Mark Kambites

JOMP—an OpenMP-like interface for Java

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

Formal Languages and Groups as Memory

We present an exposition of the theory of M-automata and G-automata, or finite automata augmented with a multiply-only register storing an element of a given monoid or group. Included are a number of new results of a foundational nature. We illustrate our techniques with a group-theoretic interpretation and proof of a key theorem of Chomsky and Schützenberger from formal language theory.

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

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 recognized 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.

Word problems recognisable by deterministic blind monoid automata

We consider blind, deterministic, finite automata equipped with a register which stores an element of a given monoid, and which is modified by right multiplication by monoid elements. We show that, for monoids M drawn from a large class including groups, such an automaton accepts the word problem of a group H if and only if H has a finite index subgroup which embeds in the group of units of M. In the case that M is a group, this answers a question of Elston and Ostheimer.

Tropical matrix groups

We study the structure of groups of finitary tropical matrices under multiplication. We show that the maximal groups of

On commuting elements and embeddings of graph groups and monoids

n \times n

Pure dimension and projectivity of tropical polytopes

n×n tropical matrices are precisely the groups of the form