971 research outputs found
Unambiguous 1-Uniform Morphisms
A morphism h is unambiguous with respect to a word w if there is no other
morphism g that maps w to the same image as h. In the present paper we study
the question of whether, for any given word, there exists an unambiguous
1-uniform morphism, i.e., a morphism that maps every letter in the word to an
image of length 1.Comment: In Proceedings WORDS 2011, arXiv:1108.341
On Uneven Ground: How Corporate Governance Prioritizes Short-term Speculative Investments, Impedes Productive Investments, and Jeopardizes Productivity Growth
The economic recovery after the Great Recession highlighted a continuous divergence between soaring profits and lagging investment. These trends are related at the corporate level, where corporate managers have stronger incentives to pursue short-term profit-seeking activities than to invest in longer-term productive activities, such as hiring and training people and investment in physical infrastructure. This prioritization results because the corporate governance system is biased towards the short run. The policy goals that we discuss aim to find a better economic balance between short-run and long-run goals by defining long-term performance measures and finding a better balance in the incentives of short-run and long-run oriented corporate stakeholders.Business investment; corporate governance; short-term speculation; long-term productivity growth
Discontinuities in pattern inference
This paper deals with the inferrability of classes of E-pattern languages—also referred
to as extended or erasing pattern languages—from positive data in Gold’s
model of identification in the limit. The first main part of the paper shows that
the recently presented negative result on terminal-free E-pattern languages over binary
alphabets does not hold for other alphabet sizes, so that the full class of these
languages is inferrable from positive data if and only if the corresponding terminal
alphabet does not consist of exactly two distinct letters. The second main part yields
the insight that the positive result on terminal-free E-pattern languages over alphabets
with three or four letters cannot be extended to the class of general E-pattern
languages. With regard to larger alphabets, the extensibility remains open.
The proof methods developed for these main results do not directly discuss the
(non-)existence of appropriate learning strategies, but they deal with structural
properties of classes of E-pattern languages, and, in particular, with the problem
of finding telltales for these languages. It is shown that the inferrability of classes
of E-pattern languages is closely connected to some problems on the ambiguity
of morphisms so that the technical contributions of the paper largely consist of
combinatorial insights into morphisms in word monoids
Discontinuities in pattern inference
This paper deals with the inferrability of classes of E-pattern languages—also referred
to as extended or erasing pattern languages—from positive data in Gold’s
model of identification in the limit. The first main part of the paper shows that
the recently presented negative result on terminal-free E-pattern languages over binary
alphabets does not hold for other alphabet sizes, so that the full class of these
languages is inferrable from positive data if and only if the corresponding terminal
alphabet does not consist of exactly two distinct letters. The second main part yields
the insight that the positive result on terminal-free E-pattern languages over alphabets
with three or four letters cannot be extended to the class of general E-pattern
languages. With regard to larger alphabets, the extensibility remains open.
The proof methods developed for these main results do not directly discuss the
(non-)existence of appropriate learning strategies, but they deal with structural
properties of classes of E-pattern languages, and, in particular, with the problem
of finding telltales for these languages. It is shown that the inferrability of classes
of E-pattern languages is closely connected to some problems on the ambiguity
of morphisms so that the technical contributions of the paper largely consist of
combinatorial insights into morphisms in word monoids
A negative result on inductive inference of extended pattern languages
A negative result on inductive inference of extended pattern language
On the equivalence problem for E-pattern languages over small alphabets
We contribute new facets to the discussion on the equivalence
problem for E-pattern languages (also referred to as extended or
erasing pattern languages). This fundamental open question asks for the
existence of a computable function that, given any pair of patterns, decides
whether or not they generate the same language. Our main result
disproves Ohlebusch and Ukkonen’s conjecture (Theoretical Computer
Science 186, 1997) on the equivalence problem; the respective argumentation,
that largely deals with the nondeterminism of pattern languages,
is restricted to terminal alphabets with at most four distinct letters
On the learnability of E-pattern languages over small alphabets
This paper deals with two well discussed, but largely open
problems on E-pattern languages, also known as extended or erasing
pattern languages: primarily, the learnability in Gold’s learning model
and, secondarily, the decidability of the equivalence. As the main result,
we show that the full class of E-pattern languages is not inferrable from
positive data if the corresponding terminal alphabet consists of exactly
three or of exactly four letters – an insight that remarkably contrasts
with the recent positive finding on the learnability of the subclass of
terminal-free E-pattern languages for these alphabets. As a side-effect of
our reasoning thereon, we reveal some particular example patterns that
disprove a conjecture of Ohlebusch and Ukkonen (Theoretical Computer
Science 186, 1997) on the decidability of the equivalence of E-pattern
languages
A non-learnable class of E-pattern languages
We investigate the inferrability of E-pattern languages (also known as extended
or erasing pattern languages) from positive data in Gold’s learning model. As the
main result, our analysis yields a negative outcome for the full class of E-pattern
languages – and even for the subclass of terminal-free E-pattern languages – if the
corresponding terminal alphabet consists of exactly two distinct letters. Furthermore,
we present a positive result for a manifest subclass of terminal-free E-pattern
languages. We point out that the considered problems are closely related to fundamental
questions concerning the nondeterminism of E-pattern languages
- …