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121
P Systems with Active Membranes: Attacking NP Complete Problems
 JOURNAL OF AUTOMATA, LANGUAGES AND COMBINATORICS
, 1999
"... P systems are parallel Molecular Computing models based on processing multisets of objects in celllike membrane structures. Various variants were already shown to be computationally universal, equal in power to Turing machines. In this paper one proposes a class of P systems whose membranes are the ..."
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Cited by 53 (1 self)
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P systems are parallel Molecular Computing models based on processing multisets of objects in celllike membrane structures. Various variants were already shown to be computationally universal, equal in power to Turing machines. In this paper one proposes a class of P systems whose membranes are the main active components, in the sense that they directly mediate the evolution and the communication of objects. Moreover, the membranes can multiply themselves by division. We prove that this variant is not only computationally universal, but also able to solve NP complete problems in polynomial (actually, linear) time. We exemplify this assertion with the wellknown SAT problem.
Abstract machines of systems biology
 Transactions on Computational Systems Biology
, 2005
"... Abstract. Living cells are extremely wellorganized autonomous systems, consisting of discrete interacting components. Key to understanding and modeling their behavior is modeling their system organization. Four distinct chemical toolkits (classes of macromolecules) have been characterized, each com ..."
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Cited by 49 (2 self)
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Abstract. Living cells are extremely wellorganized autonomous systems, consisting of discrete interacting components. Key to understanding and modeling their behavior is modeling their system organization. Four distinct chemical toolkits (classes of macromolecules) have been characterized, each combinatorial in nature. Each toolkit consists of a small number of simple components that are assembled (polymerized) into complex structures that interact in rich ways. Each toolkit abstracts away from chemistry; it embodies an abstract machine with its own instruction set and its own peculiar interaction model. These interaction models are highly effective, but are not ones commonly used in computing: proteins stick together, genes have fixed output, membranes carry activity on their surfaces. Biologists have invented a number of notations attempting to describe these abstract machines and the processes they implement. Moving up from molecular biology, systems biology aims to understand how these interaction models work, separately and together. 1
The Many Facets of Natural Computing
"... related. I am confident that at their interface great discoveries await those who seek them. ” (L.Adleman, [3]) 1. FOREWORD Natural computing is the field of research that investigates models and computational techniques inspired by nature and, dually, attempts to understand the world around us in t ..."
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Cited by 39 (2 self)
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related. I am confident that at their interface great discoveries await those who seek them. ” (L.Adleman, [3]) 1. FOREWORD Natural computing is the field of research that investigates models and computational techniques inspired by nature and, dually, attempts to understand the world around us in terms of information processing. It is a highly interdisciplinary field that connects the natural sciences with computing science, both at the level of information technology and at the level of fundamental research, [98]. As a matter of fact, natural computing areas and topics come in many flavours, including pure theoretical research, algorithms and software applications, as well as biology, chemistry and physics experimental laboratory research. In this review we describe computing paradigms abstracted
On Synchronization in P Systems
"... The P systems were recently introduced as distributed parallel computing models of a biochemical type. Multisets of objects are placed in a hierarchical structure of membranes and they evolve according to given rules, which are applied in a synchronous manner: at each step, all objects which can ..."
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Cited by 30 (3 self)
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The P systems were recently introduced as distributed parallel computing models of a biochemical type. Multisets of objects are placed in a hierarchical structure of membranes and they evolve according to given rules, which are applied in a synchronous manner: at each step, all objects which can evolve, from all membranes, must evolve. We consider here the case when this restriction is removed. As expected, unsynchronized systems (even using catalysts) are weaker than the synchronized ones, providing that no priority relation among rules is considered. The power of P systems is not diminished when a priority is used and, moreover, the catalysts can change their states, among two possible states for each catalyst.
Solving NP Complete Problems Using P Systems with Active Membranes
 Unconventional Models of Computation
, 2000
"... A variant of P systems, recently introduced, considers membranes which can multiply by division. Two types of division are considered: division for elementary membranes (i.e. membranes not containing other membranes inside) and division for nonelementary membranes. In two recent papers it is shown ..."
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Cited by 25 (6 self)
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A variant of P systems, recently introduced, considers membranes which can multiply by division. Two types of division are considered: division for elementary membranes (i.e. membranes not containing other membranes inside) and division for nonelementary membranes. In two recent papers it is shown how to solve the Satisfiability problem and the Hamiltonian Path problem (two well known NP complete problems) in linear time with respect to the input length, using this variant of P systems. We show in this paper that P systems with division for elementary membranes only suffice to solve these two problems in linear time. What about the possibility of solving NP complete problems in polynomial time using P systems without membrane division? We show, moreover, that (if P 6= NP ) Deterministic P Systems without membrane division are not able to solve NP complete problems in polynomial time.
A QuantumInspired Evolutionary Algorithm Based on P . . .
, 2008
"... This paper introduces an evolutionary algorithm which uses the concepts and principles of the quantuminspired evolutionary approach and the hierarchical arrangement of the compartments of a P system. The P system framework is also used to formally specify this evolutionary algorithm. Extensive exp ..."
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Cited by 16 (5 self)
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This paper introduces an evolutionary algorithm which uses the concepts and principles of the quantuminspired evolutionary approach and the hierarchical arrangement of the compartments of a P system. The P system framework is also used to formally specify this evolutionary algorithm. Extensive experiments are conducted on a wellknown combinatorial optimization problem, the knapsack problem, to test the effectiveness of the approach. These experimental results show that this evolutionary algorithm performs better than quantuminspired evolutionary algorithms, for certain arrangements of the compartments of the P system structure utilized.
On the computational power of spiking neural P systems
 Inter. J.Unconventional Computing
"... Summary. In this paper we study some computational properties of spiking neural P systems. In particular, we show that by using nondeterminism in a slightly extended version of spiking neural P systems it is possible to solve in constant time both the numerical NP–complete problem Subset Sum and the ..."
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Cited by 16 (4 self)
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Summary. In this paper we study some computational properties of spiking neural P systems. In particular, we show that by using nondeterminism in a slightly extended version of spiking neural P systems it is possible to solve in constant time both the numerical NP–complete problem Subset Sum and the strongly NP–complete problem 3SAT. Then, we show how to simulate a universal deterministic spiking neural P system with a deterministic Turing machine, in a time which is polynomial with respect to the execution time of the simulated system. Surprisingly, it turns out that the simulation can be performed in polynomial time with respect to the size of the description of the simulated system only if the regular expressions used in such a system are of a very restricted type. 1
Catalytic P systems, semilinear sets, and vector addition systems
 THEORETICAL COMPUTER SCIENCE
, 2004
"... We look at 1region membrane computing systems which only use rules of the form Ca Cv, where C is a catalyst anoncatalW:k and v is a(possiblW:kky string ofnoncatal sts. There are norulk of the form a v. Thus, we can think of these systems as"purelx catalxyMWe consider two types: (1) when ..."
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Cited by 15 (3 self)
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We look at 1region membrane computing systems which only use rules of the form Ca Cv, where C is a catalyst anoncatalW:k and v is a(possiblW:kky string ofnoncatal sts. There are norulk of the form a v. Thus, we can think of these systems as"purelx catalxyMWe consider two types: (1) when theinitial configuration containsonl onecatalxkA and (2) when theinitial configuration contains mulains catalsy" We show that systems of the first type are equivalyM to communicationfree Petri nets, which are aly equivalyM to commutative contextfree grammars. They defin epreciselkq semilel sets. ThispartialkyM:W"k an open question (in: WMCCdeA'02, Lecture Notes in Computer Science,vol 2597, Springer,Berlge 2003, pp. 400  409; Computational" universal P systems without priorities: two catal"k# are su#cient, availt,y at http://psystems.disco.unimib.it, 2003). Systems of the second type define exactl""# recursivelMkq""yl sets oftupl# (i.e., Turing machinecomputablWk Weal" studyan extended model where therul are of the form q :(p; Ca Cv) (where q and p are states), i.e., the appl":xyMk of therul is guided bya #nitestatecontrol For thisgeneral"yM model type (1) aswel as type (2) with some restriction correspond to vector addition systems. Finally, we briefly investigate the closure properties of catalytic systems.
A Prolog simulator for deterministic P systems with active membranes
 NEW GENERATION COMPUTING
, 2003
"... In this paper we propose a new way to represent P systems with active membranes based on Logic Programming techniques. This representation allows us to express the set of rules and the configuration of the P system in each step of the evolution as literals of an appropriate language of first order l ..."
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Cited by 12 (6 self)
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In this paper we propose a new way to represent P systems with active membranes based on Logic Programming techniques. This representation allows us to express the set of rules and the configuration of the P system in each step of the evolution as literals of an appropriate language of first order logic. We provide a Prolog program to simulate the evolution of these P systems and present some auxiliary tools to simulate the evolution of a P system with active membranes using 2division which solves the SAT problem following the techniques presented in 10).
On P systems operating in sequential mode
 International Journal of Foundations of Computer Science
, 2004
"... 1. For 1membrane catalytic systems (CS's), the sequential version is strictlyweaker than the parallel version in that the former defines (i.e. generates) exactly the semilinear sets, whereas the latter is known to define nonrecursivesets. 2. For 1membrane communicating P systems (CPS's), ..."
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Cited by 11 (7 self)
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1. For 1membrane catalytic systems (CS's), the sequential version is strictlyweaker than the parallel version in that the former defines (i.e. generates) exactly the semilinear sets, whereas the latter is known to define nonrecursivesets. 2. For 1membrane communicating P systems (CPS's), the sequential versioncan only define a proper subclass of the semilinear sets, whereas the parallel version is known to define nonrecursive sets.3. Adding a new type of rule of the form: ab! axbyccomedcome to the CPS(a natural generalization of the rule ab! axbyccome in the original model),where x; y 2 fhere; outg, to the sequential 1membrane CPS makes itequivalent to a vector addition system.