On Varieties of Ordered Automata

The Eilenberg correspondence relates varieties of regular languages to pseudovarieties of finite monoids. Various modifications of this correspondence have been found with more general classes of regular languages on one hand and classes of more complex algebraic structures on the other hand. It is also possible to consider classes of automata instead of algebraic structures as a natural counterpart of classes of languages. Here we deal with the correspondence relating positive $\mathcal C$-varieties of languages to positive $\mathcal C$-varieties of ordered automata and we present various specific instances of this correspondence. These bring certain well-known results from a new perspective and also some new observations. Moreover, complexity aspects of the membership problem are discussed both in the particular examples and in a general setting

Quantum finite automata and linear context-free languages: a decidable problem

We consider the so-called measure once finite quantum automata model introduced by Moore and Crutchfield in 2000. We show that given a language recognized by such a device and a linear context-free language, it is recursively decidable whether or not they have a nonempty intersection. This extends a result of Blondel et al. which can be interpreted as solving the problem with the free monoid in place of the family of linear context-free languages. © 2013 Springer-Verlag

Gender (in)equality, globalization and governance

This document is part of a digital collection provided by the Martin P. Catherwood Library, ILR School, Cornell University, pertaining to the effects of globalization on the workplace worldwide. Special emphasis is placed on labor rights, working conditions, labor market changes, and union organizing.ILO_Gender_in_equalityGlobalizationandGovernance.pdf: 768 downloads, before Oct. 1, 2020

Polynomial Time Algorithm for Min-Ranks of Graphs with Simple Tree Structures

The min-rank of a graph was introduced by Haemers (1978) to bound the Shannon capacity of a graph. This parameter of a graph has recently gained much more attention from the research community after the work of Bar-Yossef et al. (2006). In their paper, it was shown that the min-rank of a graph G characterizes the optimal scalar linear solution of an instance of the Index Coding with Side Information (ICSI) problem described by the graph G. It was shown by Peeters (1996) that computing the min-rank of a general graph is an NP-hard problem. There are very few known families of graphs whose min-ranks can be found in polynomial time. In this work, we introduce a new family of graphs with efficiently computed min-ranks. Specifically, we establish a polynomial time dynamic programming algorithm to compute the min-ranks of graphs having simple tree structures. Intuitively, such graphs are obtained by gluing together, in a tree-like structure, any set of graphs for which the min-ranks can be determined in polynomial time. A polynomial time algorithm to recognize such graphs is also proposed.Comment: Accepted by Algorithmica, 30 page

The Future Impact of Same-Sex Marriage: More Questions Than Answers

Same-sex relationships have already significantly altered family law, by leading to new formal relationship statuses and incorporation of the principle that both of a child’s legal parents can be of the same sex. This essay explores further changes that may lie ahead as same-sex marriage debates increasingly affect both family law and the social meanings of marriage. Marriage as an institution has changed most dramatically because of the cumulative effects of the last half-century of de-gendering family law. Same-sex marriage–and perhaps even more so, the highly visible cultural debate over it–is contributing to this process. The author argues that the greatest potential for changes in social meaning will arise in three areas for which there is empirical evidence of significant differences between gay and straight couples: division of household labor, sexual exclusivity, and childrearing. In each, although recent data indicate some signs of converging behaviors between the two types of couples, major differences appear likely to continue. While the number of same-sex couples in the population is too small to produce significant change in overall patterns of behavior, the issue of gay marriage has generated so much attention and debate that a mixed process of gay assimilation to and effect on the social meaning of marriage is a reasonable expectation. As to future legal change, the author identifies three questions likely to arise in the relatively near future that will flow, directly or indirectly, from same-sex marriage: First, we may see an increasing uptake by different-sex couples of marriage equivalent and marriage alternative statuses (e.g., domestic partnerships) that have grown out of LGBT rights efforts. If present demographic trends continue, the group of different-sex couples most likely to seek access to these new statuses will be persons middle-aged or older. Second, federal recognition of same-sex marriage, which will occur if the Defense of Marriage Act is invalidated or repealed, could significantly increase the number of same-sex couples who marry. The end of DOMA is also likely to further complicate the law of interstate recognition, as more gay couples have their marriages recognized for federal law purposes, such as tax, but not under state laws that regulate divorce, custody and property division. Since 60 per cent of same-sex marriages are performed for out-of-state residents, the complexity of federal-state conflict regarding recognition of particular marriages is likely to increase dramatically. Lastly, the author questions whether the issue of “accidental procreation” that has become a theme in court decisions related to same-sex marriage may migrate to marriage law more generally. In particular, she suggests that a more stringent set of rules expanding support obligations in marriages (whether of different- or same-sex spouses) in which children are born or adopted would better serve the purposes advanced by social conservatives who purport to argue on behalf of children’s welfare