Fixed Polarity Reed-muller Minimization of Incompletely Specified Boolean Functions Based on Information Estimations on Decision Trees
نویسنده
چکیده
This paper presents algorithm to find minimal Fixed Polarity Reed-Muller expressions, twolevel fixed polarity AND-EXOR canonical representations, for incompletely specified Boolean functions that based on information measures on decision trees. We study the Free Reed-Muller Tree as acceptable representation and manipulation structure to find minimal Fixed Polarity Reed-Muller expressions. In contrast to previously published methods, the algorithm can handle incompletely specified Boolean functions up to one thousand variables for reasonable time.
منابع مشابه
Exact Minimization of Fixed Polarity Reed-Muller Expressions for Incompletely Speci ed Functions
This paper presents an exact minimization algorithm for fixed polarity Reed-Muller expressions (FPRMs) for incompletely specified functions. For an n-variable function with unspecified minterms there are 2 distinct FPRMs. A minimum FPRM is one with the fewest products. The minimization algorithm is based on the multi-terminal binary decision diagrams. Experimental results for a set of functions...
متن کاملExact Minimization of FPRMs for Incompletely Specified Functions by Using MTBDDs
Fixed polarity Reed-Muller expressions (FPRMs) exhibit several useful properties that make them suitable for many practical applications. This paper presents an exact minimization algorithm for FPRMs for incompletely specified functions. For an n-variable function with α unspecified minterms there are 2n+α distinct FPRMs, and a minimum FPRM is one with the fewest product terms. To find a minimu...
متن کاملOn the Calculation of Generalized Reed-muller Canonical Expansions from Disjoint Cube Representation of Boolean Functions
A new algorithm is shown that converts disjoint cube representation of Boolean functions into fixed-polarity Generalized Reed-Muller Expansions (GRME). Since the known fast algorithm Ihal generates the GRME based on the factorization or thc Reed-Muller transform matrix always starts from the truth table (minterms) of Boolean function, then the described method has the advantages due to smaller ...
متن کاملGeneralised k-variable-mixed-polarity Reed-Muller expansions for system of Boolean functions and their minimisation
A lookup table based method to minimise generalised partially-mixed-polarity ReedMuller (GPMPRM) expansions with k mixed polarity variables is presented. The developed algorithm can produce solutions based on the desired cost criteria for the systems of completely specified functions. A heuristic approach based on the exclusion rule is adopted to extract the best dual polarity variables from an...
متن کاملInformation Theoretic Approach to Minimization of Polynomial Expressions over GF(4)
This paper addresses a new information theoretic approach to minimization of polynomial expressions for Multiple Valued Logic (MVL) functions. Its focus is to determine the so-called pseudo Reed-Muller and pseudo Kronecker expressions of MVL functions. A key point of our approach is the use of information theoretic measures for efficient design of Decision Trees (DTs) to represent MVL functions...
متن کامل