# The minimal number of layers of a perceptron that sorts

P.J. Zwietering, E.H.L. Aarts, J. Wessels

Research output: Book/ReportBookScientific

### Abstract

In this paper we consider the problem of determining the minimal number of layers required by a multi-layered perceptron for solving the sorting problem. We discuss two formulations of the sorting problem; ABSSORT, which can be considered as the standard form of the sorting problem, and where, given an array of numbers, a new array with the original numbers in non-decreasing order is requested, and RELSORT, where, given an array of numbers, one wants to find the smallest number and for each number -except the largest- one wants to find the next largest number. We show that, if one uses classical multi-layered perceptrons with the hard-limiting response function, the minimal number of layers needed is 3 and 2 for solving ABSSORT and RELSORT, respectively. Keywords: multi-layered perceptrons, minimal number of layers, neural networks, sorting.
Original language English Eindhoven Technische Universiteit Eindhoven Published - 1992 Yes

### Publication series

Name Memorandum COSOR

### Fingerprint

Perceptron
Sort
Sorting
Scientific notation
Response Function
Limiting
Neural Networks
Formulation

### Cite this

Zwietering, P. J., Aarts, E. H. L., & Wessels, J. (1992). The minimal number of layers of a perceptron that sorts. (Memorandum COSOR). Eindhoven: Technische Universiteit Eindhoven.
Zwietering, P.J. ; Aarts, E.H.L. ; Wessels, J. / The minimal number of layers of a perceptron that sorts. Eindhoven : Technische Universiteit Eindhoven, 1992. (Memorandum COSOR).
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author = "P.J. Zwietering and E.H.L. Aarts and J. Wessels",
year = "1992",
language = "English",
series = "Memorandum COSOR",
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Zwietering, PJ, Aarts, EHL & Wessels, J 1992, The minimal number of layers of a perceptron that sorts. Memorandum COSOR, Technische Universiteit Eindhoven, Eindhoven.

The minimal number of layers of a perceptron that sorts. / Zwietering, P.J.; Aarts, E.H.L.; Wessels, J.

Eindhoven : Technische Universiteit Eindhoven, 1992. (Memorandum COSOR).

Research output: Book/ReportBookScientific

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AB - In this paper we consider the problem of determining the minimal number of layers required by a multi-layered perceptron for solving the sorting problem. We discuss two formulations of the sorting problem; ABSSORT, which can be considered as the standard form of the sorting problem, and where, given an array of numbers, a new array with the original numbers in non-decreasing order is requested, and RELSORT, where, given an array of numbers, one wants to find the smallest number and for each number -except the largest- one wants to find the next largest number. We show that, if one uses classical multi-layered perceptrons with the hard-limiting response function, the minimal number of layers needed is 3 and 2 for solving ABSSORT and RELSORT, respectively. Keywords: multi-layered perceptrons, minimal number of layers, neural networks, sorting.

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Zwietering PJ, Aarts EHL, Wessels J. The minimal number of layers of a perceptron that sorts. Eindhoven: Technische Universiteit Eindhoven, 1992. (Memorandum COSOR).