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Molecular computing is potentially one of the most powerful tools for the development of massive parallel computing protocols. In the present paper, a first example of the use of PNA:PNA interactions in molecular computing is described. A series of short PNA sequences have been designed with a four base stretch coding for variables and solutions. Hybridization of the components in different combinations was tested both in solution and in a microarray format. A series of PNA representing the solutions were spotted on a microarray surface in order to simulate the hardware. A series of PNA representing the variables, labeled with TAMRA, were used to interrogate the device enabling to solve nondeterministic logic operations. The system was shown to be able to solve a two-variable equation with a high signal to noise ratio. This paper intends to provide a proof of principle that PNA, on account of their stability and specificity of binding, are most suitable for constructing organic-type computers.