Abstract
Ordered binary decision diagrams (OBDDs) are one of the most common dynamic data structures for Boolean functions. Nevertheless, many basic graph problems are known to be PSPACE-hard if their input graphs are represented by OBDDs. Despite the hardness results there are not many concrete nontrivial lower bounds known for the complexity of problems on OBDD-represented graph instances. Computing the set of vertices that are reachable from some predefined vertex s ∈ V in a directed graph G = (V,E) is an important problem in computer-aided design, hardware verification, and model checking. Until now only exponential lower bounds on the space complexity of a restricted class of OBDD-based algorithms for the reachability problem have been known. Here, the result is extended by presenting an exponential lower bound on the space complexity of an arbitrary OBDD-based algorithm for the reachability problem. As a by-product a general exponential lower bound is obtained for the computation of OBDDs representing all connected node pairs in a graph, the transitive closure.
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Bollig, B. (2010). Symbolic OBDD-Based Reachability Analysis Needs Exponential Space. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11266-9_19
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DOI: https://doi.org/10.1007/978-3-642-11266-9_19
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