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Ternary Simulation: A Refinement of Binary Functions or an Abstraction of RealTime Behaviour?
 PROCEEDINGS OF THE 3RD WORKSHOP ON DESIGNING CORRECT CIRCUITS (DCC96
, 1996
"... We prove the equivalence between the ternary circuit model and a notion of intuitionistic stabilization bounds. The results are obtained as an application of the timing interpretation of intuitionistic propositional logic presented in [12]. We show that if one takes an intensional view of the ternar ..."
Abstract

Cited by 9 (3 self)
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We prove the equivalence between the ternary circuit model and a notion of intuitionistic stabilization bounds. The results are obtained as an application of the timing interpretation of intuitionistic propositional logic presented in [12]. We show that if one takes an intensional view of the ternary model then the delays that have been abstracted away can be completely recovered. Our intensional soundness and completeness theorems imply that the extracted delays are both correct and exact; thus we have developed a framework which unifies ternary simulation and functional timing analysis. Our focus is on the combinational behaviour of gatelevel circuits with feedback.
Buridan's Principle
, 1986
"... ither bale of hay within t seconds. Such a range of values of x exists for any time t, including times large enough to insure that the ass has starved to death by then. Thus, there exists a finite range of starting positions for which the ass starves to death. The key assumption in this argument is ..."
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Cited by 4 (0 self)
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ither bale of hay within t seconds. Such a range of values of x exists for any time t, including times large enough to insure that the ass has starved to death by then. Thus, there exists a finite range of starting positions for which the ass starves to death. The key assumption in this argument is continuity: the ass's position at a later time is a continuous function of its initial position. Continuity has been a guiding principle in the development of modern physics. Phenomena that appear discontinuous, such as discrete atomic spectral lines, are explained in terms of continuous physical laws, such as Schroedinger's equation. The assumption of continuity is discussed at length in Section 6. For now, let us accept it and investigate its consequences. The general principle underlying the starvation of Buridan's ass can be stated as follows: Buridan's Principle. A discrete decision based upon an input having a continuo
Buridan’s Principle Leslie
, 2012
"... The problem of Buridan’s Ass, named after the fourteenth century French philosopher Jean Buridan, states that an ass placed equidistant between two bales of hay must starve to death because it has no reason to choose one bale over the other. With the benefit of modern mathematics, the argument can b ..."
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The problem of Buridan’s Ass, named after the fourteenth century French philosopher Jean Buridan, states that an ass placed equidistant between two bales of hay must starve to death because it has no reason to choose one bale over the other. With the benefit of modern mathematics, the argument can be expressed as follows. Assume that, at time 0, the ass is placed at position x along the line joining the bales of hay, where one bale is at position 0 and the other at position 1, so 0 < x < 1. The position of the ass at time t> 0 is a function of two arguments: the time t and the starting position x. Let At(x) denote that position. For simplicity, assume that when the ass reaches a bale of hay it stays there forever, so for all t ≥ 0: At(0) = 0, At(1) = 1, and 0 ≤ At(x) ≤ 1 for any x with 0 < x < 1. The ass is a physical mechanism subject to the laws of physics. Any such mechanism is continuous, so At(x) is a continuous function of x. Since At(0) = 0 and At(1) = 1, by continuity there must be a finite range of values of x for which 0 < At(x) < 1. These values represent initial positions of the ass for which it does not reach either
Buridan’s Principle Leslie
, 1984
"... The problem of Buridan’s Ass, named after the fourteenth century French philosopher Jean Buridan, states that an ass placed equidistant between two bales of hay must starve to death because it has no reason to choose one bale over the other. With the benefit of modern mathematics, the argument can b ..."
Abstract
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The problem of Buridan’s Ass, named after the fourteenth century French philosopher Jean Buridan, states that an ass placed equidistant between two bales of hay must starve to death because it has no reason to choose one bale over the other. With the benefit of modern mathematics, the argument can be expressed as follows. Assume that, at time 0, the ass is placed at position x along the line joining the bales of hay, where one bale is at position 0 and the other at position 1, so 0 < x < 1. The position of the ass at time t> 0 is a function of two arguments: the time t and the starting position x. Let At(x) denote that position. For simplicity, assume that when the ass reaches a bale of hay it stays there forever, so for all t ≥ 0: At(0) = 0, At(1) = 1, and 0 ≤ At(x) ≤ 1 for any x with 0 < x < 1. The ass is a physical mechanism subject to the laws of physics. Any such mechanism is continuous, so At(x) is a continuous function of x. Since At(0) = 0 and At(1) = 1, by continuity there must be a finite range of values of x for which 0 < At(x) < 1. These values represent initial positions of the ass for which it does not reach either