Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Zero-suppressed BDDs for set manipulation in combinatorial problems
DAC '93 Proceedings of the 30th international Design Automation Conference
Stochastic process algebras—between LOTOS and Markov chains
Computer Networks and ISDN Systems - Special issue: trends in formal description techniques
Representations of Discrete Functions
Representations of Discrete Functions
Introduction to the Special Issue on Multi-Terminal BinaryDecision Diagrams
Formal Methods in System Design
Advances in Model Representations
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Symbolic Model Checking of Probabilistic Processes Using MTBDDs and the Kronecker Representation
TACAS '00 Proceedings of the 6th International Conference on Tools and Algorithms for Construction and Analysis of Systems: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
Analysis of Markov reward models using zero-suppressed multi-terminal BDDs
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Exploiting interleaving semantics in symbolic state-space generation
Formal Methods in System Design
IEEE Transactions on Computers
A uniform framework for weighted decision diagrams and its implementation
International Journal on Software Tools for Technology Transfer (STTT)
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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 Decision Diagram (DD) is not always the best choice, since finite functions with small satisfaction sets, and where the fulfilling assignments possess many 0-assigned positions, may yield relatively large MTBDD based representations. Therefore, this article introduces zero-suppressed MTBDDs and proves that they are canonical representations of multi-valued functions on finite input sets. For manipulating DDs of this new type, possibly defined over different sets of function variables, the concept of partially-shared zero-suppressed MTBDDs and respective algorithms are developed. The efficiency of this new approach is demonstrated by comparing it to the well-known standard type of MTBDDs, where both types of DDs have been implemented by us within the C++-based DD-package JINC. The benchmarking takes place in the context of Markovian analysis and probabilistic model checking of systems. In total, the presented work extends existing approaches, since it not only allows one to directly employ (multi-terminal) zero-suppressed DDs in the field of quantitative verification, but also clearly demonstrates their efficiency.