A fast algorithm for boolean function minimization.
01 Dec 1968-
TL;DR: The isomorphic relation between the cells of the n-Cube and the products of a Boolean function is discussed and a computer oriented algorithm is derived in terms of the cellular representation for the generation of prime implicants for Boolean functions.
Abstract: : The structure of the cellular n-dimensional cube is studied with emphasis placed on containment of vertices by cells. The isomorphic relation between the cells of the n-Cube and the products of a Boolean function is discussed. A computer oriented algorithm is derived in terms of the cellular representation for the generation of prime implicants for Boolean functions. Time consuming numerical calculations are replaced by logical operations and storage of terms is limited to minterms and prime implicants. (Author)
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IBM1
TL;DR: MINI is a heuristic logic minimization technique for many-variable problems that seeks a minimal implicant solution, without generating all prime implicants, which can be converted to primeimplicants if desired.
Abstract: MINI is a heuristic logic minimization technique for many-variable problems. It accepts as input a Boolean logic specification expressed as an input-output table, thus avoiding a long list of minterms. It seeks a minimal implicant solution, without generating all prime implicants, which can be converted to prime implicants if desired. New and effective subprocesses, such as expanding, reshaping, and removing redundancy from cubes, are iterated until there is no further reduction in the solution. The process is general in that it can minimize both conventional logic and logic functions of multi-valued variables.
327 citations
TL;DR: It is shown that all presented algorithms are polynomial in the number of minterms occurring in the canonical disjunctive normal form representation of a Boolean function.
54 citations
01 Jan 1980
TL;DR: This dissertation is devoted to the construction of a new algebraic structure for the K-map so that algorithms and theorems can be derived for the minimization of Boolean functions and at the same time provide for the manipulation of Boolean function functions as freely as one could on theK-map.
Abstract: This dissertation is devoted to the construction of a new algebraic structure for the K-map so that algorithms and theorems can be derived for the minimization of Boolean functions and at the same time provide for the manipulation of Boolean functions as freely as one could on the K-map. Computer programs have been included to demonstrate the theory and numerous examples of various complexity have been worked out in the appendices.
5 citations
01 Jan 1971
TL;DR: This chapter presents an algorithmic approach to sequential automata design, which identifies all states of a sequential machine that can be combined into a single state and determines the best selection of which states to merge.
Abstract: Publisher Summary This chapter presents an algorithmic approach to sequential automata design. Many of the processes or systems, which are encountered in engineering, can be modeled as sequential machines or sequential automata if the appropriate software is available. This software representation is used to model problems in many different areas of engineering. Some of these are: sequential system design, models of learning systems and adaptive processes, artificial language problems, some probabilistic processes, and models to study the efficiency of system simulation programs. The automation of the procedure is a necessity for machines having more than a few states because of the large amount of calculation. The procedure consists of two main parts: the final class program and the state-assignment program. The final class program identifies all states of a sequential machine that can be combined into a single state. The best selection of which states to merge is currently an unsolved problem in automata theory, and this determination of a minimum-state machine from the final class is the only point in the procedure that is not automated. However, this problem does not arise for completely specified machines and incompletely specified machines, and the procedure is fully automated for these cases.