Results 1  10
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18
From cells to computers: Computing with membranes (P systems
 Biosystems
, 2001
"... The aim of this paper is to introduce to the reader the main ideas of computing with membranes, a recent branch of (theoretical) molecular computing. In short, in a celllike system, multisets of objects evolve according to given rules in the compartments defined by a membrane structure and compute ..."
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Cited by 24 (0 self)
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The aim of this paper is to introduce to the reader the main ideas of computing with membranes, a recent branch of (theoretical) molecular computing. In short, in a celllike system, multisets of objects evolve according to given rules in the compartments defined by a membrane structure and compute natural numbers as the result of halting sequences of transitions. The model is parallel, nondeterministic. Many variants have already been considered and many problems about them were investigated. We present here some of these variants, focusing on two central classes of results: (1) characterizations of the recursively enumerable sets of numbers and (2) possibilities to solve NPcomplete problems in polynomial — even linear — time (of course, by making use of an exponential space). The results are given without proofs. An almost complete bibliography of the domain, at the middle of October 2000, is
Transcending the Limits of Turing Computability
, 1998
"... Hypercomputation or superTuring computation is a “computation ” that transcends the limit imposed by Turing’s model of computability. The field still faces some basic questions, technical (can we mathematically and/or physically build a hypercomputer?), cognitive (can hypercomputers realize the AI ..."
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Cited by 18 (7 self)
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Hypercomputation or superTuring computation is a “computation ” that transcends the limit imposed by Turing’s model of computability. The field still faces some basic questions, technical (can we mathematically and/or physically build a hypercomputer?), cognitive (can hypercomputers realize the AI dream?), philosophical (is thinking more than computing?). The aim of this paper is to address the question: can we mathematically build a hypercomputer? We will discuss the solutions of the Infinite Merchant Problem, a decision problem equivalent to the Halting Problem, based on results obtained in [9, 2]. The accent will be on the new computational technique and results rather than formal proofs. 1
On properties of bondfree DNA languages
, 2005
"... The input data for DNA computing must be encoded into the form of single or double DNA strands. As complementary parts of single strands can bind together forming a doublestranded DNA sequence, one has to impose restrictions on these sets of DNA words (languages) to prevent them from interacting in ..."
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Cited by 9 (4 self)
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The input data for DNA computing must be encoded into the form of single or double DNA strands. As complementary parts of single strands can bind together forming a doublestranded DNA sequence, one has to impose restrictions on these sets of DNA words (languages) to prevent them from interacting in undesirable ways. We recall a list of known properties of DNA languages which are free of certain types of undesirable bonds. Then we introduce a general framework in which we can characterize each of these properties by a solution of a uniform formal language inequation. This characterization allows us among others to construct (i) a uniform algorithm deciding in polynomial time whether a given DNA language possesses any of the studied properties, and (ii) in many cases also an algorithm deciding whether a given DNA language is maximal with respect to the desired property.
A glimpse into natural computing
 J. Multi Valued Logic
, 1999
"... Abstract. We consider as pertaining to Natural Computing (in some sense, characterizing it) the following five domains: Neural Networks, Genetic Algorithms, ..."
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Abstract. We consider as pertaining to Natural Computing (in some sense, characterizing it) the following five domains: Neural Networks, Genetic Algorithms,
Sai shankar and Sunghyun Choi. “QoS Siganling for Parameterized Traffic
 in IEEE 802.11e Wireless LANs”. In AISA 2002
, 2002
"... Summary. Purely catalytic P systems can generate all recursively enumerable sets of natural numbers with only three catalysts in one membrane, whereas we know that one catalyst in one membrane is not enough. On the other hand, P systems also allowing (noncatalytic) noncooperative evolution rules w ..."
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Summary. Purely catalytic P systems can generate all recursively enumerable sets of natural numbers with only three catalysts in one membrane, whereas we know that one catalyst in one membrane is not enough. On the other hand, P systems also allowing (noncatalytic) noncooperative evolution rules with only two catalysts in one membrane are already computationally complete, too. We here investigate special variants of P systems with only one catalyst in one membrane that are not computationally complete, i.e., variants of P systems with only one catalyst in one membrane that cannot generate all recursively enumerable sets of natural numbers. 1
Small Universal Antiport P Systems and Universal Multiset Grammars
"... Summary. Based on the construction of a universal register machine (see [7]) we construct a universal antiport P system working with 31 rules in the maximally parallel mode in one membrane, and a universal antiport P system with forbidden context working with 16 rules in the sequential derivation mo ..."
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Summary. Based on the construction of a universal register machine (see [7]) we construct a universal antiport P system working with 31 rules in the maximally parallel mode in one membrane, and a universal antiport P system with forbidden context working with 16 rules in the sequential derivation mode in one membrane for computing any partial recursive function on the set of natural numbers. For accepting/generating any arbitrary recursively enumerable set of natural numbers we need 31/33 and 16/18 rules, respectively. As a consequence of the result for antiport P systems with forbidden context we immediately infer similar results for forbidden random context multiset grammars with arbitrary rules. 1
W. Shakespeare, Macbeth, I, 3. Coins, Quantum Measurements, and
, 2008
"... If you can look into the seeds of time, ..."
Quantum Principles and Mathematical Computability
, 2008
"... Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then outline a quantum mechanical “algorithm” for one of the insoluble ..."
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Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then outline a quantum mechanical “algorithm” for one of the insoluble problems of mathematics, the Hilbert’s tenth and equivalently the Turing halting problem. The key element of this algorithm is the computability and measurability of both the values of physical observables and of the quantummechanical probability distributions for these values. The fact is that quantum computers can prove theorems by methods that neither a human brain nor any other Turingcomputational arbiter will ever be able to reproduce. What if a quantum algorithm delivered a theorem that it was infeasible to prove classically. No such algorithm is yet known, but nor is anything known to rule out such a possibility, and this raises a question of principle: should we still accept such a theorem as undoubtedly proved? We believe that the rational answer ot this question is yes, for our confidence in quantum proofs rests upon the same foundation as our confidence in classical proofs: our acceptance of the physical laws underlying the computing operations. D. Deustch, A. Ekert and R. Lupacchini [1] 1
BioSystems 77 (2004) 175–194 Biosteps beyond Turing
, 2004
"... Are there ‘biologically computing agents ’ capable to compute Turing uncomputable functions? It is perhaps tempting to dismiss this question with a negative answer. Quite the opposite, for the first time in the literature on molecular computing we contend that the answer is not theoretically negativ ..."
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Are there ‘biologically computing agents ’ capable to compute Turing uncomputable functions? It is perhaps tempting to dismiss this question with a negative answer. Quite the opposite, for the first time in the literature on molecular computing we contend that the answer is not theoretically negative. Our results will be formulated in the language of membrane computing (P systems). Some mathematical results presented here are interesting in themselves. In contrast with most speedup methods which are based on nondeterminism, our results rest upon some universality results proved for deterministic P systems. These results will be used for building “accelerated P systems”. In contrast with the case of Turing machines, acceleration is a part of the hardware (not a quality of the environment) and it is realised either by decreasing the size of “reactors ” or by speedingup the communication channels. Consequently, two acceleration postulates of biological inspiration are introduced; each of them poses specific questions to biology. Finally, in a more speculative part of the paper, we will deal with Turing noncomputability activity of the brain and possible forms of (extraterrestrial) intelligence.