On the power of parallel communicating Watson–Crick automata systems

AbstractParallel communicating Watson–Crick automata systems were introduced in [E. Czeizler, E. Czeizler, Parallel communicating Watson–Crick automata systems, in: Z. Ésik, Z. Fülöp (Eds.), Proc. Automata and Formal Languages, Dobogókő, Hungary, 2005, pp. 83–96] as possible models of DNA computations. This combination of Watson–Crick automata and parallel communicating systems comes as a natural extension due to the new developments in DNA manipulation techniques. It is already known, see [D. Kuske, P. Weigel, The Role of the Complementarity Relation in Watson–Crick Automata and Sticker Systems, DLT 2004, Lecture Notes in Computer Science, Vol. 3340, Auckland, New Zealand, 2004, pp. 272–283], that for Watson–Crick finite automata, the complementarity relation plays no active role. However, this is not the case when considering parallel communicating Watson–Crick automata systems. In this paper we prove that non-injective complementarity relations increase the accepting power of these systems. We also prove that although Watson–Crick automata are equivalent to two-head finite automata, this equivalence is not preserved when comparing parallel communicating Watson–Crick automata systems and multi-head finite automata

Bounded Languages Meet Cellular Automata with Sparse Communication

Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell communication by bounding the number of allowed uses of the links between cells. Moreover, we consider the devices as acceptors for bounded languages in order to explore the borderline at which non-trivial decidability problems of cellular automata classes become decidable. It is shown that even devices with drastically reduced communication, that is, each two neighboring cells may communicate only constantly often, accept bounded languages that are not semilinear. If the number of communications is at least logarithmic in the length of the input, several problems are undecidable. The same result is obtained for classes where the total number of communications during a computation is linearly bounded

The Power of Centralized PC Systems of Pushdown Automata

Parallel communicating systems of pushdown automata (PCPA) were introduced in (Csuhaj-Varj{\'u} et. al. 2000) and in their centralized variants shown to be able to simulate nondeterministic one-way multi-head pushdown automata. A claimed converse simulation for returning mode (Balan 2009) turned out to be incomplete (Otto 2012) and a language was suggested for separating these PCPA of degree two (number of pushdown automata) from nondeterministic one-way two-head pushdown automata. We show that the suggested language can be accepted by the latter computational model. We present a different example over a single letter alphabet indeed ruling out the possibility of a simulation between the models. The open question about the power of centralized PCPA working in returning mode is then settled by showing them to be universal. Since the construction is possible using systems of degree two, this also improves the previous bound three for generating all recursively enumerable languages. Finally PCPAs are restricted in such a way that a simulation by multi-head automata is possible

Multi-Head Finite Automata: Characterizations, Concepts and Open Problems

Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg, 1966). Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these devices has been developed. Although multi-head finite automata are a simple concept, their computational behavior can be already very complex and leads to undecidable or even non-semi-decidable problems on these devices such as, for example, emptiness, finiteness, universality, equivalence, etc. These strong negative results trigger the study of subclasses and alternative characterizations of multi-head finite automata for a better understanding of the nature of non-recursive trade-offs and, thus, the borderline between decidable and undecidable problems. In the present paper, we tour a fragment of this literature

Proceedings of JAC 2010. Journées Automates Cellulaires

The second Symposium on Cellular Automata “Journ´ees Automates Cellulaires” (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route Turku–Mariehamn–Turku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku. The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume. The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible. These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast