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A Pretty Complete Combinatorial Algorithm for the Threshold Synthesis Problem

Schilling, Christian and Smaus, Jan-Georg and Wenzelmann, Fabian A Pretty Complete Combinatorial Algorithm for the Threshold Synthesis Problem. (2014) In: International Workshop on Combinatorial Algorithms (IWOCA 2013), 10 July 2013 - 12 July 2013 (Rouen, France).

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Official URL: https://doi.org/10.1007/978-3-642-45278-9_43

Abstract

A linear pseudo-Boolean constraint (LPB) is an expression of the form a_1 l_1+...+a_m l_m>= d$, where each l_i is a literal (it assumes the value 1 or 0 depending on whether a propositional variable x_i is true or false) and a_1,...,a_m,d are natural numbers. An LPB represents a Boolean function, and those Boolean functions that can be represented by exactly one LPB are called threshold functions. The problem of finding an LPB representation of a Boolean function if possible is called threshold recognition problem or threshold synthesis problem. The problem has an O(m^7t^5) algorithm using linear programming, where m is the dimension and t the number of clauses in the DNF input. There is also an entirely combinatorial procedure, which works by decomposing the DNF and "counting" the variable occurrences in it. We have implemented both algorithms and report here on the experiments.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to Springer editor. This papers appears in Volume 8288 of Lecture Notes in Computer Science ISSN : 0302-9743 ISBN: 978-3-642-45277-2 The original PDF is available at: https://link.springer.com/chapter/10.1007/978-3-642-45278-9_43
HAL Id:hal-01671327
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Universität Freiburg (GERMANY)
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Deposited By: IRIT IRIT
Deposited On:06 Dec 2017 15:00

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