Abstract
One of the known methods for solving the problems with exponential time complexity such as NP-complete problems is using the brute force algorithms. Recently, a new parallel computational framework called Membrane Computing is introduced which can be applied in brute force algorithms. The usual way to find a solution for the problems with exponential time complexity with Membrane Computing techniques is byPSystem with active membrane using division rule. It makes an exponential workspace and solves the problems with exponential complexity in a polynomial (even linear) time. On the other hand, searching is currently one of the most used methods for finding solution for problems in real life, that the blind search algorithms are accurate, but their time complexity is exponential such as breadth-first search (BFS) algorithm. In this paper, we proposed a new approach for implementation of BFS by usingPsystem with division rule technique for first time. The theorem shows time complexity of BSF in this framework on randomly binary trees reduced fromO(2d)toO(d).
Highlights
Membrane Computing, introduced in 1998, is an area of study in computer science [1]
Membrane Computing could be considered as a framework in the distributed parallel computing, and it is inspired from the computing ideas, structures, models, the living cells activities, and the cells organized in a hierarchy
The proposed method for BSF based on P system with membrane division is presented in Section 5, in which we provided some guidelines of the implementation of P system with membrane division for breadth-first search (BFS)
Summary
Membrane Computing, introduced in 1998, is an area of study in computer science [1]. Membrane Computing could be considered as a framework in the distributed parallel computing, and it is inspired from the computing ideas, structures, models, the living cells activities, and the cells organized in a hierarchy. The Euclidean space is divided by membranes into some regions consisting of some objects (that are generally signified by alphabetical symbols) and the evolution rules. Applying these rules, the objects can be evolved and/or moved from a region to their adjacent regions. The objects can be evolved and/or moved from a region to their adjacent regions These rules are employed in a nondeterministic and maximally parallel manner. After an initial system configuration, the computation starts, and it terminates once no evolution rule could be applied. The computation result can be a multiset of objects that are embedded in an output membrane or discharged from the system skin
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