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14
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 23 (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
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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Cited by 2 (0 self)
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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
S.: Passages of proof
 Bull. Eur. Assoc. Theor. Comput. Sci. EATCS
, 2004
"... Whether ’tis nobler in the mind to suffer The slings and arrows of outrageous fortune, Or to take arms against a sea of troubles And by opposing end them? Hamlet 3/1, by W. Shakespeare In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs w ..."
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Whether ’tis nobler in the mind to suffer The slings and arrows of outrageous fortune, Or to take arms against a sea of troubles And by opposing end them? Hamlet 3/1, by W. Shakespeare In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs will be studied at three levels: syntactical, semantical and pragmatical. Computerassisted proofs will be give a special attention. Finally, in a highly speculative part, we will anticipate the evolution of proofs under the assumption that the quantum computer will materialize. We will argue that there is little ‘intrinsic ’ difference between traditional and ‘unconventional ’ types of proofs. 2 Mathematical Proofs: An Evolution in Eight Stages Theory is to practice as rigour is to vigour. D. E. Knuth Reason and experiment are two ways to acquire knowledge. For a long time mathematical
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
Who Is Afraid of Randomness?
, 2000
"... Introduction Randomness## mark of anxiety, the cause of disarray or misfortune, the cure for boring repetitiveness, is, like it or not, one of the most powerful driving forces of life. Is it bad? Is it good? The struggle with uncertainty and risk caused by natural disasters, market downturns or ..."
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Introduction Randomness## mark of anxiety, the cause of disarray or misfortune, the cure for boring repetitiveness, is, like it or not, one of the most powerful driving forces of life. Is it bad? Is it good? The struggle with uncertainty and risk caused by natural disasters, market downturns or terrorism is balanced by the role played by randomness in generating diversity and innovation, in allowing complicated structures to emerge through the exploitation of serendipitous accidents. To many minds any discussion about randomness is purely academic, just another mathematical or philosophical pedantry. False! Randomness could be a matter of life or death, as in the case of Sudden Infant Death Syndrome (SIDS), a merciless childkiller. The present paper describes some di#culties regarding the mathematical modelling of randomness, contrasts siliconcomputer generated pseudorandom bits with quantumcomputer "random" bits, succinctly presents the algorithmic definition of random
Coins, Quantum Measurements, and Turing's Barrier
, 2002
"... Is there any hope for quantum computing to challenge the Turing barrier, i.e. to solve an undecidable problem, to compute an uncomputable function? According to Feynman's '82 argument, the answer is negative. This paper reopens the case: we will discuss solutions to a few simple problems which s ..."
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Is there any hope for quantum computing to challenge the Turing barrier, i.e. to solve an undecidable problem, to compute an uncomputable function? According to Feynman's '82 argument, the answer is negative. This paper reopens the case: we will discuss solutions to a few simple problems which suggest that quantum computing is theoretically capable of computing uncomputable functions.
Decidability of Divergence for Catalytic P Systems
"... Summary. P systems are a biologically inspired model introduced by Gheorghe Păun with the aim of representing the structure and the functioning of the cell. Since their introduction, several variants of P systems have been proposed and explored. We concentrate on the class of catalytic P systems wit ..."
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Summary. P systems are a biologically inspired model introduced by Gheorghe Păun with the aim of representing the structure and the functioning of the cell. Since their introduction, several variants of P systems have been proposed and explored. We concentrate on the class of catalytic P systems without priorities associated to the rules. We show that the divergence problem (i.e., checking for the existence of an infinite computation) is decidable in such a class of P systems. As a corollary, we obtain an alternative proof of the nonuniversality of deterministic catalytic P systems, an open problem recently solved by Ibarra and Yen. 1
legitimise the conquests of intuition... J.
, 2008
"... The object of mathematical rigour is to sanction and ..."