On groups and counter automata

We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of rank n; this result, which answers a question of Gilman, is in a very precise sense an abelian analogue of the Muller-Schupp theorem. More generally, if G is a virtually abelian group then every group with word problem recognised by a G-automaton is virtually abelian with growth class bounded above by the growth class of G. We consider also other types of counter automata.Comment: 18 page

Monoid automata for displacement context-free languages

In 2007 Kambites presented an algebraic interpretation of Chomsky-Schutzenberger theorem for context-free languages. We give an interpretation of the corresponding theorem for the class of displacement context-free languages which are equivalent to well-nested multiple context-free languages. We also obtain a characterization of k-displacement context-free languages in terms of monoid automata and show how such automata can be simulated on two stacks. We introduce the simultaneous two-stack automata and compare different variants of its definition. All the definitions considered are shown to be equivalent basing on the geometric interpretation of memory operations of these automata.Comment: Revised version for ESSLLI Student Session 2013 selected paper

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

Silent Transitions in Automata with Storage

We consider the computational power of silent transitions in one-way automata with storage. Specifically, we ask which storage mechanisms admit a transformation of a given automaton into one that accepts the same language and reads at least one input symbol in each step. We study this question using the model of valence automata. Here, a finite automaton is equipped with a storage mechanism that is given by a monoid. This work presents generalizations of known results on silent transitions. For two classes of monoids, it provides characterizations of those monoids that allow the removal of \lambda-transitions. Both classes are defined by graph products of copies of the bicyclic monoid and the group of integers. The first class contains pushdown storages as well as the blind counters while the second class contains the blind and the partially blind counters.Comment: 32 pages, submitte

D-semigroups and constellations

In a result generalising the Ehresmann–Schein–Nambooripad Theorem relating inverse semigroups to inductive groupoids, Lawson has shown that Ehresmann semigroups correspond to certain types of ordered (small) categories he calls Ehresmann categories. An important special case of this is the correspondence between two-sided restriction semigroups and what Lawson calls inductive categories. Gould and Hollings obtained a one-sided version of this last result, by establishing a similar correspondence between left restriction semigroups and certain ordered partial algebras they call inductive constellations (a general constellation is a one-sided generalisation of a category). We put this one-sided correspondence into a rather broader setting, at its most general involving left congruence D-semigroups (which need not satisfy any semiadequacy condition) and what we call co-restriction constellations, a finitely axiomatized class of partial algebras. There are ordered and unordered versions of our results. Two special cases have particular interest. One is that the class of left Ehresmann semigroups (the natural one-sided versions of Lawson’s Ehresmann semigroups) corresponds to the class of co-restriction constellations satisfying a suitable semiadequacy condition. The other is that the class of ordered left Ehresmann semigroups (which generalise left restriction semigroups and for which semigroups of binary relations equipped with domain operation and the inclusion order are important examples) corresponds to a class of ordered constellations defined by a straightforward weakening of the inductive constellation axioms

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)

Quasi-isometry and finite presentations for left cancellative monoids

We show that being finitely presentable and being finitely presentable with solvable word problem are quasi-isometry invariants of finitely generated left cancellative monoids. Our main tool is an elementary, but useful, geometric characterization of finite presentability for left cancellative monoids. We also give examples to show that this characterization does not extend to monoids in general, and indeed that properties such as solvable word problem are not isometry invariants for general monoids

Groups acting on semimetric spaces and quasi-isometries of monoids

Abstract. We study groups acting by length-preserving transformations on spaces equipped with asymmetric, partially-defined distance functions. We introduce a natural notion of quasi-isometry for such spaces and exhibit an extension of the ˇ Svarc-Milnor lemma to this setting. Among the most natural examples of these spaces are finitely generated monoids and semigroups and their Cayley and Schützenberger graphs. We apply our results to show that a number of important properties of monoids are quasi-isometry invariants. 1

An OpenMP-like Interface for Parallel Programming in Java

This paper describes the definition and implementation of an OpenMP-like set of directives and library routines for shared memory parallel programming in Java. A specification of the directives and routines is proposed and discussed. A prototype implementation, consisting of a compiler and a runtime library, both written entirely in Java, is presented, which implements a significant subset of the proposed specification

An OpenMP-like interface for parallel programming in Java

This paper describes the definition and implementation of an OpenMP-like set of directives and library routines for shared memory parallel programming in Java. A specification of the directives and routines is proposed and discussed. A prototype implementation, consisting of a compiler and a runtime library, both written entirely in Java, is presented, which implements most of the proposed specification. Some preliminary performance results are reported. Copyright # 2001 John Wiley & Sons, Lt