MIS: A Multiple-Level Logic Optimization System

Brayton, Robert K.; Rudell, R.; Sangiovanni‐Vincentelli, Alberto; Wang, A.R.

doi:10.1109/tcad.1987.1270347

Cited by 948 publications

(304 citation statements)

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“…These ideas are based on the notion of algebraic factorization applied to sum-of-products (SOP) expressions; the technique is described in [6] and [53]. For the definition of sum-of-products form, see Section 2.2.…”

Section: Global Transformation Methodsmentioning

confidence: 99%

“…It can lead to the loss of a compact description of the original equations, and algebraic decomposition is too restrictive to rediscover their structure. Examples of systems which rely on algebraic techniques are MIS [53], SOCRATES [74], and SIS [3]. In more recent years much attention has also been given to And-Xor decompositions [75,76,40,77,78].…”

Section: Global Transformation Methodsmentioning

confidence: 99%

“…A work of milestone importance is [6], where the notions of kernels was introduced and a method for fast algebraic decomposition based on kernels was developed. This technique with minor modifications are used in [56,57,58,53,59,3]. Techniques for conjunctive decomposition can be found in [22,21].…”

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confidence: 99%

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Integrated logic synthesis using simulated annealing

Färm

Dubrova

Kuehlmann

2011

Proceedings of the 21st Edition of the Great Lakes Symposium on Great Lakes Symposium on VLSI

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KTH School of Information andCommunication Technology SE-164 40 Kista SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie doktorsexamen i elektronik fredagen den 26 januari 2007 klockan 9.00 i Sal E, Forumhuset, Kungl Tekniska högskolan, Isafjordsgatan 39, Kista. © Petra Färm, januari 2007Tryck: Universitetsservice US AB iii Abstract A conventional logic synthesis flow is composed of three separate phases: technology independent optimization, technology mapping, and technology dependent optimization. A fundamental problem with such a three-phased approach is that the global logic structure is decided during the first phase without any knowledge of the actual technology parameters considered during later phases. Although technology dependent optimization algorithms perform some limited logic restructuring, they cannot recover from fundamental mistakes made during the first phase, which often results in non-satisfiable solutions.We present a global optimization approach combining technology independent optimization steps with technology dependent objectives in an annealing-based framework. We prove that, for the presented move set and selection distribution, detailed balance is satisfied and thus the annealing process asymptotically converges to an optimal solution. Furthermore, we show that the presented approach can smoothly trade-off complex, multiple-dimensional objective functions and achieve competitive results. The combination of technology independent and technology dependent objectives is handled through dynamic weighting. Dynamic weighting reflects the sensitivity of the local graph structures with respect to the actual technology parameters such as gate sizes, delays, and power levels. The results show that, on average, the presented advanced annealing approach can improve the area and delay of circuits optimized using the Boolean optimization technique provided by SIS with 11.2% and 32.5% respectively.Furthermore, we demonstrate how the developed logic synthesis framework can be applied to two emerging technologies, chemically assembled nanotechnology and molecule cascades. New technologies are emerging because a number of physical and economic factors threaten the continued scaling of CMOS devices. Alternatives to silicon VLSI have been proposed, including techniques based on molecular electronics, quantum mechanics, and biological processes. We are hoping that our research in how to apply our developed logic synthesis framework to two of the emerging technologies might provide useful information for other designers moving in this direction.iv

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Section: Global Transformation Methodsmentioning

confidence: 99%

Section: Global Transformation Methodsmentioning

confidence: 99%

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Integrated logic synthesis using simulated annealing

Färm

Dubrova

Kuehlmann

2011

Proceedings of the 21st Edition of the Great Lakes Symposium on Great Lakes Symposium on VLSI

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“…Finally, GRMs have applications in signal coding and image processing [12]. In recent years a logic with multiple valued inputs has been introduced with applications in synthesis of PLAs with decoders and function generators [13][14][15], multilevel logic synthesis and factorisation [16,171. A multiple valued input, binary output function can be readily implemented with currently available digital circuits, while a real multiple valued function cannot.…”

Section: Introductionmentioning

confidence: 99%

Multiple valued input generalised reed—muller forms

Schäfer

Perkowski

1992

IEE Proc. E Comput. Digit. Tech. UK

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Abstract:The concept of canonical multiple valued input generalised Reed-Muller (MIGRM) forms is introduced. The MIGRM is a direct extension of the well known generalised ReedMuller (GRM) forms to the logic with multiple valued inputs. The concept of the polarity of a GRM form is generalised to the polarity matrix of a MIGRM form. A tabular pattern-matching method is presented for the calculation of a MIGRM form. The MIGRM transform has been implemented for further investigations of such forms and their comparison with other circuit realisations. IntroductionThe concept of a fixed-polarity generalised Reed-Muller (GRM) form [l, 23 of an n-input Boolean function has been studied extensively in the literature. One reason for studying such forms is that, for each of the 2" polarities, they are canonical, which has several applications in both theory and practice. The existence of new programmable devices such as the Xilinx LCA 3000, the 1020 series from Actel, or the LHS5Ol from Signetics allows for the direct implementation of the form introduced here. For instance, in Xilinx LCA 3000 devices, every module realisation of a Boolean function of five variables has the same cost and speed. The use of EXORs is then reasonable, as they are more powerful than the inclusive gates. It has been proven that the circuits with EXOR gates have lower worst-case complexity than the circuits which use only inclusive gates [lS]. Moreover, EXOR-based circuits such as MIGRMs, GRMs or ESOPs have much better testability properties than SOPS. This paper presents the basic research on MIGRMs for completely specified multiple valued input, binary multioutput functions. We introduce the general concept of a tabular pattern matching method to calculate the MIGRM. Section 2 presents the theory of the MIGRM forms, and Section 3 gives the algorithm for the MIGRM transform. Section 4 illustrates the transformation of the multiple valued input, multioutput SOP (sum-of-products) function of a two-bit adder to a MIGRM form.

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“…In the procedure, we utilize the technique used in Boolean division [5] to synthesize a given Boolean function with extracted XOR terms. For example, suppose a Boolean function such as…”

Section: Exact Methodsmentioning

confidence: 99%