How many decomposition types do we need? [decision diagrams]

Decision Diagrams (DDs) are used in many applications in CAD. Various types of DDs, e.g. BDDs, FDDs, KFDDs, differ by their decomposition types. In this paper we investigate the different decomposition types and prove that there are only three that really help to reduce the size of DDs.<<ETX>>

[1]  Ingo Wegener,et al.  On the complexity of branching programs and decision trees for clique functions , 1988, JACM.

[2]  Randal E. Bryant,et al.  Symbolic Boolean manipulation with ordered binary-decision diagrams , 1992, CSUR.

[3]  Jacob A. Abraham,et al.  IBDDs: an efficient functional representation for digital circuits , 1992, [1992] Proceedings The European Conference on Design Automation.

[4]  Marek A. Perkowski The generalized orthonormal expansion of functions with multiple-valued inputs and some of its applications , 1992, [1992] Proceedings The Twenty-Second International Symposium on Multiple-Valued Logic.

[5]  Wolfgang Rosenstiel,et al.  Multilevel logic synthesis based on functional decision diagrams , 1992, [1992] Proceedings The European Conference on Design Automation.

[6]  Rolf Drechsler,et al.  Synthesis for testability: circuits derived from ordered Kronecker functional decision diagrams , 1995, Proceedings the European Design and Test Conference. ED&TC 1995.

[7]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[8]  Albert R. Wang,et al.  Logic verification using binary decision diagrams in a logic synthesis environment , 1988, [1988] IEEE International Conference on Computer-Aided Design (ICCAD-89) Digest of Technical Papers.

[9]  Rolf Drechsler,et al.  Sympathy: fast exact minimization of fixed polarity Reed-Muller expressions for symmetric functions , 1995, EDTC '95.

[10]  Randal E. Bryant,et al.  Efficient implementation of a BDD package , 1991, DAC '90.

[11]  Jerry R. Burch,et al.  Using bdds to verify multipliers , 1991, 28th ACM/IEEE Design Automation Conference.

[12]  Rolf Drechsler,et al.  Sympathy: fast exact minimization of fixed polarity Reed-Muller expressions for symmetric functions , 1995, Proceedings the European Design and Test Conference. ED&TC 1995.

[13]  Rolf Drechsler,et al.  On the Relation Betwen BDDs and FDDs , 1995, LATIN.

[14]  Rolf Drechsler,et al.  Efficient Representation and Manipulation of Switching Functions Based on Ordered Kronecker Functional Decision Diagrams , 1994, 31st Design Automation Conference.

[15]  R. Rudell Dynamic variable ordering for ordered binary decision diagrams , 1993, ICCAD 1993.

[16]  Tsutomu Sasao EXMIN2: a simplification algorithm for exclusive-OR-sum-of-products expressions for multiple-valued-input two-valued-output functions , 1993, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[17]  Tsutomu Sasao,et al.  Logic Synthesis and Optimization , 1997 .

[18]  Richard Rudell Dynamic variable ordering for ordered binary decision diagrams , 1993, ICCAD.

[19]  Seh-Woong Jeong,et al.  Extended BDD's: trading off canonicity for structure in verification algorithms , 1991, 1991 IEEE International Conference on Computer-Aided Design Digest of Technical Papers.

[20]  Rolf Drechsler,et al.  On the Relation between BDDs and FDDs , 1995, Inf. Comput..

[21]  Malgorzata Marek-Sadowska,et al.  Boolean Matching Using Generalized Reed-Muller Forms , 1994, 31st Design Automation Conference.

[22]  Bernd Becker,et al.  Fast OFDD based minimization of fixed polarity Reed-Muller expressions , 1994, EURO-DAC '94.

[23]  Randal E. Bryant,et al.  On the Complexity of VLSI Implementations and Graph Representations of Boolean Functions with Application to Integer Multiplication , 1991, IEEE Trans. Computers.