Formal Methods in System Design

, Volume 36, Issue 3, pp 198-222

First online:

Partially-shared zero-suppressed multi-terminal BDDs: concept, algorithms and applications

  • Kai LampkaAffiliated withComputer Engineering and Communication Networks Lab., ETH Zurich Email author 
  • , Markus SiegleAffiliated withInst. for Comp. Eng., Univ. of the German Federal Armed Forces Munich
  • , Joern OssowskiAffiliated withInst. for Theoretical Comp. Sc., Technical University Dresden
  • , Christel BaierAffiliated withInst. for Theoretical Comp. Sc., Technical University Dresden

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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.


Binary Decision Diagrams and their algorithms Quantitative verification of systems Symbolic data structures for performance analysis