An Algorithm for Testing 2-Asummability of Boolean Functions

On Necessary and Sufficient Conditions for Multiple Fault Undetectability

“…The 2-monotonicity is tested by a novel algorithm developed in Section II. The relationship between 2-monotonicity and 2-asummability investigated in Section III makes the 2-asummability algorithm of the authors [8] very fast, since it has been discovered there that 2-monotonicity is equivalent to testing 2-asummability for upto-five-1 2-sums. 2-asummability testing is normally done to ascertain linear separability of switching functions of upto eight variables.…”

An efficient heuristic to identify threshold logic functions

“…2-Summable Property is used to identify these test functions. In this article, the method of Sarje and Biswas [1977] is used for checking the 2-Summability and referred to as the Nonscalable Method. The total number of TFs and total number of RTFs for each input is shown in column 2 of Table I and Table II, respectively. For inputs greater than eight, the total number of RTFs is very large.…”

“…To make fair comparison with the method of Sarje and Biswas [1977] for functions with less than eight inputs, the input function to the ITM is given as a truth table. This version of the proposed method is called ITM-TruthTable (ITM-TT).…”

“…The average execution time for 1 and 2 input functions by all methods is less than 1 millisecond. There is a huge increase in average execution time for the method of Sarje and Biswas [1977], when the number of inputs increases. The method of Gowda and Vrudhula [2008] takes much less time, when comparing with the method of Sarje and Biswas [1977] due to the lesser number of implicants.…”

“…When the number of inputs exceeds eight one has to check the higher-order asummable properties, which is a time-consuming process. Techniques for checking 2-Summability are found in Sarje and Biswas [1977] and Pal [1981]. Obviously, such methods are of little interest in implementing a TF.…”