Abstract
We propose a solution based on networks of picture processors to the problem of picture pattern matching. The network solving the problem can be informally described as follows: it consists of two subnetworks, one of them extracts at each step, simultaneously, all subpictures of identical (progressively decreasing) size from the input picture and sends them to the other subnetwork which checks whether any of the received pictures is identical to the pattern. We present an efficient solution based on networks with evolutionary processors only, for patterns with at most three rows or columns. Afterward, we present a solution based on networks containing both evolutionary and hiding processors running in \({\mathcal {O}}(n+m+kl)\) computational (processing and communication) steps, for any size (n, m) of the input picture and (k, l) of the pattern. From the proofs of these results, we infer that any (k, l)-local language with \(1\le k\le 3\) can be decided in \({\mathcal {O}}(n+m+l)\) computational steps by networks with evolutionary processors only, while any (k, l)-local language with arbitrary k, l can be decided in \({\mathcal {O}}(n+m+kl)\) computational steps by networks containing both evolutionary and hiding processors.
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Acknowledgments
Victor Mitrana gratefully acknowledges the support of the Alexander von Humboldt Foundation and of the Visiting Professor Programme—“Sapienza” University of Rome.
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Communicated by C. M. Vide and A. H. Dediu.
A preliminary version of this work has been published in the Proceedings of the Third International Conference on Theory and Practice of Natural Computing-TPNC 2014, LNCS 8890, 2014, pp. 157–168.
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Bordihn, H., Bottoni, P., Labella, A. et al. Networks of picture processors as problem solvers. Soft Comput 21, 5529–5541 (2017). https://doi.org/10.1007/s00500-016-2206-y
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DOI: https://doi.org/10.1007/s00500-016-2206-y