Name
Title | ||
|---|---|---|
Algebraic and Combinatorial Methods for Reducing the Number of Variables of Partially Defined Discrete Functions |
Abstract | ||
|---|---|---|
Applications of pattern recognition, design of fault tolerant systems and communications have key problems that are naturally described by partially defined (incompletely defined) discrete functions. Such partially defined functions arising from practical demands usually have a large number of variables and so their direct implementations require complex systems. Thus it is important to have at hand an efficient method to reduce the number of their variables. Here we review recent results to linearly decompose a discrete function using a transform that can be efficiently implemented as a Galois field deconvolution. We also study the question: What are the general bounds for the dimension of the range space for an arbitrary linear transform to reduce a partially defined discrete function? We derive a bound for the dimension of the range for arbitrary linear transformation. We also estimate how good linear decomposition can be obtained by the use of random transformations and show that with a randomly generated transform we can reach the above discussed bound. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1109/ISMVL.2017.23 | 2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL) |
Keywords | Field | DocType |
index generation function,partially defined function,linear decomposition | Complex system,Kernel (linear algebra),Signal processing,Discrete mathematics,Algebraic number,Computer science,Deconvolution,Algorithm,Discrete functions,Galois theory | Conference |
ISBN | Citations | PageRank |
978-1-5090-5497-8 | 0 | 0.34 |
References | Authors | |
4 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jaakko Astola | 1 | 1515 | 230.41 |
| Pekka Astola | 2 | 20 | 4.98 |
| Radomir S. Stankovic | 3 | 188 | 47.07 |
| Ioan Tabus | 4 | 276 | 38.23 |