TY - GEN

T1 - Linearization of functions represented as a set of disjoint cubes at the autocorrelation domain

AU - Osnat, K.

AU - Levin, I.

AU - Stankovic, Radomir S.

N1 - Place of conference:Germany

PY - 2006

Y1 - 2006

N2 - The implementation cost of a multi-output Boolean function, in terms of the number
of two-input AND-OR gates, can be reduced by using a linear decomposition. The linearly
decomposed Boolean function consists of a linear function followed by the corresponding
linearly transformed function. A complexity of the linearized function and therefore, its
implementation cost, depends on the linear transform chosen. In this paper we suggest a
spectral technique of the linear transformation of functions defined by disjoint cubes.
The proposed linearization procedure is defined over the autocorrelation domain where
the autocorrelation function is represented as an arithmetic sum of products. The computation
complexity of the suggested method is polynomial in both the number of input
variables and the number of cubes of the original function. Hence the suggested method is
applicable to functions of a large number of input variables.
Experimental results over standard benchmarks show reduction in the implementation
complexity in comparison with the implementation of the initially given non linearized
functions. The efficiency in terms of the computation time is demonstrated on randomly
generated functions of large number of inputs.

AB - The implementation cost of a multi-output Boolean function, in terms of the number
of two-input AND-OR gates, can be reduced by using a linear decomposition. The linearly
decomposed Boolean function consists of a linear function followed by the corresponding
linearly transformed function. A complexity of the linearized function and therefore, its
implementation cost, depends on the linear transform chosen. In this paper we suggest a
spectral technique of the linear transformation of functions defined by disjoint cubes.
The proposed linearization procedure is defined over the autocorrelation domain where
the autocorrelation function is represented as an arithmetic sum of products. The computation
complexity of the suggested method is polynomial in both the number of input
variables and the number of cubes of the original function. Hence the suggested method is
applicable to functions of a large number of input variables.
Experimental results over standard benchmarks show reduction in the implementation
complexity in comparison with the implementation of the initially given non linearized
functions. The efficiency in terms of the computation time is demonstrated on randomly
generated functions of large number of inputs.

UR - https://scholar.google.co.il/scholar?q=Linearization+of+Functions+Represented+as+a+Set+of+Disjoint+Cubes+at+the+Autocorrelation+Domain&btnG=&hl=en&as_sdt=0%2C5

M3 - Conference contribution

BT - The 7th International Workshop on Boolean Problems

ER -