Phase Space Invertible Asynchronous Cellular Automata

While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call phase space invertible asynchronous cellular automata in more detail. We will show that for each Turing machine there is such a cellular automaton simulating it, and that it is decidable whether an asynchronous cellular automaton has this property or not, even in higher dimensions.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

On parallel Turing machines with multi-head control units

This paper deals with parallel Turing machines with multi-head control units on one or more tapes which can be considered as a generalization of cellular automata. We discuss the problem of finding an appropriate measure of space complexity. A definition is suggested which implies that the model is in the first machine class. It is shown that without loss of generality it suffices to consider only parallel Turing machines of certain normal forms

Simulations between alternating CA, alternating TM and circuit families

Variants of cellular automata consisting of alternating instead of deterministic finite automata are investigated, so-called uniform alternating CA (ACA) and two types of nonuniform ACA. The former two have been considered by Matamala (1997). It is shown that the nonuniform ACA are time equivalent. The main contributions are fast simulations of ACA by uniform circuit families and vice versa. It is shown that nonuniform ACA are time equivalent to circuit families with unbounded fan-in, and that uniform ACA are time equivalent to circuit families with constant fan-in. Hence uniform ACA and alternating TM are time equivalent, too, solving a problem left open by Matamala. The results also give some evidence that a linear time simulation of nonuniform ACA by ATM is ``unlikely\u27\u27 to exist

MFCS\u2798 Satellite Workshop on Cellular Automata

For the 1998 conference on Mathematical Foundations of Computer Science (MFCS\u2798) four papers on Cellular Automata were accepted as regular MFCS\u2798 contributions. Furthermore an MFCS\u2798 satellite workshop on Cellular Automata was organized with ten additional talks. The embedding of the workshop into the conference with its participants coming from a broad spectrum of fields of work lead to interesting discussions and a fruitful exchange of ideas. The contributions which had been accepted for MFCS\u2798 itself may be found in the conference proceedings, edited by L. Brim, J. Gruska and J. Zlatuska, Springer LNCS 1450. All other (invited and regular) papers of the workshop are contained in this technical report. (One paper, for which no postscript file of the full paper is available, is only included in the printed version of the report). Contents: F. Blanchard, E. Formenti, P. Kurka: Cellular automata in the Cantor, Besicovitch and Weyl Spaces K. Kobayashi: On Time Optimal Solutions of the Two-Dimensional Firing Squad Synchronization Problem L. Margara: Topological Mixing and Denseness of Periodic Orbits for Linear Cellular Automata over Z_m B. Martin: A Geometrical Hierarchy of Graph via Cellular Automata K. Morita, K. Imai: Number-Conserving Reversible Cellular Automata and Their Computation-Universality C. Nichitiu, E. Remila: Simulations of graph automata K. Svozil: Is the world a machine? H. Umeo: Cellular Algorithms with 1-bit Inter-Cell Communications F. Reischle, Th. Worsch: Simulations between alternating CA, alternating TM and circuit families K. Sutner: Computation Theory of Cellular Automat

Feasible models of computation: three- dimensionality and energy consumption

Using cellular automata as models of parallel machines we investigate the relation between (r-1)- and r-dimensional machines and constraints for the energy consumption of r-dimensional machines which are motivated by fundamental physical limitations for the case r=3. Depending on the operations which must be considered to dissipate energy (state changes, communication over unit-length wires, ...), some relations between the relative performance of 2-dimensional and 3-dimensional machines are derived. In the light of these results it seems imperative that for feasible models of computation energy consumption has to be considered as an additional complexity measure

Parallel turing machines with one-head control units and cellular automata

Parallel Turing machines (PTM) can be viewed as a generalization of cellular automata (CA) where an additional measure called processor complexity can be defined which indicates the ``amount of parallelism\u27\u27 used. In this paper PTM are investigated with respect to their power as recognizers of formal languages. A combinatorial approach as well as diagonalization are used to obtain hierarchies of complexity classes for PTM and CA. In some cases it is possible to keep the space complexity of PTM fixed. Thus for the first time it is possible to find hierarchies of complexity classes (though not CA classes) which are completely contained in the class of languages recognizable by CA with space complexity n and in polynomial time. A possible collapse of the time hierarchy for these CA would therefore also imply some unexpected properties of PTM

On relations between arrays of processing elements of different dimensionality

We are examining the power of $d$-dimensional arrays of processing elements in view of a special kind of structural complexity. In particular simulation techniques are shown, which allow to reduce the dimension at an increased cost of time only. Conversely, it is not possible to regain the speed by increasing the dimension. Moreover, we demonstrate that increasing the computation time (just by a constant factor) can have a more favorable effect than increasing the dimension (arbitrari