F. Somenzi. Colorado University Decision Diagram Package. Technical report, University of Colorado, Boulder, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are far away from the POs in the circuit, since these PIs are expected to greatly influence the circuit behavior. The order of BDD variables can be further improved during the BDD construction by the dynamic sifting heuristic 2 [13] that is now considered an integral part of every BDD package [15] and entails pair wise swaps of variables. In addition to ordering the BDD variables (PIs in circuit) the order in which gates are processed can also be varied. It has been shown that different gate traversals orders can lead to large intermediate BDD sizes [12] In our approach, after the BDD ....

....Results In this section, we present experimental evidence of the improvements obtained by using rain cut hypergraph partitioning to represent Boolean functions in BDDs. Empirical results are given for the ISCAS85 circuit benchmarks [3] All algorithms are implemented in C and use the CUDD [15] package to build the BDDs. We used CAPe [5] as our rain cut circuit placer. The experiments were conducted on a Pentium II 333 MHz, running Linux and equipped with 512 MB of RAM. The runtime and memory limit were set to 1,000 seconds and 500MB, respectively. Tables 1 and 2 summarize the runtime ....

F. Somenzi, "Colorado University Decision Diagram Package, " hto://vlsi. colorado. edu/-fabio/CUDD, 1997.

....heuristic for a given application can dramatically affect its competitiveness and is often considered an important part of implementation. For example, the leading edge SAT solver GRASP [27] is typically used with the dynamic variable ordering heuristic DLIS, and the renowned CUDD package [29] for BDDmanipulation incorporates the dynamic variable sifting heuristic which is applied many times in the course of BDD transformations. Variable sifting is affected by the initial order, but can also be completely turned off to improve runtime. Sifting for BDDs is relatively more expensive than ....

....g j j 7 away from the POs in the circuit, since these PIs are expected to greatly influence the circuit behavior. The order of BDD variables can be further improved during the BDD construction by the dynamic sifting heuristic [25] that is now considered an integral part of every BDD package [29] and entails pairwise swaps of variables. In addition to ordering the BDD variables (PIs in circuit) the order in which gates are processed can also be varied. After the BDD variables are ordered as explained above, we consider three ways to order gates: 1) use the gate order from the DFS ....

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F. Somenzi, "Colorado University Decision Diagram package," http://vlsi.colorado. edu/~fabio/CUDD, 1997.

.... SAT solver GRASP [24] is typically used with the dynamic variable ordering heuristic DLCS (select the variable that appears in the maximum number of unresolved clauses) or DLIS (select the literal that appears in the maximum number of unresolved clauses) and the reknowned CUDD package [26] for BDD manipulation incorporates the dynamic variable sifting heuristic which is applied many times in the course of BDD transformations. Variable sifting is affected by the initial order, but can also be completely turned off. We noticed that, for some benchmark CNF formulae in Table II and ....

....to track fewer variables beyond their neighborhoods. 3 Application of MinCut to SAT BDDs In the following section, we present experimental evidence for the improvements obtained by the new static variable ordering. We decided to use GRASP as our SAT solver [24] and CUDD as our BDD solver [26]. All experiments were conducted on a Pentium II 333 MHz, running Linux with 512 Mb. of physical memory. In terms of CNF problems, we used the DIMACS benchmarks [9] in addition to the n queens problem. We also used a flat version of the ISCAS89 circuit benchmarks [3] expressed in CNF. For all ....

F. Somenzi, "Colorado University Decision Diagram package (CUDD)," http://vlsi.colorado.edu/~fabio/CUDD, 1997.

....versions of Quicksort. Then we show the impact of the three improvements listed above by presenting the running times when one of the improvements is switched o . All computations were carried out on an Ultrasparc 60 with 1.5 GB memory. Operations on BDDs were implemented using the CUDD package [6]. 5.1 Quicksort We intend to sort the global array a in ascending order; a call to the quicksort function in gure 2 should sort the fragment of the array starting at index left and ending at index right. The program is parametrised by two variables: n, the number of bits used to represent the ....

F. Somenzi. Colorado University Decision Diagram Package. Technical report, University of Colorado, Boulder, 1998.

....600 800 1000 N (b) Fig. 4. Boolean program template T for performance test and performance results. with N . Figure 4(b) shows how the peak memory usage of Bebop varies with N . The two curves in Figure 4(a) represent two di erent BDD packages: CU is the CUDD package from Colorado University [Som98] and CMU is the BDD package from Carnegie Mellon University [Lon93] We note that the program T (800) has 2401 variables. Model checking of this program takes a minute and a half with the CMU package and four and a half minutes with the CUDD package. Both times are quite reasonable considering ....

F. Somenzi. Colorado university decision diagram package. ftp://vlsi.colorado.edu/pub, University of Colorado, Boulder, 1998.

....current system status. In case of a crash the scheduler will automatically recover from these dumps and resume computations without the need for manual intervention. Available Decision Diagram Tools At the moment we have integrated current heuristics added to nanotrav (part of the CUDD system, [Som96]) by a number of researchers. These heuristics are not part of the CUDD standard distribution, but rather actual research code by the developers of the speci c heuristics. There are as well some heuristics that are part of the CUDD standard distribution for the purpose of comparison. We also have ....

F. Somenzi. Colorado university decision diagram package. ftp://vlsi.colorado.edu/pub/, 1996.

....Scheduler Figure 3: Structure of the system 3 Available OBDD Tools The tool functionality that we offer consists of a couple of new and innovative BDD heuristics. At the moment these are Block Restricted Sifting ( MS97] integrated both in the traversal tool Nanotrav (part of the CUDD system, [Som96]) and the well known model checker SMV ( oCS] Furthermore, Sample Sifting ( MS98] and Linear Sifting ( MT96] integrated into Nanotrav are available and Sample Sifting integrated into SMV will be added shortly. The set of available tools will constantly grow, as new research results will lead ....

F. Somenzi. Colorado university decision diagram package. ftp://vlsi.colorado.edu/pub/, 1996. 5

....those applied to the Class WD mutants and reported in [13] We are omitting Treatments 1 5, described in [13] since we encountered problems with the static variable ordering. An Experiment with ALU4r WD. Here, we consider Treatment 8, available from the three BDD packages in VIS [14] CU from [15], CAL from [14] and CMU from [16] Treatment 8 from each package is applied to one hundred instances of the graph isomorphic and logically equivalent circuits from the equivalence class 4 525 625 725 825 925 0 10 20 30 40 50 BDD Size (nodes) CU BDD Package (Treatment 8) 525 625 725 825 925 0 10 ....

....isomorphic classes. However, the entropy invariant classes remain distinct from the isomorphic classes despite optimization. Pairwise comparisons of BDD packages. Unlike the illustrative experiment with ALU4r WD only in Section 2, we apply Treatment 8 from the three BDD packages, CU from [15], CAL from [14] and CMU from [16] to three equivalence classes (4 minterm logic invariant, 2 and 4 minterm entropy invariant, and two reference circuits (ALU4r and C432) a total of 3 Theta 100 Theta 2 = 600 experiments. The results are summarized in Figure 9. For each class and each ....

F. Somenzi et al. Colorado University Decision Diagram package (CUDD), release

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F. Somenzi. Colorado University Decision Diagram Package. Technical report, University of Colorado, Boulder, 1998.

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F. Somenzi. Colorado university decision diagram package. http://vlsi.colorado.edu/pub, 1998.

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