Decision P Systems and the P≠NP Conjecture

Pérez–Jiménez, Mario J.; Romero–Jiménez, Álvaro; Sancho-Caparrini, Fernando

doi:10.1007/3-540-36490-0_27

Cited by 14 publications

(26 citation statements)

References 4 publications

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“…We speculate that this is not the case if P≠NP: there is a limit to the amount of 'intelligence' that can be built into the graph while keeping its dimension polynomial in the size of the input (for NP-hard problems). A similar situation seems to occur in membrane computing: it has recently been shown [18] that if P≠NP, then P-system without membrane division cannot solve NP-complete problems in polynomial time.…”

Section: Discussionmentioning

confidence: 75%

Computing with motile bio-agents

Nicolau

Burrage

2006

Biomedical Applications of Micro- And Nanoengineering III

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We describe a model of computation of the parallel type, which we call 'computing with bio-agents', based on the concept that motions of biological objects such as bacteria or protein molecular motors in confined spaces can be regarded as computations. We begin with the observation that the geometric nature of the physical structures in which model biological objects move modulates the motions of the latter. Consequently, by changing the geometry, one can control the characteristic trajectories of the objects; on the basis of this, we argue that such systems are computing devices. We investigate the computing power of mobile bio-agent systems and show that they are computationally universal in the sense that they are capable of computing any Boolean function in parallel. We argue also that using appropriate conditions, bio-agent systems can solve NP-complete problems in probabilistic polynomial time.

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Section: Discussionmentioning

confidence: 75%

Computing with motile bio-agents

Nicolau

Burrage

2006

Biomedical Applications of Micro- And Nanoengineering III

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“…if we start recording agent positions at time 0 and stop recording at time τ). Finally, the set of trajectories of all the agents, defined using (10) (10) where M is the number of agents.…”

Section: Computing With Tagged Bio-agentsmentioning

confidence: 99%

Biocomputation schemes based on the directed and directional movements of motile biological objects

Nicolau

2005

SPIE Proceedings

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In earlier work, we proposed "computing with bio-agents", a new model of computation, of the distributed parallel type, based on the notion that motions of biological objects such as bacteria or protein molecular motors in confined spaces can be regarded as computations. Beginning with the observation that the geometric nature of the physical structures in which model biological objects move modulates the motions of the latter, we inferred that by altering the geometry, one can control the characteristic trajectories of the objects and thus perform meaningful computations. In the present work we describe designed geometries and structures that can be used to achieve various computational tasks in this framework. Specifically, we describe methods for solving difficult combinatorial problems from graph and number theory in an efficient way using bio-agents.

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“…Decision problems are associated with languages in such a manner that solving a decision problem is defined by recognizing the language associated with it. Hence, recognizer membrane systems were defined in [10] (called decision P systems) and complexity classes associated with these systems were introduced in [11]. Over the last few years, the previous methodology for addressing the P versus NP problem has been applied in the framework of membrane computing.…”

Section: Introductionmentioning

confidence: 99%

Tuning Frontiers of Efficiency in Tissue P Systems with Evolutional Communication Rules

et al. 2021

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Over the last few years, a new methodology to address the P versus NP problem has been developed, based on searching for borderlines between the nonefficiency of computing models (only problems in class P can be solved in polynomial time) and the presumed efficiency (ability to solve NP-complete problems in polynomial time). These borderlines can be seen as frontiers of efficiency, which are crucial in this methodology. “Translating,” in some sense, an efficient solution in a presumably efficient model to an efficient solution in a nonefficient model would give an affirmative answer to problem P versus NP. In the framework of Membrane Computing, the key of this approach is to detect the syntactic or semantic ingredients that are needed to pass from a nonefficient class of membrane systems to a presumably efficient one. This paper deals with tissue P systems with communication rules of type symport/antiport allowing the evolution of the objects triggering the rules. In previous works, frontiers of efficiency were found in these kinds of membrane systems both with division rules and with separation rules. However, since they were not optimal, it is interesting to refine these frontiers. In this work, optimal frontiers of the efficiency are obtained in terms of the total number of objects involved in the communication rules used for that kind of membrane systems. These optimizations could be easier to translate, if possible, to efficient solutions in a nonefficient model.

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Decision P Systems and the P≠NP Conjecture

Cited by 14 publications

References 4 publications

Computing with motile bio-agents

Computing with motile bio-agents

Biocomputation schemes based on the directed and directional movements of motile biological objects

Tuning Frontiers of Efficiency in Tissue P Systems with Evolutional Communication Rules

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