Title
Hierarchical Set Decision Diagrams and Automatic Saturation
Abstract
Shared decision diagram representations of a state-space have been shown to provide efficient solutions for model-checking of large systems. However, decision diagram manipulation is tricky, as the construction procedure is liable to produce intractable intermediate structures (a.k.a peak effect). The definition of the so-called saturation method has empirically been shown to mostly avoid this peak effect, and allows verification of much larger systems. However, applying this algorithm currently requires deep knowledge of the decision diagram data-structures, of the model or formalism manipulated, and a level of interaction that is not offered by the API of public DD packages.Hierarchical Set Decision Diagrams (SDD) are decision diagrams in which arcs of the structure are labeled with sets, themselves stored as SDD. This data structure offers an elegant and very efficient way of encoding structured specifications using decision diagram technology. It also offers, through the concept of inductive homomorphisms, unprecedented freedom to the user when defining the transition relation. Finally, with very limited user input, the SDD library is able to optimize evaluation of a transition relation to produce a saturation effect at runtime. We further show that using recursive folding, SDD are able to offer solutions in logarithmic complexity with respect to other DD. We conclude with some performances on well known examples.
Year
DOI
Venue
2008
10.1007/978-3-540-68746-7_16
Petri Nets
Keywords
Field
DocType
decision diagram manipulation,shared decision diagram representation,hierarchical set decision diagrams,decision diagram technology,decision diagram data-structures,automatic saturation,transition relation,saturation effect,decision diagram,data structure,sdd library,peak effect,model checking,saturation,state space
Discrete mathematics,Data structure,Decision tree,Model checking,Computer science,Algorithm,Theoretical computer science,Influence diagram,Homomorphism,Logarithm,Recursion,Encoding (memory)
Conference
Volume
ISSN
Citations 
5062
0302-9743
14
PageRank 
References 
Authors
0.83
14
3
Name
Order
Citations
PageRank
Alexandre Hamez1503.61
Yann Thierry-Mieg222518.17
Fabrice Kordon360361.72