Abstract
Zero-Suppressed Binary Decision Diagrams (ZDDs) are widely used data structures for representing and handling combination sets and Boolean functions. In particular, ZDDs are commonly used in CAD for the synthesis and verification of integrated circuits. The purpose of this article is to design an error-resilient version of this data structure: a self-repairing ZDD. More precisely, we design a new ZDD canonical form, called index-resilient reduced ZDD, such that a faulty index can be reconstructed in time O(k), where k is the number of nodes with a corrupted index. Moreover, we propose new versions of the standard algorithms for ZDD manipulation and construction that are error resilient during their execution and produce an index-resilient ZDD as output. The experimental results validate the proposed approach.
- S. Akers. 1978. Binary decision diagrams. IEEE Transactions on Computers 27, 6 (1978). Google ScholarDigital Library
- Y. Aumann and M. A. Bender. 1996. Fault tolerant data structures. In Proceedings of the 37th Annual Sympo sium on Foundations of Computer Science (FOCS). Burlington, Vermont, USA, 580--589. Google ScholarDigital Library
- Bernd Becker, Rolf Drechsler, and Michael Theobald. 1997. On the expressive power of OKFDDs. Formal Methods in System Design 11, 1 (1997), 5--21. Google ScholarDigital Library
- Anna Bernasconi and Valentina Ciriani. 2014. Zero-suppressed binary decision diagrams resilient to index faults. In Proceedings of the 8th IFIP TC1/WG 2.2 International Conference on Theoretical Computer Science (TCS 2014), Rome, Italy, September 1--3, 2014. 1--12.Google ScholarCross Ref
- Anna Bernasconi, Valentina Ciriani, and Lorenzo Lago. 2013. Error resilient OBDDs. In Proceedings of the IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems (DDECS). Karlovy Vary, Czech Republic, 246--249.Google ScholarCross Ref
- Anna Bernasconi, Valentina Ciriani, and Lorenzo Lago. 2015. On the error resilience of ordered binary decision diagrams. Theoretical Computer Science 595 (2015), 11--33. Google ScholarDigital Library
- R. Bryant. 1986. Graph based algorithm for boolean function manipulation. IEEE Transactions on Computers (1986). Google ScholarDigital Library
- R. Drechsler. 1998. Verifying integrity of decision diagrams. In Proceedings of the 17th International Conference on Computer Safety, Reliability and Security (SAFECOMP'98). Heidelberg, Germany, 380--389. Google ScholarDigital Library
- R. Ebendt, G. Fey, and R. Drechsler. 2005. Advanced BDD Optimization. Springer US.Google Scholar
- I. Finocchi, F. Grandoni, and G. Italiano. 2005. Designing reliable algorithms in unreliable memories. In Proceedings of the 13th Annual European Symposium on Algorithms (ESA 2005). Palma de Mallorca, Spain, 1--8. Google ScholarDigital Library
- I. Finocchi, F. Grandoni, and G. Italiano. 2007. Designing reliable algorithms in unreliable memories. Computer Science Review 1, 2 (2007), 77--87. Google ScholarDigital Library
- Irene Finocchi, Fabrizio Grandoni, and Giuseppe F. Italiano. 2009. Optimal resilient sorting and searching in the presence of memory faults. Theoretical Computer Science 410, 44 (2009), 4457--4470. Google ScholarDigital Library
- I. Finocchi and G. Italiano. 2008. Sorting and searching in faulty memories. Algorithmica (2008).Google Scholar
- G. Italiano. 2010. Resilient algorithms and data structures. In Proceedings of the 7th International Conference on Algorithms and Complexity (CIAC 2010). Rome, Italy, 13--24. Google ScholarDigital Library
- B. Jacob, S. Ng, and D. Wang. 2008. Cache, DRAM, Disk. Morgan Kaufmann.Google Scholar
- U. Kebschull and W. Rosenstiel. 1993. Efficient graph-based computation and manipulation of functional decision diagrams. In Proceedings of the 4th European Conference on Design Automation, 1993, with the European Event in ASIC Design. 278--282.Google Scholar
- D. Knuth. 2009. The Art of Computer Programming Volume 4, Fascicle 1: Bitwise Tricks & Techniques; Binary Decision Diagrams. Addison-Wesley Professional. Google ScholarDigital Library
- Heh-Tyan Liaw and Chen-Shang Lin. 1992. On the OBDD-representation of general boolean functions. IEEE Transactions on Computers (1992). Google ScholarDigital Library
- S. Minato. 1993. Zero-suppressed BDDs for set manipulation in combinatorial problems. In Proceedings of the ACM/IEEE 30th Design Automation Conference (DAC). 272--277. Google ScholarDigital Library
- S. Minato. 2010. Data mining using binary decision diagrams. In Progress in Representation of Discrete Functions. Morgan & Claypool, Chapter 5, 97--109.Google Scholar
- S. Minato. 2013. Techniques of BDD/ZDD: brief history and recent activity. IEICE Transactions 96-D, 7 (2013), 1419--1429.Google Scholar
- S. Minato and I. Kimihito. 2007. Symmetric item set mining method using zero-suppressed BDDs and application to biological data. Information and Media Technologies 2, 1 (2007), 300--308.Google Scholar
- Alan Mishchenko. 2001. An introduction to zero-suppressed binary decision diagrams. In Proceedings of the 12th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning.Google Scholar
- José Ignacio Requeno and José Manuel Colom. 2012. Compact representation of biological sequences using set decision diagrams. In Proceedings of the 6th International Conference on Practical Applications of Computational Biology & Bioinformatics, Miguel P. Rocha, Nicholas Luscombe, Florentino Fdez-Riverola, and Juan M. Corchado Rodrguez (Eds.). Advances in Intelligent and Soft Computing, Vol. 154. Springer Berlin Heidelberg, 231--239.Google Scholar
- T. Sasao and J. Butler. 2014. Applications of Zero-Suppressed Decision Diagrams. Morgan & Claypool. 123 pages.Google Scholar
- D. J. Taylor. 1990. Error models for robust storage structures. In Proceedings of the 20th International Symposium on Fault-Tolerant Computing.Google ScholarCross Ref
- S. Yang. 1991. Logic Synthesis and Optimization Benchmarks User Guide Version 3.0. User guide. Microelectronic Center.Google Scholar
- Sungroh Yoon, Christine Nardini, Luca Benini, and Giovanni De Micheli. 2005. Discovering coherent biclusters from gene expression data using zero-suppressed binary decision diagrams. IEEE/ACM Transactions on Computational Biology and Bioinformatics 2, 4 (Oct. 2005), 339--354. Google ScholarDigital Library
Index Terms
- Index-Resilient Zero-Suppressed BDDs: Definition and Operations
Recommendations
Chain Reduction for Binary and Zero-Suppressed Decision Diagrams
AbstractChain reduction enables reduced ordered binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the other’s ability to symbolically represent Boolean functions in compact form. For any Boolean ...
Partially-shared zero-suppressed multi-terminal BDDs: concept, algorithms and applications
Multi-Terminal Binary Decision Diagrams (MTBDDs) are a well accepted technique for the state graph (SG) based quantitative analysis of large and complex systems specified by means of high-level model description techniques. However, this type of ...
Zero-suppressed Sentential Decision Diagrams
AAAI'16: Proceedings of the Thirtieth AAAI Conference on Artificial IntelligenceThe Sentential Decision Diagram (SDD) is a prominent knowledge representation language that subsumes the Ordered Binary Decision Diagram (OBDD) as a strict subset. Like OBDDs, SDDs have canonical forms and support bottom-up operations for combining SDDs,...
Comments