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

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 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

A discontinuity in pattern inference

This paper examines the learnability of a major subclass of E-pattern languages – also known as erasing or extended pattern languages – in Gold’s learning model: We show that the class of terminal-free E-pattern languages is inferrable from positive data if the corresponding terminal alphabet consists of three or more letters. Consequently, the recently presented negative result for binary alphabets is unique