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The need to reduce the power consumption of the next generation of digital systems is clearly recognized. At the system level, power management is a very powerful technique and delivers large and unambiguous savings. This paper describes the development and application of algorithms that use ideas similar to power management, but that are applicable to logic level synthesis/design. The proposed approach is termed guarded evaluation. The main idea here is to determine, on a per clock cycle basis, which parts of a circuit are computing results that will be used, and which are not. The sections that are not needed are then "shut off", thus saving the power used in all the useless transitions in that part of the circuit. Initial experiments indicate substantial power savings and the strong potential of this approach. While this paper presents the development of these ideas at the logic level of design -the same ideas have direct application at the register transfer level of design also. Guarded EvaluationWe believe in the strength of power management and its unambiguous power savings. We also believe that this idea can be pushed to lower levels of the digital system design. In particular, in this paper, we demonstrate the use of power management at logic level synthesis/design using a technique we call guarded evaluation. The essential idea here is to dynamically detect, on a per clock cycle basis, which parts of a logic circuit are being used and which are not. The ones that are not, can then be shut off. This is done by ensuring that no logic transitions propagate through this logic. Gating the clock inputs of existing latches/flip-flops/registers in a given RTL description is one way to do this. This is effective when it is known that the logic fed by the latch is not being utilized during the current clock cycle. This idea has been used in the functional aspects of logic design for a long time. Its utility in terms of power reduction is also known by now, but not completely exploited [1,2]. This idea can be pushed further to achieve power savings that may not be possible through just the gating of existing latches/registers. As an example, consider a two operation ALU which is used for either addition or shifting. This is typically implemented using an adder and a shifter, and then selecting the result of one of them using a multiplexor as shown in Figure 1. In any clock cycle only one of the two functions, addition or shifting, needs to be computed. However, the multiplexor does the selection only after both units have completed their evaluation. Clearly the evaluation of one of the two units could have been avoided. Direct gating of the clock input of the data registers will not work in this case. This is because the same data register feeds both the adder and the shifter. Duplicating this register is certainly a possibility, but may not be an acceptable solution if this register could be one of many possible ones from a register file. The duplication would involve duplicating the entire register file ...

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Abstract. Image computation nds wide application in VLSI CAD, such as state reachability analysis in formal veri cation and synthesis, combinational veri cation, combinational and sequential test. Existing BDD-based symbolic algorithms for image computation are limited by memory resources in practice, while SAT-based algorithms that can obtain the image by e n umerating satisfying assignments to a CNF representation of the Boolean relation are potentially limited by time resources. We propose new algorithms that combine BDDs and SAT i n order to exploit their complementary bene ts, and to o er a mechanism for trading o space vs. time. In particular, 1 our integrated algorithm uses BDDs to represent the input and image sets, and a CNF formula to represent the Boolean relation, 2 a fundamental enhancement called BDD Bounding is used whereby the SAT solver uses the BDDs for the input set and the dynamically changing image set to prune the search space of all solutions, 3 BDDs are used to compute all solutions below i n termediate points in the SAT decision tree, 4 a ne-grained variable quanti cation schedule is used for each BDD subproblem, based on the CNF representation of the Boolean relation. These enhancements coupled with more engineering heuristics lead to an overall algorithm that can potentially handle larger problems. This is supported by our preliminary results on exact reachability analysis of ISCAS benchmark circuits.

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This paper discusses our methodology for formal analysis and automatic verification of software programs. It is currently applicable to a large subset of the C programming language that includes bounded recursion. We consider reachability properties, in particular whether certain assertions or basic blocks are reachable in the source code. We perform this analysis via a translation to a Boolean representation based on modeling basic blocks. The program is then analyzed by a back-end SAT-based bounded model checker, where each unrolling is mapped to one step in a block-wise execution of the program. The main contributions of this paper are as follows: 1) This paper is the first to use the block-based unrollings with SAT-based bounded model checking. This allows us to take advantage of SAT-based learning inherent to the best performing bounded model checkers. 2) We also present various heuristics used in the SAT-based bounded model checking customized for models automatically generated from software, allowing a more efficient analysis. 3) We have implemented our methodology into a prototype tool called F-Soft and applied it on various case studies. We present experimental results based on eight case studies including a C-based implementation of a network protocol, and compare the performance gains using the proposed heuristics.

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