R. K. Mueller

Bio: R. K. Mueller is an academic researcher from General Mills. The author has contributed to research in topics: Implicant & Boolean network. The author has an hindex of 1, co-authored 1 publications receiving 59 citations.

A Topological Method for the Determination of the Minimal Forms of a Boolean Function

Abstract: The topology of the n-dimensional cube is used to reduce the problem of determining the minimal forms of a Boolean function of n variables to that of finding the minimal coverings of the essential vertices of the basic cell system associated with the given function. The proof of this statement is contained in the central Theorem 4. A numerical easily programmed procedure is given with which it is possible to treat problems with a greater number of variables than has heretofore been practical. The procedure by-passes the determination of the basic cells (the prime implicants of W. V. Quine) and locates the essential vertices, from which in turn the irredundant and minimal forms are obtained.

SOCRATES: A System for Automatically Synthesizing and Optimizing Combinational Logic

Abstract: This paper presents SOCRATES, a system of programs which synthesize and optimize combinational logic circuits from boolean equations. SOCRATES optimizes logic using boolean and algebraic minimization techniques, and it optimizes circuits derived from this logic in a user defined technology with a rule based expert system. This paper discusses the goals of logic synthesis and the capabilities needed in a tool to meet these goals. SOCRATES's capabilities are then presented and demonstrated with experiments run on circuits from the 1986 Design Automation Conference synthesis benchmark set.

Pattern-Based Modeling and Solution of Probabilistically Constrained Optimization Problems

Abstract: We propose a new modeling and solution method for probabilistically constrained optimization problems. The methodology is based on the integration of the stochastic programming and combinatorial pattern recognition fields. It permits the fast solution of stochastic optimization problems in which the random variables are represented by an extremely large number of scenarios. The method involves the binarization of the probability distribution and the generation of a consistent partially defined Boolean function pdBf representing the combination F,p of the binarized probability distribution F and the enforced probability level p. We show that the pdBf representing F,p can be compactly extended as a disjunctive normal form DNF. The DNF is a collection of combinatorial p-patterns, each defining sufficient conditions for a probabilistic constraint to hold. We propose two linear programming formulations for the generation of p-patterns that can be subsequently used to derive a linear programming inner approximation of the original stochastic problem. A formulation allowing for the concurrent generation of a p-pattern and the solution of the deterministic equivalent of the stochastic problem is also proposed. The number of binary variables included in the deterministic equivalent formulation is not an increasing function of the number of scenarios used to represent uncertainty. Results show that large-scale stochastic problems, in which up to 50,000 scenarios are used to describe the stochastic variables, can be consistently solved to optimality within a few seconds.

Irredundant disjunctive and conjunctive forms of a Boolean function

Abstract: A thorough algebraic method is described for the determination of the complete set of irredundant normal and conjunctive forms of a Boolean function. The method is mechanical and therefore highly programmable on a computer.