On the rational subset problem for groups

We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN extensions with finite associated subgroups. We provide a simple proof of a result of Grunschlag showing that the decidability of this problem is a virtual property. We prove further that the problem is decidable for a direct product of a group G with a monoid M if and only if membership is uniformly decidable for G-automata subsets of M. It follows that a direct product of a free group with any abelian group or commutative monoid has decidable rational subset membership.Comment: 19 page

The monoid of queue actions

We investigate the monoid of transformations that are induced by sequences of writing to and reading from a queue storage. We describe this monoid by means of a confluent and terminating semi-Thue system and study some of its basic algebraic properties, e.g., conjugacy. Moreover, we show that while several properties concerning its rational subsets are undecidable, their uniform membership problem is NL-complete. Furthermore, we present an algebraic characterization of this monoid's recognizable subsets. Finally, we prove that it is not Thurston-automatic

Contesting longstanding conceptualisations of urban green space

Ever since the Victorian era saw the creation of “parks for the people,” health and wellbeing benefits have been considered a primary benefit of urban parks and green spaces. Today, public health remains a policy priority, with illnesses and conditions such as diabetes, obesity and depression a mounting concern, notably in increasingly urbanised environments. Urban green space often is portrayed as a nature-based solution for addressing such health concerns. In this chapter, Meredith Whitten investigates how the health and wellbeing benefits these spaces provide are limited by a narrow perspective of urban green space. Whitten explores how our understandings of urban green space remain rooted in Victorian ideals and calls into question how fit for purpose they are in twenty-first-century cities. Calling on empirical evidence collected in three boroughs in London with changing and increasing demographic populations, she challenges the long-held cultural underpinnings that lead to urban green space being portrayed “as a panacea to urban problems, yet treating it as a ‘cosmetic afterthought’” (Whitten, M, Reconceptualising green space: planning for urban green space in the contemporary city. Doctoral thesis, London School of Economics and Political Science, London, U.K. http://etheses.lse.ac.uk/. Accessed 12 Jun 2019, 2019b, p 18)

Lessons from Italian Experiences: Bottlenecks, New Challenges and Opportunities

This contribution provides some conclusive arguments on the role of Ecosystem Services in Spatial planning for Green and Blue infrastructure design deduced from the Italian experiences examined in the previous chapters. The Chapter reflects on some specifically Italian aspects which make critical the integration of Ecosystem services into the definition of territorial decisions for the enhancement of human well-being, public health and quality of life. The aim is to highlight the current challenges and bottlenecks in ES-based Planning by focusing on the innovative approaches and methods adopted in the various cases to attempt or resolve critical issues. The topic of Green and Blue infrastructures is investigated in a Planning perspective as a strategic design tool which can manage and regulate multiple ES, and implement them into the spatial planning process