Abstract
We present a data structure for Boolean functions, which we call Parity-OBDDs or POBDDs, which combines the nice algorithmic properties of the well-known ordered binary decision diagrams (OBDDs) with a considerably larger descriptive power.
Beginning from an algebraic characterization of the POBDD-complexity we prove in particular that the minimization of the number of nodes, the synthesis, and the equivalence test for POBDDs, which are the fundamental operations for circuit verification, have efficient deterministic solutions.
Several functions of pratical interest, i.e. the storage access function, have exponential ODBB-size but are of polynomial size if POBDDs are used.
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References
M. Ajtai, L. Babai, P. Hajnal, J. Komlos, P. Pudlak, V. Rödel, E. Semeredi, and G. Turan, Two lower bounds for branching programs, in: Proc. 18th ACM STOC 1986, pp. 30–38.
B. Becker, R. Drechsler, How many decomposition types do we need?, in: Proc. of the European Design and Test Conference, pp. 438–443, 1995.
B. Bollig, M. Löbbing, M. Sauerhoff, I. Wegener, Complexity theoretical aspects of OFDDs, in: Proc. of the Workshop on Applications of the Reed-Muller Expansion in Circuit Design, IFIP WG 10.5, pp. 198–205, 1995.
Y. Breitbart, H. B. Hunt, D. Rosenkrantz, The size of binary decision diagrams representing Boolean functions, preprint.
R. E. Bryant, Graph-based algorithms for Boolean function manipulation, IEEE Trans. on Computers 1986, 35, pp. 677–691.
R. E. Bryant, On the complexity of VLSI implementations of Boolean functions with applications to integer multiplication, IEEE Trans. on Computers 1991, 40, pp. 205–213.
R. E. Bryant, Symbolic Boolean manipulation with ordered binary decision diagrams, ACM Comp. on Surveys 1992, 24, pp. 293–318.
J. Gergov, Ch. Meinel, Mod-2-OBDDs — a data structure that generalizes EXOR-Sum-of-Products and Ordered Binary Decision Diagrams, Formal Methods in System Design 1996, 8, pp. 273–282.
M. Krause, Separating ⊕L from L. NL, co-NL and AL (=P) for Oblivious Turing Machines of Linear Access Time in: Proc. Mathematical Foundations of Computer Science 1990, Lecture Notes in Computer Science 452 pp. 385–391.
M. Krause, St. Waack, On oblivious branching programs of linear length, Information and Computation 1991, 94, pp. 232–249.
K. Kriegel, St. Waack, Lower bounds on the complexity of real-time branching programs, RAIRO Theor. Inform. Appl. 1988, 22, pp. 447–459.
D. Sieling, I. Wegener, Reductions of OBDDs in linear time, Information Processing Lettres 1993, 48, pp. 139–144.
I. Wegener, Efficient data structures for Boolean functions, Discrete Mathematics 1994, 136, pp. 347–372.
S. Zák, An exponential lower bound for read-once branching programs, in: Proc. 11th MFCS 1984, Lecture Notes in Computer Sci. 176, Springer-Verlag 1984, pp. 562–566.
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© 1997 Springer-Verlag Berlin Heidelberg
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Waack, S. (1997). On the descriptive and algorithmic power of parity ordered binary decision diagrams. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023460
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DOI: https://doi.org/10.1007/BFb0023460
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