# Thomas Worsch's research while affiliated with Karlsruhe Institute of Technology and other places

## Publications (74)

Article
Full-text available
In cellular automata with multiple speeds for each cell i there is a positive integer $$p_i$$ p i such that this cell updates its state still periodically but only at times which are a multiple of $$p_i$$ p i . Additionally there is a finite upper bound on all $$p_i$$ p i . Manzoni and Umeo have described an algorithm for these (one-dimensional) ce...
Article
Full-text available
We study the problem of sequentializing a cellular automaton without introducing any intermediate states, and only performing reversible permutations on the tape. We give a decidable characterization of cellular automata which can be written as a single sweep of a bijective rule from left to right over an infinite tape. Such cellular automata are n...
Preprint
In cellular automata with multiple speeds for each cell $i$ there is a positive integer $p_i$ such that this cell updates its state still periodically but only at times which are a multiple of $p_i$. Additionally there is a finite upper bound on all $p_i$. Manzoni and Umeo have described an algorithm for these (one-dimensional) cellular automata wh...
Article
Full-text available
We study the problem of sequentializing a cellular automaton without introducing any intermediate states, and only performing reversible permutations on the tape. We give a decidable characterization of cellular automata which can be written as a single left-to-right sweep of a bijective rule from left to right over an infinite tape.
Conference Paper
Inspired by shrinking cellular automata (SCA), we investigate another variant of the classical one-dimensional cellular automaton: the shrinking and expanding cellular automaton (SXCA). In addition to the capability to delete some cells as in SCA, an SXCA can also create new cells between already existing ones. It is shown that there are reasonably...
Article
Full-text available
This special issue contains a selection of papers presented at the “Third In- ternational Workshop on Asynchronous Cellular Automata and Asynchronous Discrete Models” (ACA 2014), held as a satellite workshop of the 11th Inter- national Conference on Cellular Automata for Research and Industry (ACRI 2014) in Krakow (Poland) in September 2014. Six pa...
Conference Paper
The notion of k-reversibility is generalized to pushdown automata. A pushdown automaton is said to be (k,l)-reversible if its predecessor configurations can uniquely be computed by a pushdown automaton with input lookahead of size k and stack lookahead of size l. It turns out that there are problems which can be solved by (k+1,1)-reversible pushdow...
Article
We consider asynchronous one-dimensional cellular automata (CA). It is shown that there is one with von Neumann neighborhood of radius 1 which can simulate each asynchronous one-dimensional cellular automaton. Analogous constructions are described for α-asynchronous CA (where each cell independently enters a new state with probability α, and for “n...
Conference Paper
We review a few constructions for different types of simulations between asynchronous cellular automata in order to carve out properties which may be relevant for a better understanding of the notion of "simulation" for asynchronous cellular automata. We restrict the discussion to the case where no probabilities for state transitions are involved.
Conference Paper
Reversible computational models with discrete internal states are said to be time-symmetric, if they can go back and forth in time by applying the same transition function. The direction in time is adjusted by a weak transformation of the phase-space, that is, an involution. So, these machines themselves cannot distinguish whether they run forward...
Article
While for synchronous deterministic cellular automata there is an accepted definition of reversibility, this is not the case for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call phase space invertible asynchronous cellular automata. We will show that for each Turing machine there is a phase spac...
Article
Glossary Definition of the Subject Introduction Time and Space Complexity Measuring and Controlling the Activities Communication in CA Future Directions Bibliography
Conference Paper
Full-text available
We show the construction of a rotation- and reflection-invariant local function for a two-dimensional asynchronous cellular automaton with only 3 states and radius 1 Moore neighborhood in which one can implement arbitrary delay-insensitive circuits.
Article
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...
Article
A new fast (real time) sorter of binary numbers by one-dimensional cellular automata is proposed. It sorts a list of n numbers represented by k-bits each in exactly nk steps. This is only one step more than a lower bound. Comment: Journ\'ees Automates Cellulaires 2010, Turku : Finland (2010)
Article
Full-text available
These local proceedings hold the papers of two catgeories: (a) Short, non-reviewed papers (b) Full papers
Article
Abstrad From the definition of a cellular automaton $(S, Q, f, \nu)$ with $S$ a discrete cellular space, $Q$ a finite set of cell states, $f$ an n-ary local function $f(x_{1}, \ldots, x_{n})$ and $\nu$ a neighborhood function $\nu$ : $\{1, \ldots, n\}arrow S$, we pIck up a pair $(f, \nu)$ called the local structure. Introducing the local structure...
Article
We show how an infinite number of CA with different local rules can be simulated by CA using the same local rule by just changing the shape of the neighborhood. In that way one can even achieve universality.
Article
SKaMPI-5 is a micro-benchmark for MPI implementations, designed to be easily extensible. Besides a “global” parallel file system at least some parallel machines offer (many) hard disks which are local to (processors or) computing nodes. While the MPI2 standard includes functions for doing disk IO, MPI is unable to use this resource because by (our...
Conference Paper
This paper consists of two parts. In the first we pick up again the question under which circumstances different pairs of a local function and a neighborhood give rise to the same global behavior of CA and disprove a conjecture made in an earlier paper. In the second part we reconsider a construction showing that one can achieve universality by onl...
Conference Paper
We consider one-dimensional cellular automata which are extended by dynamically reconfigurable buses (RCA). It is shown that up to a constant factor it does not matter whether bus segments are directed or not. For both variants of the model their time complexity can be characterized in terms of the reversal complexity of one-tape TM. The comparison...
Chapter
SKaMPI is now an established benchmark for MPI implementations. The development of SKaMPI-5 strives for improvements in several directions: (i) extension of the benchmark to cover more functionality of MPI, (ii) construction of a collection of collective algorithm kernels which are not supported by core MPI collective operations. (iii) a redesign o...
Conference Paper
We show how an arbitrary finite number of CA with different local rules can be simulated by CA using the same local rule by just changing the (shape of the) neighborhood. In that way one can even achieve universality.
Chapter
SKaMPI is now an established benchmark for MPI implementations. Two important goals of the development of version 5 of SKaMPI were the extension of the benchmark to cover more functionality of MPI, and a redesign of the benchmark llowing it to be extended more easily (thus matching requests from SKaMPI users). In the present paper we give an overvi...
Conference Paper
SKaMPI is now an established benchmark for MPI implementations. Two important goals of the development of version 5 of SKaMPI were the extension of the benchmark to cover more functionality of MPI, and a redesign of the benchmark allowing it to be extended more easily. In the present paper we give an overview of the extension of SKaMPI 5 for the ev...
Conference Paper
Motivated by the wish to make large simulations of Bak’s sandpile model we investigate a simple method to simulate cellular automata with “few activities” efficiently on a computer.
Article
The Firing Squad Synchronization Problem is one of the classical problems for cellular automata. In this paper we consider the case of more than one general. A synchronous and an asynchronous version of the problem are considered. In the latter case the generals may start their activities at different times. In the synchronous case there are optimu...
Article
In this paper we consider cellular automata where the graph defined by the neighbourhood relations between the cells is a tree "with additional edges". This includes hyperbolic CA defined by regular tessellations of the two-dimensional hyperbolic plane. It is shown that all X-tree CA and all hyperbolic CA can C-simulate each other with constant slo...
Conference Paper
SKaMPI is a benchmark for measuring the performance of MPI implementations. Some examples of surprising behaviour of MPI libraries are presented. These result in certain new requirements for MPI benchmarks and will lead to major extensions in the new SKaMPI-Bench.
Chapter
SKaMPI is now an established benchmark for MPI implementations. In autumn 2002 the development of the “new SKaMPI” has started in three major directions: (i) extension of the benchmark to cover more functions of MPI and a redesign of the benchmark allowing it to be extended more easily (thus matching requests from SKaMPI users); (ii) construction o...
Article
This article concentrates on recent work on benchmarking collective operations with SKaMPI. The goal of the SKaMPI project is the creation of a database containing performance measurements of parallel computers in terms of MPI operations. Its data support software developers in creating portable and fast programs. Existing algorithms for measuring...
Conference Paper
This article concentrates on recent work on benchmarking collective operations with SKaMPI. The goal of the SKaMPI project is the creation of a database containing performance measurements of parallel computers in terms of MPI operations. These data support software developers in creating portable and fast programs. Existing algorithms for measurin...
Article
Using cellular automata as models of parallel machines we investigate constraints for the energy consumption of r-dimensional machines which are motivated by physical limitations for the case r = 3. Depending on the operations which must be considered to dissipate energy, some relations between the relative performance of 2-dimensional and 3-dimens...
Article
Cellular automata for the election of a leader in arbitrary d-dimensional patterns are presented which are significantly faster than the previously best known. The time needed is reduced from Θ(diam2) to , where diam denotes the diameter of the pattern.
Article
Full-text available
A necessary and sufficient condition for a one-dimensional q-state n-input cellular automaton rule to be number-conserving is established. Two different forms of simpler and more visual representations of these rules are given, and their ...
Article
We present a CA for the queen bee problem (QBP) as originally posed by Smith, which is the problem of electing a (unique) leader in arbitrary two-dimensional connected patterns. The running time is proportional to the perimeter of the pattern.
Book
This book contains all full papers presented at ACRI 2000, the Fourth International Conference on Cellular Automata for Research and Industry, held at the University of Karlsruhe (Germany), 4 - 6 October, 2000. The continuation of and growing interest in research on Cellular Automata models for real world phenomena indicates the feasibility of this...
Article
There exists quite a number of software packages for the simulation of cellular automata (CA). After a short review of the standard definition some modifications and extensions are discussed which have in particular proven to be useful or important for the use of CA as models of real phenomena. A survey of the features of several software packages...
Conference Paper
It is well-known that for classical one-dimensional one-way CA (OCA) it is possible to speed up language recognition times from (1 + r)n, r ∈ R + , to (1 + r/2)n. In this paper we show that this no longer holds for OCA in which a cell can comminucate only one bit (or more generally a fixed amount) of information to its neighbor in each step. For ar...
Article
Some modifications and generalizations of cellular automata are discussed which are sometimes useful in the modeling of real phenomenaand which therefore have found their ways into some programming environment for cellular automata. In the second part several aspects are discussed with respect to which these programming environments can be compared...
Article
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" used. In this paper Ptm are investigated with respect to their power as recognizers of formal languages. A combinatorial approach as well as dia...
Article
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 ch...
Article
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 witho...
Article
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...
Article
Apparently there is no closed form for the partial sum of a row of Pascal's triangle. In this paper lower and upper bounds for binomial coefficients and their sums are deduced. In the case of single coefficients these bounds differ only by a constant factor which is arbitrarily close to 1 for sufficiently large n. In the case of sums the gap betwee...
Article
Schloss Rauischholzhausen, 28./29.09.1995
Chapter
Die tayloristische Betrachtung von Arbeitsvorgängen führte dazu, in Fabriken zur Fließbandproduktion überzugehen. Im Zusammenhang mit der Diskussion über die Humanisierung der Arbeitswelt wird dieser Ansatz inzwischen in Frage gestellt: Die zu weit gehende Spezialisierung der Menschen und die Erfordernisse einer gleichbleibenden Aufmerksamkeit und...
Chapter
Der Vorschlag, Zellularräume zu betrachten, geht auf S. Ulam und J. von Neumann zurück. Von Neumann führte sie ein als Beispiel für ein Modell, in dem man sich selbst reproduzierende Strukturen realisieren kann. Veröffentlicht wurden diese Arbeiten erst nach seinem Tod von A. W. Burks in [Neu66].
Chapter
In diesem Kapitel werden wir uns mit SIMD-Rechnern beschäftigen. Es ist klar, daß hier keine umfassende Einführung in diesen Teil der Rechnerarchitektur gegeben werden kann. Wenn Sie ein weitergehendes Interesse an diesem Thema haben, mögen Sie hierzu die einschlägigen Bücher etwa von Giloi [Gil81], Hockney und Jesshope [HoJ88], Hwang und Briggs [H...
Chapter
Dieses Kapitel besteht aus drei Abschnitten. Im ersten werden Schaltkreise und (allgemeine) Schaltkreisfamilien eingeführt. Da sich aber zeigt, daß sie kein angemessenes Modell für Berechenbarkeit darstellen, werden wir im zweiten Abschnitt auf uniforme Schaltkreisfamilien zu sprechen kommen. Ihrem Vergleich mit sequentiellen Turingmaschinen ist da...
Chapter
“The next generation of supercomputers will be massively parallel, distributed memory MIMD architectures with thousands or ten thousands of nodes. User acceptance demands that such systems should be programmable in an appropriate, easy-to-use, application-oriented style which, nevertheless, ensures the highest possible program efficiency. The curre...
Chapter
In den ersten beiden Abschnitten werden Systeme von Turing-Automaten eingeführt und ihre Arbeit als Spracherkenner wird demonstriert. Anschließend vergleichen wir sie mit Turingmaschinen und Zellularräumen. Dabei wird sich zeigen, daß die neuen Automaten insofern die Lücke zwischen den beiden bekannten Modellen füllen, als man bei ihnen den „Grad d...
Chapter
Dieses Kapitel verlangt zunächst eine Erklärung zur Namensgebung: Nach [Qui88] ist ein Vektorrechner ein Computer mit einer Befehlsmenge, die sowohl Operationen mit Vektoren als auch mit Skalaren zuläßt. Danach gibt es zwei Wege zur Konstruktion solcher Rechner, nämlich den des arrayförmigen Aufbaus, in dem dann jedes Vektorelement von einem eigene...
Chapter
Das älteste berechnungsuniverselle Automatenmodell ist wohl die von Alan Turing 1936 in seinem Aufsatz „On computable numbers, with an application to the Entscheidungsproblem“ eingeführte und mittlerweile nach ihm benannte Maschine [Tur36]. Heute gibt es eine ganze Reihe von Modellen, die Turingmaschinen heißen, und die gegebenenfalls durch vorange...
Chapter
Wir haben inzwischen mehrere Modelle kennengelernt: Ein-Kopf-Turingmaschi-nen, Mehr-Kopf-Turingmaschinen, Systeme von Turing-Automaten, Zellularräume, parallele Registermaschinen (Crew-Prams und Nlprams), uniforme Schaltkreisfamilien und systolische Trellisautomaten. Es gibt eine Vielzahl weiterer Modelle (siehe Literaturliste). Im ersten Abschnitt...
Chapter
In den ersten drei Kapiteln haben wir uns mit Modellen beschäftigt, die eine wichtige Gemeinsamkeit haben. Jedes von ihnen kann die beiden anderen zumindest so effizient simulieren, daß der zusätzliche Zeitbedarf bei der Erkennung einer formalen Sprache polynomial beschränkt werden kann und der zusätzliche Platzbedarf sogar linear. Das werden wir f...
Article
We study the computational power of global bus systems (GB, for short) augmented with a mesh-connected computer (MCC, for short). First we show that the GB is a useful tool for designing optimum-time parallel algorithms for MCCs and for showing correctness of those algorithms once designed. We do this by giving some design examples which utilize th...
Conference Paper
The authors study the effects of broadcasting bus systems augmented with a mesh-connected computer. They develop a direct-proof technique for the elimination of broadcasting buses. As an application of the technique, they show that a rich variety of broadcasting bus systems on one- and two-dimensional arrays can be eliminated without any loss of ti...
Article
For the 1998 conference on Mathematical Foundations of Computer Science (MFCS'98) four papers on Cellular Automata were accepted as regular MFCS'98 contributions. Furthermore an MFCS'98 satellite workshop on Cellular Automata was organized with ten additional talks. The embedding of the workshop into the conference with its participants coming from...
Article
For the set of cellular automata $CA=(\mathbb{Z}^{d}, Q, f, \nu)$ with local function $f$ : $Q^{n}arrow Q$ and neighbor-hood $\nu$ of size $n$ , we define an automorphism which naturally induces a classification of CA: Two CA $A$ and $B$ are called automorphic, if and only if there is a pair of permutations $(\pi, \varphi)$ of $\nu$ and $Q$ , respe...

## Citations

... In the one-dimensional setting, one possibility is that states are updated sequentially during a left-to-right (or right-toleft) sweep across the entire infinite line of cells. Such a setup is studied in [93] where the update performed once in each position is given by a reversible block rule A n −→ A n on n consecutive cells. The authors give a precise characterisation of the one-dimensional cellular automata that can be realised by such a sweep. ...
... Combining them yields the shrinking and expanding CA (SXCA). The polynomial-time class of SXCA language deciders was shown to coincide with PSPACE (Modanese 2016; Modanese and Worsch 2016). ...
Citing conference paper
... They are useful when trying to diagnose application performance issues as they often report the average time for MPI operations. SKaMPI is no longer under active development but was extended to cater for complex communication patterns [15]. ...
... Similarly, in another work [204], Lee et al. have studied delay-insensitivity in ACAs. Recently, Schneider et al. have implemented an arbitrary delayinsensitive circuits using a two-dimensional ACAs with only 3-states and radius 1 Moore neighborhood [205]. Number conservation property in ACAs was first studied by Hazari et al. in [86]. ...
... Hence, the automaton is (k + 1)-reversible. As shown in [8,Theorem 4] we cannot do better for this language, i.e., L ∈ REV k+1 \ REV k . This can be also obtained as a consequence of results in Section 5. ...
Citing conference paper
... In the case where one is allowed to choose freely the order of update of the cells, it was shown that there are some rules which allow one to return to the initial condition and some that do not always allow this [DSS12,SMD12]. With a different perspective, Worsch and Wacker examined how to construct an "inverse" rule, in the sense that its transition graph would be the "inverse" of the transition graph of the original inverse [WW13]. The design of asynchronous circuits with reversible gates is also a current important topic of research (see e.g. ...
... This benchmarking approach is fundamentally different from above, but can lead to important outcomes that contribute to better application communication performance. The Special Karlsruhe MPI benchmark (SKaMPI) was created to benchmark MPI communications for supercomputer users and system administrators who want to tune their MPI libraries [12], evaluate and chose algorithms for collective communications [25,26], and ensure performance portability of the MPI library across platforms [17]. ...
... These automata can be seen as finite automata whose state graphs are undirected. So, this notion is even stronger than the concept of time-symmetry studied in [3,11]. Time-symmetry appears in physics when a system can go back in time by applying the same transition function as for forward computations after a weak transformation of the phase-space. ...
Citing conference paper
... Cellular Automata has been shown to be Turing Universal even in one dimension (Cook 2004). Other stronger results have been shown proving intrinsic universality of many versions of Cellular Automata (Goles et al. 2011;Worsch 2013). The Tile Automata model was introduced in Chalk et al. (2018a) merging ideas from Cellular Automata and Tile Self-Assembly. ...
... Cellular automata (CA) are mathematical discrete structures that are defined by an array of cells, each having a state that evolves in time. They were first introduced by Stanislaw Ulam et al in the 1940s [1], but much later in the 1980s was when they were studied deeply [2,4] in terms of their computational power, data parallelism, thermodynamics etc. Cellular automata have been a recent area of interest in research in the field of theory of computation [8,9,10,11,12,13], cryptography [3,14], traffic flow theory [5], parallel computation [5,6,7] and many more. Certain classes of CA have been known to be generating pseudorandom patterns [2,3,4] and as a specific example, the class 4 one dimensional CA [4] have known to generate spatio-temporally local patterns that interact in complex ways and survive for a long time. ...