Mathematical Theory of L Systems

The paper gives a survey of the different areas of the theory of developmental systems and languages. It is organized in such a way that it discusses typical results obtained in each particular problem area. The results quoted may not always be the most important ones but they are quite representative for the direction of research in this theory. Proofs are not given and, consequently, the basic techniques for solving problems in this theory are not discussed. An attempt has been made to cover also the most recent results. Most of the results have not yet appeared in print. To appear in J. Tou (ed. ), Advances in Information Systems Science, Plenum Press.

https://tidsskrift.dk/daimipb/article/download/6453/5573

The mathematical theory of L systems

This is a reissue of the book Tree Automata by F G\'ecseg and M Steinby originally published in 1984 by Akad\'emiai Kiad\'o, Budapest Some mistakes have been corrected and a few obscure passages have been clarified Moreover, some more recent contributions and current lines of research are reviewed in an appendix that also contains several new references

Tree automata

This paper extends the study and prototyping of unusual DNA motifs, unknown in nature, but founded
on principles derived from biological structures. Artificially designed DNA complexes show promise as building
blocks for the construction of useful nanoscale structures, devices, and computers. The DNA triple crossover
(TX) complex described here extends the set of experimentally characterized building blocks. It consists of
four oligonucleotides hybridized to form three double-stranded DNA helices lying in a plane and linked by
strand exchange at four immobile crossover points. The topology selected for this TX molecule allows for the
presence of reporter strands along the molecular diagonal that can be used to relate the inputs and outputs of
DNA-based computation. Nucleotide sequence design for the synthetic strands was assisted by the application
of algorithms that minimize possible alternative base-pairing structures. Synthetic oligonucleotides were purified,
stoichiometric mixtures were annealed by slow cooling, and the resulting DNA structures were analyzed by
nondenaturing gel electrophoresis and heat-induced unfolding. Ferguson analysis and hydroxyl radical
autofootprinting provide strong evidence for the assembly of the strands to the target TX structure. Ligation
of reporter strands has been demonstrated with this motif, as well as the self-assembly of hydrogen-bonded
two-dimensional crystals in two different arrangements. Future applications of TX units include the construction
of larger structures from multiple TX units, and DNA-based computation. In addition to the presence of reporter
strands, potential advantages of TX units over other DNA structures include space for gaps in molecular arrays,
larger spatial displacements in nanodevices, and the incorporation of well-structured out-of-plane components
in two-dimensional arrays.

Construction, analysis, ligation, and self-assembly of DNA triple crossover complexes

Automated and semi-automated manipulation of so-called labelled transition systems has become an important means in discovering flaws in software and hardware systems. Process algebra has been developed to express such labelled transition systems algebraically, which enhances the ways of manipulation by means of equational logic and term rewriting.The theory of process algebra has developed rapidly over the last twenty years, and verification tools have been developed on the basis of process algebra, often in cooperation with techniques related to model checking. This textbook gives a thorough introduction into the basics of process algebra and its applications.

Ian N. Sneddon

Papers

Theory of automata