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Algorithmic Aspects of Symbolic Switch Network Analysis
 IEEE Trans. CAD/IC
, 1987
"... A network of switches controlled by Boolean variables can be represented as a system of Boolean equations. The solution of this system gives a symbolic description of the conducting paths in the network. Gaussian elimination provides an efficient technique for solving sparse systems of Boolean eq ..."
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Cited by 22 (5 self)
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A network of switches controlled by Boolean variables can be represented as a system of Boolean equations. The solution of this system gives a symbolic description of the conducting paths in the network. Gaussian elimination provides an efficient technique for solving sparse systems of Boolean equations. For the class of networks that arise when analyzing digital metaloxide semiconductor (MOS) circuits, a simple pivot selection rule guarantees that most s switch networks encountered in practice can be solved with O(s) operations. When represented by a directed acyclic graph, the set of Boolean formulas generated by the analysis has total size bounded by the number of operations required by the Gaussian elimination. This paper presents the mathematical basis for systems of Boolean equations, their solution by Gaussian elimination, and data structures and algorithms for representing and manipulating Boolean formulas.
Symbolic Incompletely Specified Functions for Correct Evaluation in the Presence of Indeterminate Input Values
, 1995
"... We describe the Ordered Ternary Decision Diagram (OTDD) which can be directly evaluated even when given any number of undefined input logic values. Based on Kleeneon strong ternary logic, the OTDD unifies the concepts of “unknown input” with “don’tcare output” for incompletelyspecified Boolean fun ..."
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Cited by 5 (0 self)
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We describe the Ordered Ternary Decision Diagram (OTDD) which can be directly evaluated even when given any number of undefined input logic values. Based on Kleeneon strong ternary logic, the OTDD unifies the concepts of “unknown input” with “don’tcare output” for incompletelyspecified Boolean functions. The OTDD permits functions having nontrivial don’tcare sets to be represented as single diagmms and to be directly processed against each other. We define the full OTDD and the abbreviated OTDD. We examine advantages of the OTDD over the commonlyused dualOBDD method of representing incomplete functions, for LGSynth93 standard benchmarks. We outline a single package for computations with both shared, reduced OTDDs and OBDDs.
Ordered Ternary Decision Diagrams and the Multivalued Compiled Simulation of Unmapped Logic
 Proc. IEEE 27th Annual Simulation Symposium
, 1994
"... We describe a method for generating logic simulation code which correctly responds to any number of undefined logic values at the code inputs. The method is based on our development of the Ordered Ternary Decision Diagram, itself based on Kleenean ternary logic, which explicitly and correctly manage ..."
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Cited by 2 (0 self)
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We describe a method for generating logic simulation code which correctly responds to any number of undefined logic values at the code inputs. The method is based on our development of the Ordered Ternary Decision Diagram, itself based on Kleenean ternary logic, which explicitly and correctly manages the unknown logic value `U' in addition to the `1' and `0' of conventional OBDDs. We describe the OTDD and how to implement its reduction, application, and restriction operations. This method avoids expensive technology mapping, producing highly efficient `U'correct compiled logic simulation code in seconds rather than in hours. Our experiments toward confirming the validity of the method are reported.