$AC^0\subset ACC^0\subseteq TC^0\subseteq NC^1$ have several
robust characterizations.
In this paper we refine uniformity further and examine the impact
of these refinements on $NC^1$ and its subclasses.
When applied to the logarithmic circuit depth characterization of $NC^1$,
some refinements leave ... more >>>

TR05-136 | 14th November 2005
Anna Gal, Michal Koucky, Pierre McKenzie

Incremental branching programs

In this paper we propose the study of a new model of restricted
branching programs which we call incremental branching programs.
This is in line with the program proposed by Cook in 1974 as an
approach for separating the class of problems solvable in logarithmic
space from problems solvable ... more >>>

TR00-036 | 29th May 2000
Carsten Damm, Markus Holzer, Pierre McKenzie

The Complexity of Tensor Calculus

Tensor calculus over semirings is shown relevant to complexity
theory in unexpected ways. First, evaluating well-formed tensor
formulas with explicit tensor entries is shown complete for $\olpus\P$,
for $\NP$, and for $\#\P$ as the semiring varies. Indeed the
permanent of a matrix is shown expressible as ... more >>>

TR98-059 | 15th September 1998
C. Lautemann, Pierre McKenzie, T. Schwentick, H. Vollmer

The Descriptive Complexity Approach to LOGCFL

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
from varying the arity and nesting of groupoidal quantifiers. Our
work extends the elaborate theory relating monoidal quantifiers to
NC^1 and its subclasses. In the ... more >>>

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