From Wikipedia, the free encyclopedia
A Symbolic Analysis of Relay and Switching Circuits is the title of a
written by
while attending the
(MIT) in 1937. In his thesis, Shannon, a dual degree graduate of the , proved that
could be used to simplify the arrangement of the
that were the building blocks of the electromechanical
of the day. Shannon went on to prove that it should also be possible to use arrangements of relays to solve Boolean algebra problems.
The utilization of the
properties of electrical switches to perform logic functions is the basic concept that underlies all
designs. Shannon's thesis became the foundation of practical
design when it became widely known among the
community during and after . At the time, the methods employed to design logic circuits were
in nature and lacked the theoretical discipline that Shannon's paper supplied to later projects.
Psychologist
described Shannon's thesis as "possibly the most important, and also the most famous, master's thesis of the century". A version of the paper was published in the 1938 issue of the , and in 1940, it earned Shannon the .
(1965, Sixth Printing) [1958]. Switching Circuits and Logical Design. New York: John Wiley & Sons. p. 34. [Shannon] constructed a calculus based on a set of postulates which described b e.g., an open circuit in series with an open circuit is an open circuit. Then he showed that his calculus was equivalent to certain elementary parts of the calculus of propositions, which in turn was derived from the algebra of logic developed by George Boole.
(1987). The Mind's New Science: A History of the Cognitive Revolution. Basic Books. p. 144.  .
(1938). "A Symbolic Analysis of Relay and Switching Circuits". Trans. AIEE 57 (12): 713–723. :.
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Fractal Symbolic Analysis
Abstract: Restructuring compilers use dependence analysis to prove that the meaning of
a program is not changed by a transformation. A well-known limitation of
dependence analysis is that it examines only the memory locations read and
written by a statement, and does not assume any particular interpretation for
the operations in that statement. Exploiting the semantics of these operations
enables a wider set of transformations to be used, and is critical for
optimizing important codes such as LU factorization with pivoting.
Symbolic execution of programs enables the exploitation of such semantic
properties, but it is intractable for all but the simplest programs. In this
paper, we propose a new form of symbolic analysis for use in restructuring
compilers. Fractal symbolic analysis compares a program and its transformed
version by repeatedly simplifying these programs until symbolic analysis
becomes tractable, ensuring that equality of simplified programs is sufficient
to guarantee equality of the original programs. We present a prototype
implementation of fractal symbolic analysis, and show how it can be used to
optimize the cache performance of LU factorization with pivoting.
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From: Vijay Menon []
[v1] Wed, 12 Jan :05 GMTAKNM Circuit Magic symbolic
circuit analysis.
Symbolic circuits analysis software to simulate electrical circuits using Kirchhoffs laws.
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