Performance Analysis and Optimization of Asynchronous Circuits

Burns, Steven

doi:10.21236/ada447734

Cited by 110 publications

(74 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In particular, a ⊕ a = a for all a ∈ R, so ⊕ is idempotent. A direct consequence of this is that there is no additive inverse 2 ; that is, we don't have a nice analogue of the negative of a number 3 . This means that (R, ⊕, ⊗) is a semi-ring, albeit one that is commutative and idempotent.…”

Section: The Max-plus Semi-ringmentioning

confidence: 99%

“…It is a powerful tool for studying systems with only maximum constraints and is an essential foundation for the deeper results in the theory of min-max functions." Gunawardena noted that many of the results proved in [3,18] are instances of general theorems in max-plus algebra. Nearly twenty years on, max-plus methods do not appear to be widespread amongst the timing analysis community, with only a handful of papers in this area [15,16,20].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Algebraic approach to time borrowing

Broomhead

Furber

Johnson

2013

IET Computers & Digital Techniques

View full text Add to dashboard Cite

Abstract. This paper is about a novel application of linear algebra to the timing of digital hardware. In particular we describe a rigorous, algorithmic approach to 'time borrowing'. Time borrowing is a technique whereby the use of a multiphase clock can allow for a more flexible, efficient use of time. In this approach the system is clocked periodically, but within each clock cycle processes are allowed to interact asynchronously allowing longer processes to be juxtaposed with shorter processes. We show that this problem can be solved completely using linear algebra defined over the max-plus semi-ring, and that the method so obtained conforms with an earlier, heuristic approach to the problem.

show abstract

Section: The Max-plus Semi-ringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Algebraic approach to time borrowing

Broomhead

Furber

Johnson

2013

IET Computers & Digital Techniques

View full text Add to dashboard Cite

show abstract

“…It is a pleasure to thank David Dill for introducing us to the work of Burns (1990), which provided the initial motivation for this study, and for his continued interest in and encouragement of this work. Thanks are also due to Gerard Hoffman for pointing out the work of the Max-Plus group and to Nieke Tholen for ferreting out several misprints and confusions.…”

Section: T(ai2) -T(a~) + + T(a~) -T(ai_l) T(a~) -T(a~) S-t S-1mentioning

confidence: 99%

“…We shall use a subscript t~ to indicate the dependence of the time evolution on the initial conditions. Many authors start the system off at (0 ..... 0) and do not concern themselves with behavior under other initial conditions; in this case we shall simply write t. The following basic result about max-only systems has been proved repeatedly (see, among others, (Reiter 1968;Ramamoorthy and Ho 1980, Theorem 2;Burns 1990, Theorem 2.8)).…”

Section: Introductionmentioning

confidence: 99%

Min-max functions

Gunawardena

1994

Discrete Event Dyn Syst

View full text Add to dashboard Cite

A variety of problems in operations research, control theory, computer science, etc., can be modeled as discrete event systems with maximum and minimum constraints. When these systems require only maximum constraints (or, dually, only minimum constraints) they can be studied by linear methods based on max-plus algebra. Systems with mixed constraints, however, are nonlinear from this perspective and relatively little is known about their behavionr. The paper lays the foundations of the theory of discrete event systems with mixed constraints. We introduce min-max functions, F : R" ~ R", which are constructed using finitely many operations of min, max and +, and study them as dynamical systems. Among other results, we give a complete account of the periodic behavior of functions of dimension 2; we introduce and characterize the concept of balance which generalizes irreducibility in the linear theory; and we give a formula for the cycle time (eigenvalue) of a rain-max function which generalizes the maximum cycle mean formula.

show abstract

“…While representations similar to ATDs have been used earlier [1,3,6,12,17,21,30], applying these earlier approaches to our problem would require the designer to manually (or otherwise) identify all possible scenarios of interaction between sequencing and synchronization constraints, and then represent them explicitly in a combined diagram. This poses practical difficulties in a design-analyze-redesign setting, where a designer may wish to go through several iterations of modifying sequencing and synchronization constraints.…”

Section: Introductionmentioning

confidence: 99%

Reasoning about synchronization in GALS systems

Chakraborty

Mekie

Sharma

2006

Form Method Syst Des

View full text Add to dashboard Cite

Correct design of interface circuits is crucial for the development of System-onChips (SoC) using off-the-shelf IP cores. For correct operation, an interface circuit must meet strict synchronization timing constraints, and also respect sequencing constraints between events dictated by interfacing protocols and rational clock relations. In this paper, we propose a technique for automatically analyzing the interaction between independently specified synchronization constraints and sequencing constraints between events. We show how this analysis can be used to derive delay constraints for correct operation of interface circuits in a GALS system. Our methodology allows an SoC designer to mix and match different interfacing protocols, rational clock relations and synchronization constraints for communication between a pair of modules, and automatically explore their implications on correct interface circuit design.

show abstract

Performance Analysis and Optimization of Asynchronous Circuits

Cited by 110 publications

References 0 publications

Algebraic approach to time borrowing

Algebraic approach to time borrowing

Min-max functions

Reasoning about synchronization in GALS systems

Contact Info

Product

Resources

About