Quantum finite automata: A modern introduction

We present five examples where quantum finite automata (QFAs) outperform their classical counterparts. This may be useful as a relatively simple technique to introduce quantum computation concepts to computer scientists. We also describe a modern QFA model involving superoperators that is able to simulate all known QFA and classical finite automaton variants.Comment: 15 page

State Owned Enterprises and Redistribution: An Empirical Analysis

In the past decade many developing economies started to privatize their state owned enterprises. Recently, however, this process seems to have slowed down in some economies and have completely been stalled in others. Here we formalize the view that this is so because these enterprises are major instruments of income redistribution and, in economies with significant degrees of income inequality, segments of the population that benefit from this redistribution would use whatever political power they may have to oppose its abandonment. We find strong and robust empirical support for this hypothesis using cross-country data on the relative size of the state-owned-enterprise sector and different measures of inequality. We also find support for the propositions that dictatorships as well as democracies use this redistributive tool and that left-wing governments tend to redistribute more than right-wing governments through state owned enterprises.state-owned enterprises, inequality, redistribution, political economy

Generalized Results on Monoids as Memory

We show that some results from the theory of group automata and monoid automata still hold for more general classes of monoids and models. Extending previous work for finite automata over commutative groups, we demonstrate a context-free language that can not be recognized by any rational monoid automaton over a finitely generated permutable monoid. We show that the class of languages recognized by rational monoid automata over finitely generated completely simple or completely 0-simple permutable monoids is a semi-linear full trio. Furthermore, we investigate valence pushdown automata, and prove that they are only as powerful as (finite) valence automata. We observe that certain results proven for monoid automata can be easily lifted to the case of context-free valence grammars.Comment: In Proceedings AFL 2017, arXiv:1708.0622

Cosine Similarity Measure According to a Convex Cost Function

In this paper, we describe a new vector similarity measure associated with a convex cost function. Given two vectors, we determine the surface normals of the convex function at the vectors. The angle between the two surface normals is the similarity measure. Convex cost function can be the negative entropy function, total variation (TV) function and filtered variation function. The convex cost function need not be differentiable everywhere. In general, we need to compute the gradient of the cost function to compute the surface normals. If the gradient does not exist at a given vector, it is possible to use the subgradients and the normal producing the smallest angle between the two vectors is used to compute the similarity measure