Hierarchical Set Decision Diagrams and Automatic Saturation

Abstract

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.

Symbolic Model Checking of Stutter-Invariant Properties Using Generalized Testing Automata

“…The algorithms presented in this paper can be implemented using any kind of decision diagram (such as OBDD), but use of the SDD software library allows to easily benefit from the automatic saturation mechanism described in [12].…”

“…Each cluster typically only reads or writes a limited subset consisting of k ≤ k variables, called the support of the cluster. During the least fixpoint computing the reachable states, saturation technique consists in reordering [12] the evaluation of ("local" fixed-points on) clusters in order to avoid the construction of (useless) intermediate Decision Diagram nodes.…”

“…Since all states in the TGTA have a stuttering self-loop, T / 0 does not depend on the TGTA state. In practice, the predicate equal(q, q ) is an identity relation for variable q [5] and is simplified away (i.e., the term T / 0 can be applied to a decision diagram without consulting or updating the variable q [12]). Hence q is not part of the clusters supports in T / 0 (while q is part of the clusters supports in T * ).…”

Self-Loop Aggregation Product — A New Hybrid Approach to On-the-Fly LTL Model Checking

“…ITS are essentially an abstract interface for (a variant of) labeled transition systems, and several input formalisms are supported (discrete time Petri nets, automata, and compositions thereof). SDD are a particular type of decision diagram that a) allow hierarchy in the state encoding, yielding smaller representations, b) support rewriting rules that allow the library to automatically [11] apply the symbolic saturation algorithm [3]. These features allow the SDD/ITS package to offer very competitive performance.…”

AlPiNA: An Algebraic Petri Net Analyzer

“…For example, all the places of a Petri net that represent a process and its resources are grouped together. In this case, the cluster is called a topological cluster [9] since it is solely based on the Petri net topology. In high-level Petri nets, because of the level of abstraction, places can represent classes of similar processes and resources.…”