An improved representation of functions for partition based functional decomposition

Summary form only given. Functional decomposition is a process of representing a complex function as a function of functions with fewer variables. Earlier partition based functional decomposition tools represent the functions using r-partition. The r-partition representation is an abstract representation of the function and their memory requirements are super-exponential. An improved functional representation called ir-partition is proposed. The ir-partition representation is a complete representation of the function and requires less memory to store the functions. The main idea behind the ir-partition representation is to incorporate the values of the minterms corresponding to the variables (cubes). Hence, repeated access of the truth table is not necessary to read the value of the minterms. The computational time to calculate the ir-partition operations are three times greater than the computational time and memory requirement to calculate r-partition. However, the memory requirements for representing the function using ir-partition is half the memory requirement using the r-partition representation (abstract representation). Their partition representation also allows us to perform certain Partition Calculus operations implicitly. The representation has been implemented and tested with the MCNC benchmarks.