Algorithmic decidability of Engel's property for automaton groups

We consider decidability problems associated with Engel's identity ($[\cdots[[x,y],y],\dots,y]=1$ for a long enough commutator sequence) in groups generated by an automaton. We give a partial algorithm that decides, given $x,y$, whether an Engel identity is satisfied. It succeeds, importantly, in proving that Grigorchuk's $2$-group is not Engel. We consider next the problem of recognizing Engel elements, namely elements $y$ such that the map $x\mapsto[x,y]$ attracts to $\{1\}$. Although this problem seems intractable in general, we prove that it is decidable for Grigorchuk's group: Engel elements are precisely those of order at most $2$. Our computations were implemented using the package FR within the computer algebra system GAP

XML Publishing: Bridging Theory and Practice

Abstract. Transforming relational data into XML, as known as XML publishing, is often necessary when one wants to exchange data residing in databases or to create an XML interface of a traditional database. This paper aims to provide an overview of recent advances in XML publish-ing. We present a notion of publishing transducers recently developed for studying the expressive power and complexity of XML publishing languages. In terms of publishing transducers we then characterize XML publishing languages being used in practice. In addition, we address dy-namic aspects of XML publishing, namely, incremental maintenance and update management of XML views published from relational data.

Asynchronous automata networks can emulate any synchronous automata network

Electronic version of an article published as International Journal of Algebra and Computation 2004 Vol. 14 no.5-6 pp.719-739 DOI: 10.1142/S0218196704002043 copyright World Scientific Publishing Company http://ejournals.wspc.com.sg/journals/ijac/mkt/archive.shtml DOI : 10.1142/S0218196704002043Peer reviewe

Automata represented by products of soliton automata

AbstractSoliton valves have been proposed as molecular switching elements. A mathematical model of the logic aspects of soliton switching, called soliton automaton, was introduced by Dassow and Jürgensen. They analysed the simulation power of strongly deterministic soliton automata with respect to transition semigroups. Here, a more detailed analysis in terms of homomorphic and isomorphic representations with respect to various automaton products is given