Fabio Somenzi. "Binary Decision Diagrams". In Manfred Broy and Ralf Steinbruggen, editors, Calculational System Design, volume 173 of NATO Science Series F: Computer and Systems Sciences, pages 303--366. IOS Press, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of nodes A. They are implemented using the relational product and they have a worst case complexity which is exponential w.r.t. jAj and jGj. In the practical cases the cost of the operations img and preimg even thought acceptable is the crucial one. Thus, in the area of the symbolic algorithms [Som99] the operations img and preimg are referred as symbolic steps and the time complexities of symbolic algorithms are usually expressed as the number of symbolic steps that are performed. 9.1. The Symbolic Rank based Bisimulation Algorithm. In order to de ne a symbolic version of the algorithm ....

F. Somenzi. Binary decision diagrams. In Calculational System Design, volume 173 of NATO Science Series F: Computer and Systems Sciences, pages 303-366. IOS Press, 1999.

....function # S 1 (X) # S 2 (X) # S 3 (X) until the transitive closure of the transition relation is computed. Both the relational product operator and symbolic traversal algorithms are well studied in the symbolic model checking literature, and we refer to that literature for further details [15]. 2.4 Deterministic planning We are not the first to explore the use of decision diagrams in heuristic search. Edelkamp and Re#el [3] describe a symbolic generalization of A , called BDDA , that can solve deterministic planning problems. It uses BDDs to represent sets of states and operators on ....

Somenzi, F.: Binary decision diagrams. In Broy, M., Steinbruggen, R., eds.: Calculational System Design. Volume 173 of NATO Science Series F: Computer and Systems Sciences. IOS Press (1999) 303--366

....there is precisely one MDD representation of a function. This allows for constant time checking of function equality. Algorithms for manipulating BDDs are extensible to the multi valued case, provided they do not use optimizations that depend on a two valued boolean logic (e.g. complemented edges [Somenzi, 1999]) The differences are discussed in [Chechik et al. 2001a] The public methods required for model checking are: #####, to construct an MDD based on a function table; #####, to compute ## # and # of MDDs; ########, to existentially quantify over the primed variables; and ###### to retrieve the ....

Fabio Somenzi. "Binary Decision Diagrams ". In Manfred Broy and Ralf Steinbruggen, editors, Calculational System Design, volume 173 of NATO Science Series F: Computer and Systems Sciences, pages 303--366. IOS Press, 1999.

....So # # is replaced with the terminal node F#M = M, and # # with the terminal node F#M#T=T. In general, algorithms for manipulating BDDs are easily extensible to the multivalued case, provided they do not use any optimizations that depend on a two valued boolean logic (e.g. complemented edges [20]) The differences are discussed below. function ################ ######### find (create if not found) a node # s.t. ########### # ### ##### # ############### return # function ########(#, #) existentially quantifies over all variables # # with # # #. if ###### ## then foreach # ## ....

F. Somenzi. "Binary Decision Diagrams". In Manfred Broy and Ralf Steinbruggen, editors, Calculational System Design, vol 173 of NATO Science Series F: Computer and Systems Sciences, pp 303--366. IOS Press, 1999.

....problem in terms of efficient operations on MBTDDs, we can further improve the running times by reusing existing symbolic model checking technology. In particular, we can further optimize the MBTDD negation operation (to jJ (L)j) by using complement arcs, as in Somenzi s CUDD library [28]. The use of join irreducibility to optimize our algorithms introduces an important restriction on the logics that we can use in the model checker. We originally chose to restrict ourselves to logics whose values form a quasi boolean lattice, as these logics behave similarly to classical logic, ....

Fabio Somenzi. "Binary Decision Diagrams". In Manfred Broy and Ralf Steinbruggen, editors, Calculational System Design, volume 173 of NATO Science Series F: Computer and Systems Sciences, pages 303--366. IOS Press, 1999.

....So f 1 is replaced with the terminal node F M = M, and f 2 with the terminal node F M T = T. Algorithms for manipulating BDDs are extensible to the multi valued case very simply, provided they do not use any optimizations that depend on a two valued boolean logic (e.g. complemented edges [21]) The differences are discussed in [6] The public methods required for model checking are: Build, to construct an MDD based on a function table; Apply, to compute ; and : of MDDs; Quantify, to existentially quantify over the primed variables; and AllSat to retrieve the computed partition P ....

F. Somenzi. Binary Decision Diagrams. In M. Broy and R. Steinbruggen, editors, Calculational System Design, volume 173 of NATO Science Series F: Computer and Systems Sciences, pages 303366. IOS Press, 1999.

....problem in terms of efficient operations on MBTDDs, we can further improve the running times by reusing existing symbolic model checking technology. In particular, we can further optimize the MBTDD negation operation (to jJ (L)j) by using complement arcs, as in Somenzi s CUDD library [12]. The use of join irreducibility to optimize our algorithms introduces an important restriction on the logics that we can use in the model checker. We originally chose to restrict ourselves to logics whose values form a quasi boolean lattice, as these logics behave similarly to classical logic, ....

Fabio Somenzi. "Binary Decision Diagrams". In Manfred Broy and Ralf Steinbruggen, editors, Calculational System Design, volume 173 of NATO Science Series F: Computer and Systems Sciences, pages 303--366. IOS Press, 1999.

....1 is replaced with the terminal node F M = M, and f 2 with the terminal node F M T = T. In general, algorithms for manipulatingBDDs are extensible to the multi valuedcase very simply, provided they do not use any optimizations that depend on a two valued boolean logic (e.g. complemented edges [20]) The differences are discussed below. The most used method in an MDD (or BDD) library is MakeUnique, defined in Figure 5. This guarantees uniqueness and thus reducedness [21] MakeUnique is not a public method, but it is used by most of the public methods. The public methods required for model ....

F. Somenzi. "Binary Decision Diagrams". In M. Broy and R. Steinbruggen, editors, Calculational System Design, volume 173 of NATO Science Series F: Computer and Systems Sciences, pages 303--366. IOS Press, 1999.

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Fabio Somenzi. "Binary Decision Diagrams". In Manfred Broy and Ralf Steinbruggen, editors, Calculational System Design, volume 173 of NATO Science Series F: Computer and Systems Sciences, pages 303--366. IOS Press, 1999.

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