Years and Authors of Summarized Original Work
1952; Quine
1955; Quine
1956; McCluskey
Problem Definition
Find a minimal sum-of-products expression for a Boolean function. Consider a Boolean algebra with elements False and True. A Boolean function f(y1, y2, …, y n ) of n Boolean input variables specifies, for each combination of input variable values, the function’s value. It is possible to represent the same function with various expressions. For example, the first and last expressions in Table 1 correspond to the same function. Assuming access to complemented input variables, straightforward implementations of these expressions would require two AND gates and an OR gate for \(\left (\overline{a} \wedge \overline{b}\right ) \vee \left (\overline{a} \wedge b\right )\) and only a wire for \(\overline{a}\). Although the implementation efficiency depends on target technology, in general terser expressions enable greater efficiency. Boolean minimization is the task of deriving the tersest...
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Brayton RK, Hachtel GD, Sangiovanni-Vincentelli AL (1990) Multilevel logic synthesis. Proc IEEE 78(2):264–300
Coudert O, Madre JC (1995) New ideas for solving covering problems. In: Proceedings of the design automation conference, San Francisco, pp 641–646
Gimpel JF (1965) A reduction technique for prime implicant tables. IEEE Trans Electron Comput 14(4):535–541
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Karp RM (1972) Reducibility among combinatorial problems. In: Miller RE, Thatcher JW (eds) Complexity of computer computations. Plenum Press, New York, pp 85–103
McCluskey EJ (1956) Minimization of Boolean functions. Bell Syst Tech J 35(6):1417–1444
Quine WV (1952) The problem of simplyfying truth functions. Am Math Mon 59(8):521–531
Quine WV (1955) A way to simplify truth functions. Am Math Mon 62(9):627–631
Umans C, Villa T, Sangiovanni-Vincentelli AL (2006) Complexity of two-level logic minimization. IEEE Trans Comput-Aided Des Integr Circuits Syst 25(7):1230–1246
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Dick, R.P. (2016). Optimal Two-Level Boolean Minimization. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_446
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