3,067 research outputs found
Arithmetic Circuits and the Hadamard Product of Polynomials
Motivated by the Hadamard product of matrices we define the Hadamard product
of multivariate polynomials and study its arithmetic circuit and branching
program complexity. We also give applications and connections to polynomial
identity testing. Our main results are the following. 1. We show that
noncommutative polynomial identity testing for algebraic branching programs
over rationals is complete for the logspace counting class \ceql, and over
fields of characteristic the problem is in \ModpL/\Poly. 2.We show an
exponential lower bound for expressing the Raz-Yehudayoff polynomial as the
Hadamard product of two monotone multilinear polynomials. In contrast the
Permanent can be expressed as the Hadamard product of two monotone multilinear
formulas of quadratic size.Comment: 20 page
The set of realizations of a max-plus linear sequence is semi-polyhedral
We show that the set of realizations of a given dimension of a max-plus
linear sequence is a finite union of polyhedral sets, which can be computed
from any realization of the sequence. This yields an (expensive) algorithm to
solve the max-plus minimal realization problem. These results are derived from
general facts on rational expressions over idempotent commutative semirings: we
show more generally that the set of values of the coefficients of a commutative
rational expression in one letter that yield a given max-plus linear sequence
is a semi-algebraic set in the max-plus sense. In particular, it is a finite
union of polyhedral sets
Piecewise testable tree languages
This paper presents a decidable characterization of tree languages that can
be defined by a boolean combination of Sigma_1 sentences. This is a tree
extension of the Simon theorem, which says that a string language can be
defined by a boolean combination of Sigma_1 sentences if and only if its
syntactic monoid is J-trivial
Silent Transitions in Automata with Storage
We consider the computational power of silent transitions in one-way automata
with storage. Specifically, we ask which storage mechanisms admit a
transformation of a given automaton into one that accepts the same language and
reads at least one input symbol in each step.
We study this question using the model of valence automata. Here, a finite
automaton is equipped with a storage mechanism that is given by a monoid.
This work presents generalizations of known results on silent transitions.
For two classes of monoids, it provides characterizations of those monoids that
allow the removal of \lambda-transitions. Both classes are defined by graph
products of copies of the bicyclic monoid and the group of integers. The first
class contains pushdown storages as well as the blind counters while the second
class contains the blind and the partially blind counters.Comment: 32 pages, submitte
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