Q2. What is the name of the paper?
Winner of best paper award in category “Verification, Simulation, and Test.” Available as http://www.cs.cmu.edu/˜bryant/pubdir/dac95a.pdf.
On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication
TLDR
It is shown that the same technique used to prove that any VLSI implementation of a single output Boolean function has area-time complexity AT/sup 2/= Omega (n/Sup 2/) also proves that any OBDD representation of the function has Omega (c/sup n/) vertices for some c>1 but that the converse is not true.Abstract:
Lower-bound results on Boolean-function complexity under two different models are discussed. The first is an abstraction of tradeoffs between chip area and speed in very-large-scale-integrated (VLSI) circuits. The second is the ordered binary decision diagram (OBDD) representation used as a data structure for symbolically representing and manipulating Boolean functions. The lower bounds demonstrate the fundamental limitations of VLSI as an implementation medium, and that of the OBDD as a data structure. It is shown that the same technique used to prove that any VLSI implementation of a single output Boolean function has area-time complexity AT/sup 2/= Omega (n/sup 2/) also proves that any OBDD representation of the function has Omega (c/sup n/) vertices for some c>1 but that the converse is not true. An integer multiplier for word size n with outputs numbered 0 (least significant) through 2n-1 (most significant) is described. For the Boolean function representing either output i-1 or output 2n-i-1, where 1 >read more
Citations
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Book
Principles of Model Checking
TL;DR: Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field.
Journal ArticleDOI
Symbolic model checking: 10/sup 20/ states and beyond
TL;DR: In this paper, a model-checking algorithm for mu-calculus formulas which uses R.E. Bryant's (1986) binary decision diagrams to represent relations and formulas symbolically is described.
Journal ArticleDOI
Symbolic Boolean manipulation with ordered binary-decision diagrams
TL;DR: The OBDD data structure is described and a number of applications that have been solved by OBDd-based symbolic analysis are surveyed.
Journal ArticleDOI
Counterexample-guided abstraction refinement for symbolic model checking
TL;DR: An automatic iterative abstraction-refinement methodology that extends symbolic model checking to large hardware designs and devise new symbolic techniques that analyze such counterexamples and refine the abstract model correspondingly.
References
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Book
The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
Journal ArticleDOI
Graph-Based Algorithms for Boolean Function Manipulation
TL;DR: In this paper, the authors present a data structure for representing Boolean functions and an associated set of manipulation algorithms, which have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large.
Journal ArticleDOI
Binary Decision Diagrams
TL;DR: This paper describes a method for defining, analyzing, testing, and implementing large digital functions by means of a binary decision diagram that provides a complete, concise, "implementation-free" description of the digital functions involved.
Proceedings ArticleDOI
Some complexity questions related to distributive computing(Preliminary Report)
TL;DR: The quantity of interest, which measures the information exchange necessary for computing f, is the minimum number of bits exchanged in any algorithm.