Couceiro, Miguel and Foldes, Stephan:
*Functional equations, constraints, definability of function classes, and functions of Boolean variables.*
In: Acta cybernetica, (18) 1.
pp. 61-75. (2007)

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## Abstract

The paper deals with classes of functions of several variables defined on an arbitrary set A and taking values in a possibly different set B. Definability of function classes by functional equations is shown to be equivalent to definability by relational constraints, generalizing a fact established by Pippenger in the case A = B = {0,1}. Conditions for a class of functions to be definable by constraints of a particular type are given in terms of stability under certain functional compositions. This leads to a correspondence between functional equations with particular algebraic syntax and relational constraints with certain invariance properties with respect to clones of operations on a given set. When A = {0,1} and B is a commutative ring, such B-valued functions of n variables are represented by multilinear polynomials in n indeterminates in B[X1,..., Xn], Functional equations are given to describe classes of field-valued functions of a specified bounded degree. Classes of Boolean and pseudo-Boolean functions are covered as particular cases.

Item Type: | Article |
---|---|

Journal or Publication Title: | Acta cybernetica |

Date: | 2007 |

Volume: | 18 |

Number: | 1 |

ISSN: | 0324-721X |

Page Range: | pp. 61-75 |

Language: | angol |

Event Title: | Kalmár Workshop on Logic in Computer Science, 2003, Szeged |

Uncontrolled Keywords: | Természettudomány, Informatika |

Additional Information: | Bibliogr.: p. 74-75.; Abstract |

Date Deposited: | 2016. Oct. 15. 12:25 |

Last Modified: | 2018. Jun. 05. 13:54 |

URI: | http://acta.bibl.u-szeged.hu/id/eprint/12804 |

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