2015
DOI: 10.1007/s00224-015-9657-x
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On the Minimization of (Complete) Ordered Binary Decision Diagrams

Abstract: Ordered binary decision diagrams (OBDDs) are a popular data structure for Boolean functions. Some applications work with a restricted variant called complete OBDDs which is strongly related to nonuniform deterministic finite automata. One of its complexity measures is the width which has been investigated in several areas in computer science like machine learning, property testing, and the design and analysis of implicit graph algorithms. For a given function the size and the width of a (complete) OBDD is very… Show more

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Cited by 9 publications
(6 citation statements)
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“…Our algorithm for width minimization of ODDs parameterized by width naturally can be used to minimize the width of ordered binary decision diagrams (OBDDs), since OBDDs with a fixed variable ordering correspond to ODDs over a binary alphabet. Width minimization problems for OBDDs have been considered before in the literature [3,4], but previously known algorithms are exponential on the size of the OBDD even for OBDDs of constant width, and even in the case of when one is not allowed to vary the order of the input variables. Our FPT result shows that width minimization for OBDDs of constant width with a fixed variable ordering can be achieved in polynomial time.…”
Section: Main Technical Tool Letmentioning
confidence: 99%
“…Our algorithm for width minimization of ODDs parameterized by width naturally can be used to minimize the width of ordered binary decision diagrams (OBDDs), since OBDDs with a fixed variable ordering correspond to ODDs over a binary alphabet. Width minimization problems for OBDDs have been considered before in the literature [3,4], but previously known algorithms are exponential on the size of the OBDD even for OBDDs of constant width, and even in the case of when one is not allowed to vary the order of the input variables. Our FPT result shows that width minimization for OBDDs of constant width with a fixed variable ordering can be achieved in polynomial time.…”
Section: Main Technical Tool Letmentioning
confidence: 99%
“…This transduction simulates the process of merging equivalent states in a ODD. 4. nor is a functional 2 log -regular -transduc tion that sends each deterministic, complete ODD to its normalized version .…”
Section: Proof Of the Canonization As Transduction Theoremmentioning
confidence: 99%
“…verification phase, the NuSMV reads the generated code and transforms it into a flat hierarchical model. Then, the existing variables are encoded for constructing Ordered Binary Decision Diagram (OBDD) [75] platform. Finally, the constructed model is built for checking the behavioral correctness of the system.…”
Section: Definition 3 a Labeled Transition System Lt Is A 4-tuple Lt mentioning
confidence: 99%