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

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## Publications (68)

Fungal automata are a variation of the two-dimensional sandpile automaton of Bak, Tang and Wiesenfeld (Phys. Rev. Lett., 1987). In each step toppling cells emit grains only to some of their neighbors chosen according to a specific update sequence. We show how to embed any Boolean circuit into the initial configuration of a fungal automaton with upd...

Fungal automata are a variation of the two-dimensional sandpile automaton of Bak, Tang, and Wiesenfeld (Phys. Rev. Lett. 1987). In each step toppling cells emit grains only to some of their neighbors chosen according to a specific update sequence. We show how to embed any Boolean circuit into the initial configuration of a fungal automaton with upd...

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...

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...

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...

We study the computational capacity of self-verifying iterative arrays (). A self-verifying device is a nondeterministic device whose nondeterminism is symmetric in the following sense. Each computation path can give one of the answers yes, no, or do not know. For every input word, at least one computation path must give either the answer yes or no...

We study the computational capacity of self-verifying cellular automata with an emphasis on one-way information flow (). A self-verifying device is a nondeterministic device where each computation path can give one of the answers yes, no, or do not know. For every input word, at least one computation path must give either the answer yes or no, and...

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.

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.

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...

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...

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...

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...

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.

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...

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...

Glossary Definition of the Subject Introduction Time and Space Complexity Measuring and Controlling the Activities Communication in CA Future Directions Bibliography

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.

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...

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)

These local proceedings hold the papers of two catgeories: (a) Short, non-reviewed papers (b) Full papers

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...

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.

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...

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...

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...

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...

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.

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...

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...

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.

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...

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...

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.

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...

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...

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...

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...

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.

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 ...

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.

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...

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...

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...

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...

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...

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...

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...

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...

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...

Schloss Rauischholzhausen, 28./29.09.1995

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...

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...

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...

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. ...

Reference: Foundations of Reversible Computation

... 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). ...

... 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]. ...

... A straightforward method is to simulate a synchronous CA on an ACA via a mechanism that makes cells run in lockstep on a local scale [21,7,13], but it comes at the expense of a large overhead in cell states and transition rules. Less overhead will ensue by the direct embedding of logic circuits into cell spaces [23,24,12,15,27], but even then there is an increase in the complexities of ACAs. For example, one of Banks' synchronous cellular automata [2] employs 2 cell states and 3 rules to conduct universal computation, whereas an efficient ACA model in [12] with the same (von Neumann) neighborhood as Banks' CA requires 5 cell states and 55 rules. ...

... 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. ...

... 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. ...

Reference: Finite automata with undirected state graphs

... One recent model of self-assembly is Tile Automata [9]. This model marries the concept of state changes from Cellular Automata [21,30,39] and the assembly process from the 2-Handed Assembly model (2HAM) [7]. Previous work [4,8,9] explored Tile Automata as a unifying model for comparing the relative powers of different Tile Assembly models. ...

... 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. ...