Results 1 
6 of
6
Parallel BreadthFirst BDD Construction
 In Ninth ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming
, 1997
"... With the increasing complexity of protocol and circuit designs, formal verification has become an important research area and binary decision diagrams (BDDs) have been shown to be a powerful tool in formal verification. This paper presents a parallel algorithm for BDD construction targeted at shared ..."
Abstract

Cited by 14 (2 self)
 Add to MetaCart
With the increasing complexity of protocol and circuit designs, formal verification has become an important research area and binary decision diagrams (BDDs) have been shown to be a powerful tool in formal verification. This paper presents a parallel algorithm for BDD construction targeted at shared memory multiprocessors and distributed shared memory systems. This algorithm focuses on improving memory access locality through specialized memory managers and partial breadthfirst expansion, and on improving processor utilization through dynamic load balancing. The results on a shared memory system show speedups of over two on four processors and speedups of up to four on eight processors. The measured results clearly identify the main source of bottlenecks and point out some interesting directions for further improvements. 1 Introduction With the increasing complexity of protocol and circuit designs, formal verification has become an important research area. As an example, in 1994, In...
Reordering Based Synthesis
 in Proc. of the 3rd Int. Workshop on Applications of the ReedMuller Expansion in Circuit Design (RM'97
, 1997
"... Reordering Based Synthesis (RBS) as an alternative approach to manipulate Decision Diagrams (DDs) is presented. Based on the concept of operation nodes a single "core" operation, i.e. an extended Level Exchange (LE), is sufficient to perform the usual synthesis operations on several types of DDs. RB ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
Reordering Based Synthesis (RBS) as an alternative approach to manipulate Decision Diagrams (DDs) is presented. Based on the concept of operation nodes a single "core" operation, i.e. an extended Level Exchange (LE), is sufficient to perform the usual synthesis operations on several types of DDs. RBS allows the integration of dynamic variable ordering (even) within a single synthesis operation (e.g. an ANDoperation) and thus provides the possibility of avoiding huge peak sizes during the construction. The optimization potential is significantly enlarged by allowing LEs even between operation nodes. A large number of experimental results for the BDD case confirm the validity of the concept.
Parallel DiskBased Computation for Large, Monolithic Binary Decision Diagrams
"... Binary Decision Diagrams (BDDs) are widely used in formal verification. They are also widely known for consuming large amounts of memory. For larger problems, a BDD computation will often start thrashing due to lack of memory within minutes. This work uses the parallel disks of a cluster or a SAN (s ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Binary Decision Diagrams (BDDs) are widely used in formal verification. They are also widely known for consuming large amounts of memory. For larger problems, a BDD computation will often start thrashing due to lack of memory within minutes. This work uses the parallel disks of a cluster or a SAN (storage area network) as an extension of RAM, in order to efficiently compute with BDDs that are orders of magnitude larger than what is available on a typical computer. The use of parallel disks overcomes the bandwidth problem of single disk methods, since the bandwidth of 50 disks is similar to the bandwidth of a single RAM subsystem. In order to overcome the latency issues of disk, the Roomy library is used for the sake of its latencytolerant data structures. A breadthfirst algorithm is implemented. A further advantage of the algorithm is that RAM usage can be very modest, since its largest use is as buffers for open files. The success of the method is demonstrated by solving the 16queens problem, and by solving a more unusual problem — counting the number of tie games in a threedimensional 4×4×4 tictactoe board.
Space and TimeEfficient BDD Construction via Working Set Control
, 1998
"... Binary decision diagrams (BDDs) have been shown to be a powerful tool in formal verification. Efficient BDD construction techniques become more important as the complexity of protocol and circuit designs increases. This paper addresses this issue by introducing three techniques based on working set ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Binary decision diagrams (BDDs) have been shown to be a powerful tool in formal verification. Efficient BDD construction techniques become more important as the complexity of protocol and circuit designs increases. This paper addresses this issue by introducing three techniques based on working set control. First, we introduce a novel BDD construction algorithm based on partial breadthfirst expansion. This approach has the good memory locality of the breadthfirst BDD construction while maintaining the low memory overhead of the depthfirst approach. Second, we describe how memory management on a pervariable basis can improve spatial locality of BDD construction at all levels, including expansion, reduction, and rehashing. Finally, we introduce a memory compacting garbage collection algorithm to remove unreachable BDD nodes and minimize memory fragmentation. Experimental results show that when the applications fit in physical memory, our approach has speedups of up to 1.6 in comparis...
Parallel approaches to BDD manipulation
"... Abstract Symbolic model checking is an automatic method for system verification in which the system is given as a Binary Decision Diagram (BDD) encoded finite state machine. BDD is a common data structure for representation of mathematical objects. The main issue in symbolic model checking is a sta ..."
Abstract
 Add to MetaCart
Abstract Symbolic model checking is an automatic method for system verification in which the system is given as a Binary Decision Diagram (BDD) encoded finite state machine. BDD is a common data structure for representation of mathematical objects. The main issue in symbolic model checking is a state explosion problem that restricts the verification domain. In this paper we present possibilities for the parallelization of BDD manipulation algorithms in order to enable the verification of complex systems. We also demonstrate results of our parallel algorithm for computing BDD operations. I.