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BioSteps Beyond Turing
 BIOSYSTEMS
, 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 nega ..."
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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.
SuperTuring or NonTuring? Extending the Concept of Computation
"... “Hypercomputation ” is often defined as transcending Turing computation in the sense of computing a larger class of functions than can Turing machines. While this possibility is important and interesting, this paper argues that there are many other important senses in which we may “transcend Turing ..."
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“Hypercomputation ” is often defined as transcending Turing computation in the sense of computing a larger class of functions than can Turing machines. While this possibility is important and interesting, this paper argues that there are many other important senses in which we may “transcend Turing computation. ” Turing computation, like all models, exists in a frame of relevance, which underlies the assumptions on which it rests and the questions that it is suited to answer. Although appropriate in many circumstances, there are other important applications of the idea of computation for which this model is not relevant. Therefore we should supplement it with new models based on different assumptions and suited to answering different questions. In alternative frames of relevance, including natural computation and nanocomputation, the central issues include realtime response, continuity, indeterminacy, and parallelism. Once we understand computation in a broader sense, we can see new possibilities for using physical processes to achieve computational goals, which will increase in importance as we approach the limits of electronic binary logic. Key words: hypercomputation, ChurchTuring thesis, natural computation, theory of computation, model of computation, Turing computation,
Causality in Membrane 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. P systems are usually equipped with the maximal parallelism semantics; however, since their introduction, some alternative semantics have been ..."
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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. P systems are usually equipped with the maximal parallelism semantics; however, since their introduction, some alternative semantics have been proposed and investigated. We propose a semantics that describes the causal dependencies occurring between the reactions of a P system. We investigate the basic properties that are satisfied by such a semantics. The notion of causality turns out to be quite relevant for biological systems, as it permits to point out which events occurring in a biological pathway are necessary for another event to happen. 1
A Quantum Scattering Approach to Undecidable Problems: Preliminary Version
, 2002
"... In [12] a probabilistic solution to the Infinite Merchant's Problem, an undecidable problem equivalent to the Halting Problem, was proposed. The solution uses a real Hilbert space and is based on the estimation of the exponential growth of an unbounded semigroup. The aim of this paper is to o#er ..."
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In [12] a probabilistic solution to the Infinite Merchant's Problem, an undecidable problem equivalent to the Halting Problem, was proposed. The solution uses a real Hilbert space and is based on the estimation of the exponential growth of an unbounded semigroup. The aim of this paper is to o#er an alternative solution in terms of scattering processes on quantum dots. We will reduce the problem to a special scattering problem, observe the results of multiple acts of scattering and, finally, estimate the deviation of the scattered data from the input data.
Computing with Membranes: P Systems with WormObjects
, 2000
"... We consider a combination of P systems with objects described by symbols with P systems with objects described by strings. Namely, we work with multisets of strings and consider as the result of a computation the number of strings in a given output membrane. The strings (also called worms) are proce ..."
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We consider a combination of P systems with objects described by symbols with P systems with objects described by strings. Namely, we work with multisets of strings and consider as the result of a computation the number of strings in a given output membrane. The strings (also called worms) are processed by replication, splitting, mutation, and recombination; no priority among rules and no other ingredient is used. In these circumstances, it is proved that (1) P systems of this type can generate all recursively enumerable sets of numbers, and, moreover, (2) the Hamiltonian Path Problem in a directed graph can be solved in a quadratic time, while the SAT problem can be solved in a linear time.
Parallel Grammars  A Phenomenology
"... The aim of this paper is at least twofold: − to give prospective PhD students in the area hints at where to start a promising research and − to supplement earlier reference lists on parallel grammars, trying to cover recent papers as well as “older” papers which were somehow neglected in other revi ..."
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The aim of this paper is at least twofold: − to give prospective PhD students in the area hints at where to start a promising research and − to supplement earlier reference lists on parallel grammars, trying to cover recent papers as well as “older” papers which were somehow neglected in other reviews. Together with the nowadays classical book on L systems by G. Rozenberg and A. Salomaa and with the articles on L systems in the “Handbook of Formal Languages,” researchers will be equipped with a hopefully comprehensive list of references and ideas around parallel grammars.
Computationally universal Psystems without
, 2004
"... priorities: two catalysts are sufficient ..."
Rewriting P Systems with Conditional Communication
"... Abstract. A membrane system (P system) is a model of computation inspired by some basic features of the structure and behaviour of living cells. In this paper we consider systems with stringobjects processed by rewriting, with the communication controlled by conditions on the contents of the string ..."
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Abstract. A membrane system (P system) is a model of computation inspired by some basic features of the structure and behaviour of living cells. In this paper we consider systems with stringobjects processed by rewriting, with the communication controlled by conditions on the contents of the strings. Symbols, substrings (in an arbitrary place, or as a prefix/suffix), or the shape of the whole string are used as permitting and as forbidding conditions when moving strings from a membrane to a neighboring membrane. Many of the obtained variants lead to new characterizations of recursively enumerable languages (as expected, these characterizations indicate a tradeoff between the number of membranes and the strength of the communication conditions used). Several open problems are also formulated. 1