An algorithm for bi-decomposition of logic functions
Proceedings of the 38th annual Design Automation Conference
Machine Learning by Function Decomposition
ICML '97 Proceedings of the Fourteenth International Conference on Machine Learning
VLSID '99 Proceedings of the 12th International Conference on VLSI Design - 'VLSI for the Information Appliance'
Some Properties of Discrete Interval Truth Valued Logic
ISMVL '00 Proceedings of the 30th IEEE International Symposium on Multiple-Valued Logic
ISMVL '01 Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic
ISMVL '01 Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic
ISMVL '01 Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic
Flash Analog-to-Digital Converter Using Resonant-Tunneling Multiple-Valued Circuits
ISMVL '01 Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic
A Three-valued D-Flip-Flop and Shift Register Using Multiple-Junction Surface Tunnel Transistors
ISMVL '01 Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic
Realization of NMAX and NMIN Functions with Multi-Valued Voltage Comparators
ISMVL '01 Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic
Decomposition of Multi-Valued Functions into Min- and Max-Gates
ISMVL '01 Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic
Bi-Decomposition of Function Sets in Multiple-Valued Logic for Circuit Design and Data Mining
Artificial Intelligence Review
Artificial Intelligence Review
Bi-Decomposition of Function Sets in Multiple-Valued Logic for Circuit Design and Data Mining
Artificial Intelligence Review
A relational approach to functional decomposition of logic circuits
ACM Transactions on Database Systems (TODS)
| Hi-index | 0.00 |
This article presents a theory for the bi-decomposition of functions in multi-valued logic (MVL). MVL functions are applied in logic design of multi-valued circuits and machine learning applications. Bi-decomposition is a method to decompose a function into two decomposition functions that are connected by a two-input operator called gate. Each of the decomposition functions depends on fewer variables than the original function. Recursive bi-decomposition represents a function as a structure of interconnected gates. For logic synthesis, the type of the gate can be chosen so that it has an efficient hardware representation. For machine learning, gates are selected to represent simple and understandable classification rules.Algorithms are presented for non-disjoint bi-decomposition, where the decomposition functions may share variables with each other. Bi-decomposition is discussed for the min- and max-operators. To describe the MVL bi-decomposition theory, the notion of incompletely specified functions is generalized to function intervals. The application of MVL differential calculus leads to particular efficient algorithms. To ensure complete recursive decomposition, separation is introduced as a new concept to simplify non-decomposable functions. Multi-decomposition is presented as an example of separation.The decomposition algorithms are implemented in a decomposition system called YADE. MVL test functions from logic synthesis and machine learning applications are decomposed. The results are compared to other decomposers. It is verified that YADE finds decompositions of superior quality by bi-decomposition of MVL function sets.