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Programming Environments for Cellular Automata
 Mauri (Eds.), Cellular Automata for Research and Industry (ACRI 96
, 1997
"... In the first part some modifications and generalizations of cellular automata are discussed which are sometimes useful in the modeling of real phenomena and which therefore have found their ways into one or more programming environment for cellular automata. In the second part several aspects are ..."
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In the first part some modifications and generalizations of cellular automata are discussed which are sometimes useful in the modeling of real phenomena and which therefore have found their ways into one or more programming environment for cellular automata. In the second part several aspects are discussed with respect to which these programming environments can be compared. In the third part this is done for a number of available software packages. 1 Introduction This technical report is the long version of a paper (Worsch, 1996) presented at the Second Conference on CA in Research and Industry, ACRI 96. 1.1 Why CA simulations? It is reasonable to use computers whenever computations have to be done and the number and/or the complexity of the operations involved exceeds what can reasonably be done by a human. It is not reasonable to use the results of a few mechanical computations as a replacement for theoretical arguments, but sometimes computer simulations can give some hints...
Computational Complexity of an Optical Model of Computation
, 2005
"... We investigate the computational complexity of an optically inspired model of computation. The model is called the continuous space machine and operates in discrete timesteps over a number of twodimensional complexvalued images of constant size and arbitrary spatial resolution. We define a number ..."
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We investigate the computational complexity of an optically inspired model of computation. The model is called the continuous space machine and operates in discrete timesteps over a number of twodimensional complexvalued images of constant size and arbitrary spatial resolution. We define a number of optically inspired complexity measures and data representations for the model. We show the growth of each complexity measure under each of the model's operations. We characterise the power of an important discrete restriction of the model. Parallel time on this variant of the model is shown to correspond, within a polynomial, to sequential space on Turing machines, thus verifying the parallel computation thesis. We also give a characterisation of the class NC. As a result the model has computational power equivalent to that of many wellknown parallel models. These characterisations give a method to translate parallel algorithms to optical algorithms and facilitate the application of the complexity theory toolbox to optical computers. Finally we show that another variation on the model is very powerful;
On parallel Turing machines with multihead control units
 Parallel Computing
, 1996
"... This paper deals with parallel Turing machines with multihead 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 ..."
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This paper deals with parallel Turing machines with multihead 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. 1 Introduction Hemmerling (1979) was probably the first to consider a model where several finite automata are working cooperatively on one common tape. It is known that this model can simulate cellular automata and vice versa in linear time and linear space simultaneously. Wiedermann (1984) considered these finite automata as TM control units and generalized the model to socalled Parallel Turing Machines (PTM) in the same way as onetape onehead Turing machines have been generalized to Turing machines with possibly several tapes and severa...
A Paraconsistent Approach to Quantum Computing
, 2008
"... We propose a method to define axiomatic theories for deterministic Turing machine computations. This method, when applied to axiomatizing computations in nondeterministic Turing machines, produces (in some cases) contradictory theories, therefore trivial theories (considering classical logic as the ..."
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We propose a method to define axiomatic theories for deterministic Turing machine computations. This method, when applied to axiomatizing computations in nondeterministic Turing machines, produces (in some cases) contradictory theories, therefore trivial theories (considering classical logic as the underlying logic). Substituting in such theories the underlying logic by the paraconsistent logic LFI1 ∗ permits us to define a new model of computation which we call paraconsistent Turing machine. We show that this initial model of computation allows the simulation of important quantum computing features. In particular, it allows to simulate the quantum solution of the wellknown Deutsch’s and DeutschJozsa problems. However, we show that this initial model of computation does not adequately represent the notion of entangled states, a key feature in quantum computing. In this way, the construction is refined by defining a paraconsistent logic with a connective expressing entangled states in a logical fashion, and this logic is used to define a more sharpened model of paraconsistent Turing machines, better approaching the quantum computing features. Finally, we define complexity classes for the models introduced and establish some surprising relationships with classical complexity classes.
Cellular Automata Workshop 1996
"... We study the evolution of an empty linear sand pile system which receives a sand grain in its first pile each time. We encode it with another cellular automata, the Chip Firing Game. Geometrical observations lead to a signal encoding of configurations. The interactions of signals are studied. Config ..."
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We study the evolution of an empty linear sand pile system which receives a sand grain in its first pile each time. We encode it with another cellular automata, the Chip Firing Game. Geometrical observations lead to a signal encoding of configurations. The interactions of signals are studied. Configurations are divided in two parts of slopes 1 and 2. We make asymptotic approximations of various parameters defining the configurations. Especially, we find that the configurations are expanding regularly in terms of the square root of the number of fallen grains and the ratio of the width of the two parts of the configurations is p 2. Sand Piles Model (spm) and Chip Firing Games (cfg) are very simple systems based on local interactions which conserve the total number of grains. In spm, a grain moves to a neighbor site if the number of grains in the two piles differs by more than a given threshold, whereas in cfg a site gives a chip to each of its neighbors if its number of chips is abov...
Proc. CS&P '06 Concurrent Turing Machines as Rewrite Theories
"... Abstract. We define Concurrent Turing Machines (CTMs) as Turing machines with Petri nets as finite control. This leads to machines with arbitrary many tape heads, thus subsuming any class of (constant) khead Turing machines. Concurrent Turing machines correspond to a class of multiset rewriting syst ..."
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Abstract. We define Concurrent Turing Machines (CTMs) as Turing machines with Petri nets as finite control. This leads to machines with arbitrary many tape heads, thus subsuming any class of (constant) khead Turing machines. Concurrent Turing machines correspond to a class of multiset rewriting systems. The definition of a CTMs as a rewrite theory avoids the need for encoding multisets as words and using an equivalence relation on configurations. Multiset rewriting lends itself to be used in rewriting systems and tools like the rewriting engine Maude. For the rewriting system, a configuration is given by a varying sequence of strings and multisets. 1
Parallel Turing Machines With OneHead Control Units And Cellular Automata
, 1997
"... 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 ..."
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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 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. Key words: cellular automata, parallel Turing machines, computational complexity, theory of parallel computation 1 Introduction Since their introdu...