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**1 - 2**of**2**### Finding Compact BDDs Using Genetic Programming

"... Abstract. Binary Decision Diagrams (BDDs) can be used to design multiplexor based circuits. Unfortunately, the most commonly used kind of BDDs – ordered BDDs – has exponential size in the number of variables for many functions. In some cases, more general forms of BDDs are more compact. In constrast ..."

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Abstract. Binary Decision Diagrams (BDDs) can be used to design multiplexor based circuits. Unfortunately, the most commonly used kind of BDDs – ordered BDDs – has exponential size in the number of variables for many functions. In some cases, more general forms of BDDs are more compact. In constrast to the minimization of OBDDs, which is well understood, there are no heuristics for the construction of compact BDDs up to today. In this paper we show that compact BDDs can be constructed using Genetic Programming. 1

### On the OBDD Size for Graphs of Bounded Tree- and Clique-Width

"... Abstract. We study the size of OBDDs (ordered binary decision diagrams) for representing the adjacency function fG of a graph G on n vertices. Our results are as follows:- for graphs of bounded tree-width there is an OBDD of size O(log n) for fG that uses encodings of size O(log n) for the vertices; ..."

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Abstract. We study the size of OBDDs (ordered binary decision diagrams) for representing the adjacency function fG of a graph G on n vertices. Our results are as follows:- for graphs of bounded tree-width there is an OBDD of size O(log n) for fG that uses encodings of size O(log n) for the vertices;- for graphs of bounded clique-width there is an OBDD of size O(n) for fG that uses encodings of size O(n) for the vertices;- for graphs of bounded clique-width such that there is a reduced term for G (to be defined below) that is balanced with depth O(log n) there is an OBDD of size O(n) for fG that uses encodings of size O(log n) for the vertices;- for cographs, i.e. graphs of clique-width at most 2, there is an OBDD of size O(n) for fG that uses encodings of size O(log n) for the vertices. This last result improves a recent result by Nunkesser and Woelfel [14]. 1