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Pcompleteness of cellular automaton Rule 110
 In International Colloquium on Automata Languages and Programming (ICALP), volume 4051 of LNCS
, 2006
"... We show that the problem of predicting t steps of the 1D cellular automaton Rule 110 is Pcomplete. The result is found by showing that Rule 110 simulates deterministic Turing machines in polynomial time. As a corollary we find that the small universal Turing machines of Mathew Cook run in polyn ..."
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Cited by 21 (7 self)
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We show that the problem of predicting t steps of the 1D cellular automaton Rule 110 is Pcomplete. The result is found by showing that Rule 110 simulates deterministic Turing machines in polynomial time. As a corollary we find that the small universal Turing machines of Mathew Cook run in polynomial time, this is an exponential improvement on their previously known simulation time overhead.
On the time complexity of 2tag systems and small universal turing machines
 In 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS
, 2006
"... We show that 2tag systems efficiently simulate Turing machines. As a corollary we find that the small universal Turing machines of Rogozhin, Minsky and others simulate Turing machines in polynomial time. This is an exponential improvement on the previously known simulation time overhead and improve ..."
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Cited by 16 (7 self)
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We show that 2tag systems efficiently simulate Turing machines. As a corollary we find that the small universal Turing machines of Rogozhin, Minsky and others simulate Turing machines in polynomial time. This is an exponential improvement on the previously known simulation time overhead and improves a forty year old result in the area of small universal Turing machines. 1
A small fast universal Turing machine
 Theoretical Computer Science
, 2005
"... We present a small timeefficient universal Turing machine with 5 states and 6 symbols. This Turing machine simulates our new variant of tag system. It is the smallest known universal Turing machine that simulates Turing machine computations in polynomial time. ..."
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Cited by 15 (8 self)
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We present a small timeefficient universal Turing machine with 5 states and 6 symbols. This Turing machine simulates our new variant of tag system. It is the smallest known universal Turing machine that simulates Turing machine computations in polynomial time.
Four Small Universal Turing Machines
, 2009
"... We present universal Turing machines with statesymbol pairs of (5, 5), (6, 4), (9, 3) and (15, 2). These machines simulate our new variant of tag system, the bitag system and are the smallest known singletape universal Turing machines with 5, 4, 3 and 2symbols, respectively. Our 5symbol machin ..."
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Cited by 13 (4 self)
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We present universal Turing machines with statesymbol pairs of (5, 5), (6, 4), (9, 3) and (15, 2). These machines simulate our new variant of tag system, the bitag system and are the smallest known singletape universal Turing machines with 5, 4, 3 and 2symbols, respectively. Our 5symbol machine uses the same number of instructions (22) as the smallest known universal Turing machine by Rogozhin. Also, all of the universal machines we present here simulate Turing machines in polynomial time.
Small semiweakly universal Turing machines
 Machines, Computations and Universality (MCU), volume 4664 of LNCS
, 2007
"... Abstract. We present three small universal Turing machines that have 3 states and 7 symbols, 4 states and 5 symbols, and 2 states and 13 symbols, respectively. These machines are semiweakly universal which means that on one side of the input they have an infinitely repeated word, and on the other s ..."
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Cited by 10 (4 self)
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Abstract. We present three small universal Turing machines that have 3 states and 7 symbols, 4 states and 5 symbols, and 2 states and 13 symbols, respectively. These machines are semiweakly universal which means that on one side of the input they have an infinitely repeated word, and on the other side there is the usual infinitely repeated blank symbol. This work can be regarded as a continuation of early work by Watanabe on semiweak machines. One of our machines has only 17 transition rules, making it the smallest known semiweakly universal Turing machine. Interestingly, two of our machines are symmetric with Watanabe’s 7state and 3symbol, and 5state and 4symbol machines, even though we use a different simulation technique. 1.
Programmability of Chemical Reaction Networks
"... Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a wellstirred solution according to standard c ..."
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Cited by 8 (2 self)
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Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a wellstirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and
Systemic computation: A model of interacting systems with natural characteristics,” International journal of parallel, emergent and distributed systems
, 2007
"... Abstract. Natural systems provide unique examples of computation in a form very different from contemporary computer architectures. Biology also demonstrates capabilities such as adaptation, selfrepair and selforganisation that are becoming increasingly desirable for our technology. To address the ..."
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Cited by 8 (7 self)
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Abstract. Natural systems provide unique examples of computation in a form very different from contemporary computer architectures. Biology also demonstrates capabilities such as adaptation, selfrepair and selforganisation that are becoming increasingly desirable for our technology. To address these issues a new computer model and architecture with natural characteristics is presented. Systemic computation is Turing Complete; it is designed to support biological algorithms such as neural networks, evolutionary algorithms and models of development, and shares the desirable capabilities of biology not found in conventional architectures. Systemic computation may also be implemented using natural systems, enabling the potential for future computational analysis and control of biology.
Small weakly universal Turing machines
"... Abstract. We give small universal Turing machines with statesymbol pairs of (6, 2), (3,3) and (2,4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest ..."
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Cited by 7 (4 self)
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Abstract. We give small universal Turing machines with statesymbol pairs of (6, 2), (3,3) and (2,4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest known weakly universal Turing machines. Despite their small size these machines are efficient polynomial time simulators of Turing machines. 1
The role of redundancy in the robustness of random boolean networks
 In Artificial Life X, Proceedings of the Tenth International Conference on the Simulation and Synthesis of
, 2006
"... Evolution depends on the possibility of successfully exploring fitness landscapes via mutation and recombination. With these search procedures, exploration is difficult in ”rugged” fitness landscapes, where small mutations can drastically change functionalities in an organism. Random Boolean network ..."
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Cited by 6 (3 self)
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Evolution depends on the possibility of successfully exploring fitness landscapes via mutation and recombination. With these search procedures, exploration is difficult in ”rugged” fitness landscapes, where small mutations can drastically change functionalities in an organism. Random Boolean networks (RBNs), being general models, can be used to explore theories of how evolution can take place in rugged landscapes; or even change the landscapes. In this paper, we study the effect that redundant nodes have on the robustness of RBNs. Using computer simulations, we have found that the addition of redundant nodes to RBNs increases their robustness. We conjecture that redundancy is a way of ”smoothing ” fitness landscapes. Therefore, redundancy can facilitate evolutionary searches. However, too much robustness could reduce the rate of adaptation of an evolutionary process.
2008): A particular universal cellular automaton
"... Signals are a classical tool used in cellular automata constructions that proved to be useful for language recognition or firingsquad synchronisation. Particles and collisions formalize this idea one step further, describing regular nets of colliding signals. In the present paper, we investigate th ..."
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Cited by 6 (1 self)
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Signals are a classical tool used in cellular automata constructions that proved to be useful for language recognition or firingsquad synchronisation. Particles and collisions formalize this idea one step further, describing regular nets of colliding signals. In the present paper, we investigate the use of particles and collisions for constructions involving an infinite number of interacting particles. We obtain a highlevel construction for a new smallest intrinsically universal cellular automaton with 4 states.