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17
Boolean analysis of MOS circuits
 IEEE Transactions on Computeraided Design
, 1987
"... The switchlevel model represents a digital metaloxide semiconductor (MOS) circuit as a network of charge storage nodes connected by resistive transistor switches. The functionality of such a network can be expressed as a series of systems of Boolean equations. Solving these equations symbolically ..."
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Cited by 63 (14 self)
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The switchlevel model represents a digital metaloxide semiconductor (MOS) circuit as a network of charge storage nodes connected by resistive transistor switches. The functionality of such a network can be expressed as a series of systems of Boolean equations. Solving these equations symbolically yields a set of Boolean formulas that describe the mapping from input and current state to the new network state. This analysis supports the same class of networks as the switchlevel simulator MOSSIM II and provides the same functionality, including the handling of bidirectional e ects and indeterminate (X) logic values. In the worst case, the analysis of an n node network can yield a set of formulas containing a total of O(n 3) operations. However, all but a limited set of dense, passtransistor networks give formulas with O(n) total operations. The analysis can serve as the basis of e cient programs for a variety oflogic design tasks, including: logic simulation (on both conventional and special purpose computers), fault simulation, test generation, and symbolic veri cation.
COSMOS: A compiled simulator for MOS circuits
 PROCEEDINGS OF THE 24TH DESIGN AUTOMATION CONFERENCE
, 1987
"... The cosmos simulator provides fast and accurate switchlevel modeling of mos digital circuits. It attains high performance by preprocessing the transistor network into a functionally equivalent Boolean representation. This description, produced by the symbolic analyzer anamos, captures all aspects o ..."
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Cited by 52 (0 self)
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The cosmos simulator provides fast and accurate switchlevel modeling of mos digital circuits. It attains high performance by preprocessing the transistor network into a functionally equivalent Boolean representation. This description, produced by the symbolic analyzer anamos, captures all aspects of switchlevel networks including bidirectional transistors, stored charge, different signal strengths, and indeterminate (X) logic values. The lgcc program translates the Boolean representation into a set of machine language evaluation procedures and initialized data structures. These procedures and data structures are compiled along with code implementing the simulation kernel and user interface to produce the simulation program. The simulation program runs an order of magnitude faster than our previous simulator mossim ii.
Exploiting Symmetry When Verifying TransistorLevel Circuits by Symbolic Trajectory Evaluation
, 1997
"... In this paper we describe the use of symmetry for verification of transistorlevel circuits by symbolic trajectory evaluation. We show that exploiting symmetry can allow one to verify systems several orders of magnitude larger than otherwise possible. We classify symmetries in circuits as struct ..."
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Cited by 23 (5 self)
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In this paper we describe the use of symmetry for verification of transistorlevel circuits by symbolic trajectory evaluation. We show that exploiting symmetry can allow one to verify systems several orders of magnitude larger than otherwise possible. We classify symmetries in circuits as structural symmetries, arising from similarities in circuit structure, data symmetries, arising from similarities in the handling of data values, and mixed structuraldata symmetries. We use graph isomorphism testing and symbolic simulation to verify the symmetries in the original circuit. Using conservative approximations, we partition a circuit to expose the symmetries in its components, and construct reduced system models which can be verified efficiently. We have verified Static Random Access Memory circuits with up to 1.5 Million transistors.
Extraction of Gate Level Models from Transistor Circuits by FourValued Symbolic Analysis
, 1991
"... The program TRANALYZE generates a gatelevel representation of an MOS transistor circuit. The resulting model contains only fourvalued unit and zero delay logic primitives, suitable for evaluation by conventional gatelevel simulators and hardware simulation accelerators. TRANALYZE has the same gen ..."
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Cited by 20 (2 self)
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The program TRANALYZE generates a gatelevel representation of an MOS transistor circuit. The resulting model contains only fourvalued unit and zero delay logic primitives, suitable for evaluation by conventional gatelevel simulators and hardware simulation accelerators. TRANALYZE has the same generality and accuracy as switchlevel simulation, generating models for a wide range of technologies and design styles, while expressing the detailed effects of bidirectional transistors, stored charge, and multiple signal strengths. It produces models with size comparable to ones generated by hand.
Representing Boolean Functions with IfThenElse DAGs
, 1988
"... This article describes the use of binary decision diagrams (BDDs) and ifthenelse dags for ..."
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Cited by 8 (1 self)
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This article describes the use of binary decision diagrams (BDDs) and ifthenelse dags for
Symbolic Functional and Timing Verification of TransistorLevel Circuits
 ACM/IEEE INTERNATIONAL CONFERENCE ON COMPUTER AIDED DESIGN
, 1999
"... We introduce a new method of verifying the timing of custom CMOS circuits. Due to the exponential number of patterns required, traditional simulation methods are unable to exhaustively verify a mediumsized modern logic block. Static analysis can handle much larger circuits but is not robust with re ..."
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Cited by 6 (3 self)
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We introduce a new method of verifying the timing of custom CMOS circuits. Due to the exponential number of patterns required, traditional simulation methods are unable to exhaustively verify a mediumsized modern logic block. Static analysis can handle much larger circuits but is not robust with respect to variations from standard circuit structures. Our approach applies symbolic simulation to analyze a circuit over all input combinations without these limitations. We present a prototype simulator (SirSim) and experimental results. We also discuss using SirSim to verify an industrial design which previously required a specialpurpose verification methodology.
Combining ATPG and symbolic simulation for efficient validation of embedded array systems
 International Test Conference (ITC ’02), October
, 2002
"... In the past, Symbolic Trajectory Evaluation (STE) has been shown to be effective for verifying individual array blocks. However, when applying STE to verify multiple array blocks together as a single system, the runtime OBDD sizes would often blow up. In this paper, we propose the use of both ATPG ..."
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Cited by 4 (1 self)
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In the past, Symbolic Trajectory Evaluation (STE) has been shown to be effective for verifying individual array blocks. However, when applying STE to verify multiple array blocks together as a single system, the runtime OBDD sizes would often blow up. In this paper, we propose the use of both ATPGbased justification engine and symbolic simulation to facilitate the application of STE proof methodology for array systems. Our method translates a given verification problem instance into ATPG justification objectives, and partitions a given design into ATPG and symbolic simulation domains. Then, by developing a scheme that enables ATPG justification engine to work closely with the symbolic simulator, the runtime OBDD sizes during each symbolic simulation run can be limited. We demonstrate the effectiveness of our approach by verifying the Memory Management Unit (MMU) in Motorola highperformance microprocessors. The verification of MMU as a whole was not possible before because of the OBDD size blowup problem when symbolic simulation is used in the STE proof process. 1
Automated Equivalence Checking of Switch Level Circuits
 In Proceedings of the 39th Design Automation Conference, DAC 2002
, 2002
"... A chip that is required to meet strict operating criteria in terms of speed, power, or area is commonly custom designed at the switch level. Traditional techniques for verifying these designs, based on simulation, are expensive in terms of resources and cannot completely guarantee correct operation. ..."
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Cited by 2 (0 self)
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A chip that is required to meet strict operating criteria in terms of speed, power, or area is commonly custom designed at the switch level. Traditional techniques for verifying these designs, based on simulation, are expensive in terms of resources and cannot completely guarantee correct operation. Formal verification methods, on the other hand, provide for a complete proof of correctness, and require less effort to setup. This paper presents Motorola's Switch Level Verification (SLV) tool, which employs detailed switch level analysis to model the behavior of MOS transistors and obtain an equivalent RTL model. This tool has been used for equivalence checking at the switch level for several years within Motorola for the PowerPC, M*Core and DSP custom blocks. We focus on the novel techniques employed in SLV, particularly in the areas of precharged and sequential logic analysis, and provide details on the automated and integrated equivalence checking flow in which the tool is used.
Mixed Algebraic and Boolean Symbolic Analysis of Switched Linear Networks: Theory and Applications to Coupled Gate and Interconnect Delay Modeling
, 2003
"... Abstraction of digital MOS circuits as switchlevel networks has proven very useful for VLSI automation. Symbolic analysis of switchlevel networks by representing the signal at the gate of a MOS transistor as a Boolean variable has been shown to be efficient for verification in terms of functional ..."
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Cited by 1 (0 self)
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Abstraction of digital MOS circuits as switchlevel networks has proven very useful for VLSI automation. Symbolic analysis of switchlevel networks by representing the signal at the gate of a MOS transistor as a Boolean variable has been shown to be efficient for verification in terms of functionality and timing. For this work, in addition to expressing the signal at the gate of MOS transistors as Boolean variables, we represent the design parameters of the transistors as algebraic symbols. In this paper, we present the theory for unified symbolic analysis in terms of both algebraic and Boolean symbols. Our formulation is general and is valid for extensions of conventional switched linear networks with various circuit elements like passive elements, current sources, etc. The theory developed for mixed algebraic and Boolean symbolic analysis is applied for symbolic delay estimation in logicstages with interconnects. Instead of conventional numeric delay estimation techniques, our method provides a single closedform analytic delay expression that is symbolic in terms of both Boolean variables and the geometric design parameters of transistors and interconnects. Such expressions provide accurate estimations of signal delay over any input pattern and extensive variation in design variables like width and lengths of transistors
Symbolic Analysis Methods for Masks, Circuits, and Systems
 IN PROCEEDINGS OF THE IEEE INTERNATIONAL CONFERENCE ON COMPUTER DESIGN
, 1993
"... Symbolic representations of systems can achieve a high degree of compaction relative to more explicit forms. By casting an analysis task in terms of operations on a symbolic representation, large and complex systems can be analyzed efficiently. This paper summarizes research in applying symbolic ana ..."
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Cited by 1 (0 self)
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Symbolic representations of systems can achieve a high degree of compaction relative to more explicit forms. By casting an analysis task in terms of operations on a symbolic representation, large and complex systems can be analyzed efficiently. This paper summarizes research in applying symbolic analysis methods to systems at several levels of abstraction.