## 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.

## Keywords

Picture Picture processor Hiding processor Picture matching \((k{, } l)\)-Local language## Notes

### Acknowledgments

Victor Mitrana gratefully acknowledges the support of the Alexander von Humboldt Foundation and of the Visiting Professor Programme—“Sapienza” University of Rome.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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