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- W4315705788 abstract "A linear pseudo-Boolean constraint (LPB) is an expression of the form $a_1 cdot ell_1 + dots + a_m cdot ell_m geq d$, where each $ell_i$ is a literal (it assumes the value 1 or 0 depending on whether a propositional variable $x_i$ is true or false) and $a_1, dots, a_m, d$ 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 $O(m^7 t^5)$ algorithm using linear programming, where $m$ is the dimension and $t$ the number of terms in the DNF input. It has been an open question whether one can recognise threshold functions through an entirely combinatorial procedure. Smaus has developed such a procedure for doing this, which works by decomposing the DNF and counting the variable occurrences in it. We have implemented both algorithms as a thesis project. We report here on this experience. The most important insight was that the algorithm by Smaus is, unfortunately, incomplete." @default.
- W4315705788 created "2023-01-12" @default.
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- W4315705788 date "2023-01-09" @default.
- W4315705788 modified "2023-09-26" @default.
- W4315705788 title "Implementations of two Algorithms for the Threshold Synthesis Problem" @default.
- W4315705788 doi "https://doi.org/10.48550/arxiv.2301.03667" @default.
- W4315705788 hasPublicationYear "2023" @default.
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