In-Ho Moon, James H. Kukula, Kavita Ravi, and Fabio Somenzi. To split or to conjoin: The question in image computation. In Proceedings of the 37th Design Automation Conference (DAC'00), pages 26--28, Los Angeles, June 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....area in the mid 90s, see for example [1, 2] the researchers concentrated on other topics of the reachability analysis galaxy, namely approximate reachability analysis, guided traversal, etc. Only recently the question of image computation gained again the attention of the scientific community [3,4,5,6,7]. We basically follow this recent trend and we try to further optimize image computation introducing an approach based on dynamic sorting, dynamic clustering and partitioning. We start from an ordering technique derived from [1] but with major modifications introduced keeping into account the ....

....around the ones producing these peaks. To avoid BDD blow up we also maintain a threshold mechanism similar to the one introduced in [1] i.e. we avoid creating too large BDDs during clustering. Finally, we apply partitioning during image computation somehow following the trend introduced by [3, 10]. Following [10] we disjunctively partition BDDs as soon as they become too large, but we have a double threshold mechanism. Whereas the first threshold enables partitioning, the second one limits the number of recursive splittings. This methodology allows us to further reduce intermediate peaks, ....

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I. H. Moon, J. H. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In Proc. 37th Design Automat. Conf., Los Angeles, California, June 2000.

....need to be constructed can grow extremely large, exhausting the memory resources of the simulation host machine and or causing severe performance degration. In order to overcome this limitation, various solutions have been proposed that try to contain the size of the BDDs involved, for instance: [4, 5, 6]. An alternative approach is symbolic simulation. This me thod verifies a set of scalar tests with a single symbolic vector. Symbolic functions (represented by BDD) are assigned to the inputs and propagated through the circuit to the outputs. see Figure 1. below) This method is used in [7] and ....

I. Moon, J. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In DAC, Proceedings of the Design Automation Conference, pages 23--28, June 2000.

....check whether a circuit implementation fulfills its specification, is a crucial task in VLSI CAD. Growing interest in universities and industry has lead to new results and significant advances concerning topics like property checking, state space traversal and combinational equivalence checking [4, 7, 14, 11]. For the purpose of this paper combinational equivalence checking is of particular interest. Here, the task is to check whether the Boolean functions corresponding to the specification and the implementation are the same. Besides functional validation by the application of test patterns, mainly ....

I.-H. Moon, J. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In Design Automation Conf., pages 23--28, 2000.

....bring a good spatial improvement compared to traditional BDDs. The second important research direction is the enhancement of symbolic model checking algorithms. Several algorithms are very efficient for a particular class of circuits, but can give bad results if applied to another class [9] In [7], a heuristic analysis of the circuit representation, based on variable dependency matrices, is presented, and can be used to choose the appropriate verification algorithm, if it exists. Despite these improvements, the asymptotic exponential complexity has not been eliminated. Besides, some of ....

. Moon, J. H. Kukula, K. Ravi and F. Somenzi, To Split or to Conjoin: The question in Image Computation, in Proceedings of DAC, Los Angeles, CA., June 2000, pp. 23-28

....check whether a circuit implementation fulfills its specification, is a crucial task in VLSI CAD. Growing interest in universities and industry has lead to new results and significant advances concerning topics like property checking, state space traversal and combinational equivalence checking [7, 10, 24, 19, 8, 26, 18]. For the purpose of this paper combinational equivalence checking is of particular interest. Here, the task is to check whether the Boolean functions corresponding to the specification and the implementation are the same. Besides functional validation by the application of test patterns, mainly ....

I.-H. Moon, J. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In Design Automation Conf., pages 23--28, 2000.

....Part of the reason for this, ironically, is the fact that it is in general not feasible to construct a single BDD for R. Instead, R is represented as the conjunction of several BDDs. The problem then arises how to compute EX(Q) without actually computing R. In a recent series of papers [7, 26, 27], improved algorithms for image computation have been investigated. Theoretical Limitations of Symbolic Model Checking. Potentially, the BDD representation of a Kripke structure may be exponentially more succinct than the explicit representation. Practical experience with symbolic verification ....

I. Moon, J. H. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In Proceedings of the 37th Design Automation Conference (DAC'00), pages 26--28, Los Angeles, June 2000.

....check whether a circuit implementation fulfills its specification, is a crucial task in VLSI CAD. Growing interest in universities and industry has lead to new results and significant advances concerning topics like property checking, state space traversal and combinational equivalence checking [4, 7, 14, 11]. For the purpose of this paper combinational equivalence checking is of particular interest. Here, the task is to check whether the Boolean functions corresponding to the specification and the implementation are the same. Besides functional validation by the application of test patterns, mainly ....

I.-H. Moon, J. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In Design Automation Conf., pages 23--28, 2000.

....of reachable states in a given Finite State Machine (FSM) is the underlying problem in most cases. To handle designs with a huge number of states symbolic techniques based on Binary Decision Diagrams (BDDs) 1, 8] are the state ofthe art approach, avoiding an explicit representation of state sets [15, 5, 18]. Basically, there are two methods to compute the set of reachable states: one uses Transition Functions [7] the other uses Transition Relations [2] Recently, a method to combine both approaches has been presented [18] In this paper, we restrict to the latter approach. There are two common ....

.... art approach, avoiding an explicit representation of state sets [15, 5, 18] Basically, there are two methods to compute the set of reachable states: one uses Transition Functions [7] the other uses Transition Relations [2] Recently, a method to combine both approaches has been presented [18]. In this paper, we restrict to the latter approach. There are two common ways to improve reachability analysis: the rst one is based on partitioned transition relations [23, 3, 6, 4, 19] the second one uses partial and focused traversals [21, 5, 13] Most of these approaches bene t from ....

I.-H. Moon, J. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In Design Automation Conf., pages 23-28, 2000.

....check whether a circuit implementation fulfills its specification, is a crucial task in VLSI CAD. Growing interest in universities and industry has lead to new results and significant advances concerning topics like property checking, state space traversal and combinational equivalence checking [7, 9, 19, 15]. For the purpose of this paper combinational equivalence checking is of particular interest. Here, the task is to check whether the Boolean functions corresponding to the specification and the implementation are the same. Besides functional validation by the application of test patterns, mainly ....

I.-H. Moon, J. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In Design Automation Conf., pages 23--28, 2000.

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In-Ho Moon, James H. Kukula, Kavita Ravi, and Fabio Somenzi. To split or to conjoin: The question in image computation. In Proceedings of the 37th Design Automation Conference (DAC'00), pages 26--28, Los Angeles, June 2000.

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I.-H. Moon, J. H. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In Proceedings of the Design Automation Conference, pages 23--28, Los Angeles, CA, June 2000.

....between normalization and parameterization. Experimental results are shown in Section 9 and we conclude with Section 10. 2 Preliminaries Image computation is finding all successor states from a given set of states in one step and is a key step in model checking to deal with sequential circuits [15, 17, 16]. Let x and y be the sets of present and next state variables and w be the set of primary input variables. Suppose we have a transition relation T (x; w; y) that represents all transitions, being true of just those triples of a, b, and c, such that there is a transition from state a to state c, ....

I.-H. Moon, J. H. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In Proceedings of the Design Automation Conference, pages 23--28, Los Angeles, CA, June 2000.

....we also want to consider Q to estimate the hardness. If there is no good quanti cation schedule for the variables in Q in the range computation, the number of variables in Q will also a ect the hardness signi cantly. Moon et al. proposed the use of variable lifetimes in the dependence matrix [13]. Also Moon et al. proposed the MLP (Minimal Lifetime Permutation) method to get a good quanti cation schedule by trying to decrease variable lifetime by using the dependence matrix [12] We use the variable lifetime in the MLP method to see whether there is a good quanti cation schedule for Q. ....

I.-H. Moon, J. H. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In Proceedings of the Design Automation Conference, pages 23-28, Los Angeles, CA, June 2000.

....was the topic of [10] The context there was image computation with the transition function method input splitting in particular [5, 4] From the dependence matrix one could extract information about the BDD variable order and the choice of the splitting variable. More recently, Moon et al. [12] have used the dependence matrix to dynamically guide the choice of image computation algorithm. The rest of this paper is organized as follows. Section 2 reviews background material. Section 3 discusses the conjunction scheduling problem and presents our ordering algorithm, while Section 4 ....

....matrix, the average row length, the number of connected components of the graph associated to the matrix (CCs) which will be discussed in Section 5, and the time required to run the algorithm. The speed of the procedure makes it suitable for use in image computation algorithms like the one of [12], which may benefit from changing the conjunction schedule dynamically several times during an image computation. Fig.3 shows a log log plot of time required to run the MLP algorithm as a function of the number of memory elements. The solid line has a slope of 2. One can see that, in practice, ....

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I.-H. Moon, J. H. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In Proceedings of the Design Automation Conference, Los Angeles, CA, June 2000. To appear.

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I.-H. Moon, J. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In Design Automation Conf., pages 23--28, 2000.

No context found.

I. Moon, J. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. In Design Automation Conf, pages 23--28, 2000.

No context found.

I. Moon, J. H. Kukula, K. Ravi, and F Somenzi. To split or to conjoin: The question in image computation. In Proceedings of the 37th Design Automation Conference, pages 23--28, 2000.

No context found.

I.-H. Moon, J. H. Kukula, K. Ravi, and F. Somenzi. To Split or to Conjoin: the Question in Image Computation. In Proceedings of the 37th Design Automation Conference (DAC'00), pages 23--28, 2000.

No context found.

I.-H. Moon, H. H. Kukula, K. Ravi, and F. Somenzi. To split or to conjoin: The question in image computation. Proc. DAC, pages 23--28, 2000.

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