Spectral Interpretation of Decision Diagrams

* Signals * Algebraic structures for signal processing * Further readings in discrete functions * Spectral techniques * Spectral transforms * Further readings in Fourier analysis on groups * Spectral interpretation of DDs * Further readings in decision diagrams * DDs and order of variables * Further readings in optimization of DD by variables ordering * Free BDDs * Further readings in free BDDs * Word-level DDs * Spectral interpretation of edge-valued DDs * Spectral interpretation of TDDs * Further readings in ternary DDs * Spectral interpretation of optimization of DDs * Group-theoretic approach to optimization of DDs * Further readings in DD on finite groups * Closing remarks * References * Index

[1]  Svetlana Yanushkevich,et al.  Edge - Valued Decision Diagrams , 2005 .

[2]  E. Macii,et al.  Using symbolic Rademacher-Walsh spectral transforms to evaluate the agreement between Boolean functions , 1996 .

[3]  Tsutomu Sasao,et al.  A method to represent multiple-output switching functions by using multi-valued decision diagrams , 1996, Proceedings of 26th IEEE International Symposium on Multiple-Valued Logic (ISMVL'96).

[4]  Chip-Hong Chang,et al.  Paired Haar spectra computation through operations on disjoint cubes , 1999 .

[5]  R. Drechsler,et al.  Overview of decision diagrams , 1997 .

[6]  S. Rahardja,et al.  Family of unified complex Hadamard transforms , 1999 .

[7]  R. Stankovic.  A Note of the Relation between Reed-Muller Expansions and Walsh Transforms , 1982, IEEE Transactions on Electromagnetic Compatibility.

[8]  Bogdan J. Falkowski,et al.  Identification of Boolean symmetries in spectral domain of Reed-Muller transform , 1999 .

[9]  Radomir S. Stankovic.  Some remarks about spectral transform interpretation of MTBDDs and EVBDDs , 1995, ASP-DAC '95.

[10]  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.

[11]  M. Kline.  Mathematical Thought from Ancient to Modern Times , 1972 .

[12]  J. Seberry,et al.  Hadamard matrices, Sequences, and Block Designs , 1992 .

[13]  Rolf Drechsler,et al.  Fast and Efficient Equivalence Checking based on NAND-BDDs , 2001 .

[14]  S. Rahardja,et al.  Efficient algorithm to calculate Reed-Muller expansions over GF(4) , 2001 .

[15]  Bogdan J. Falkowski,et al.  Analysis of disjoint decomposition of balanced Boolean functions through the Walsh spectrum , 2001 .

[16]  Rolf Drechsler,et al.  Binary Decision Diagrams - Theory and Implementation , 1998 .

[17]  Elena Dubrova,et al.  On disjoint covers and ROBDD size , 1999, 1999 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM 1999). Conference Proceedings (Cat. No.99CH36368).

[18]  Rolf Drechsler,et al.  OKFDDs — Algorithms, Applications and Extensions , 1996 .

[19]  Shin-ichi Minato,et al.  Graph-Based Representations of Discrete Functions , 1996 .

[20]  Tsutomu Sasao.  And-Exor Expressions and their Optimization , 1993 .

[21]  Chip-Hong Chang,et al.  Haar spectra-based entropy approach to quasi-minimisation of FBDDs , 1999 .

[22]  Masahiro Fujita,et al.  Spectral Transforms for Large Boolean Functions with Applications to Technology Mapping , 1993, 30th ACM/IEEE Design Automation Conference.

[23]  Bogdan J. Falkowski,et al.  Relationship between arithmetic and Haar wavelet transforms in the form of layered Kronecker matrices , 1999 .

[24]  Claudio Moraga,et al.  Readings in Fourier Analysis on Finite Non-Abelian Groups , 1999 .

[25]  Marek Perkowski,et al.  A fast computer implementation of adding and arithmetic multi-polarity transforms for logic design , 1991, [1991] Proceedings of the 34th Midwest Symposium on Circuits and Systems.

[26]  Radomir S. Stankovic,et al.  Decision diagrams for discrete functions: classification and unified interpretation , 1998, Proceedings of 1998 Asia and South Pacific Design Automation Conference.

[27]  C. R. Edwards.  The generalised dyadic differentiator and its application to 2-valued functions defined on an n-space , 1978 .

[28]  Marek Perkowski,et al.  Generation of adding and arithmetic multi-polarity transforms for incompletely specified boolean functions , 1992 .

[29]  Radomir S. Stankovic,et al.  A discussion on the history of research in arithmetic andReed-Muller expressions , 2001, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[30]  Tsutomu Sasao.  A transformation of multiple-valued input two-valued output functions and its application to simplification of exclusive-or sum-of-products expressions , 1991, [1991] Proceedings of the Twenty-First International Symposium on Multiple-Valued Logic.

[31]  J. E. Gibbs.  Transmission of Information by Orthogonal Functions , 1970 .

[32]  D. Michael Miller.  Spectral transformation of multiple-valued decision diagrams , 1994, Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94).

[33]  Don H. Johnson,et al.  Gauss and the history of the fast Fourier transform , 1985 .

[34]  J. Walsh.  A Closed Set of Normal Orthogonal Functions , 1923 .

[35]  Svetlana Yanushkevich,et al.  Logic differential calculus in multi-valued logic design , 1998 .

[36]  Tsutomu Sasao,et al.  Shared multiple-valued decision diagrams for multiple-output functions , 1999, Proceedings 1999 29th IEEE International Symposium on Multiple-Valued Logic (Cat. No.99CB36329).

[37]  Chip-Hong Chang,et al.  Mutual conversions between generalised arithmetic expansions and free binary decision diagrams , 1998 .

[38]  Dragan Jankovic,et al.  Quaternion groups versus dyadic groups in representations and processing of switching functions , 1999, Proceedings 1999 29th IEEE International Symposium on Multiple-Valued Logic (Cat. No.99CB36329).

[39]  Tsutomu Sasao,et al.  A design method for look-up table type FPGA by pseudo-Kronecker expansion , 1994, Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94).

[40]  Jaakko Astola,et al.  Edge-valued decision diagrams for multiple-valued functions , 2004, Proceedings. 34th International Symposium on Multiple-Valued Logic.

[41]  Chip-Hong Chang,et al.  Hadamard–Walsh spectral characterization of Reed–Muller expansions , 1999 .

[42]  R. I. Bahar,et al.  Algebraic decision diagrams and their applications , 1993, Proceedings of 1993 International Conference on Computer Aided Design (ICCAD).

[43]  Radomir S. Stankovic,et al.  Foundations for Applications of Gibbs Derivatives in Logic Design and VLSI , 2002, VLSI Design.

[44]  Tsutomu Sasao.  Input VariableAssignment andOutput PhaseOptimization ofPLA's , 1984 .

[45]  Christoph Meinel,et al.  Efficient Boolean Manipulation With OBDD's can be Extended to FBDD's , 1994, IEEE Trans. Computers.

[46]  Shuzo Yajima,et al.  Efficient construction of binary moment diagrams for verifying arithmetic circuits , 1995, Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[47]  H. Rademacher,et al.  Einige Sätze über Reihen von allgemeinen Orthogonalfunktionen , 1922 .

[48]  L.A.M. Bennett.  Synthesis of multioutput logic networks using spectral techniques , 1995 .

[49]  M. Sekine,et al.  Synthesis by spectral translation using Boolean decision diagrams , 1996, 33rd Design Automation Conference Proceedings, 1996.

[50]  Chip-Hong Chang,et al.  Properties and applications of paired Haar transform , 1997, Proceedings of ICICS, 1997 International Conference on Information, Communications and Signal Processing. Theme: Trends in Information Systems Engineering and Wireless Multimedia Communications (Cat..

[51]  Yung-Te Lai,et al.  Edge-valued binary decision diagrams for multi-level hierarchical verification , 1992, DAC '92.

[52]  S. Rahardja,et al.  Efficient computation of quaternary fixed polarity Reed-Muller expansions , 1995 .

[53]  Stanley L. Hurst.  The logical processing of digital signals , 1978 .

[54]  Bogdan J. Falkowski,et al.  A Note on the Polynomial Form of Boolean Functions and Related Topics , 1999, IEEE Trans. Computers.

[55]  Stanley L. Hurst,et al.  Spectral techniques in digital logic , 1985 .

[56]  Ingo Wegener,et al.  Optimal ordered binary decision diagrams for read-once formulas , 2000, Discret. Appl. Math..

[57]  C. K. Yuen.  Walsh Functions and Gray Code , 1971 .

[58]  A. Haar.  Zur Theorie der orthogonalen Funktionensysteme , 1910 .

[59]  Susanto Rahardja,et al.  Classifications and graph-based representations of switching functions using a novel complex spectral technique , 1997 .

[60]  Tsutomu Sasao,et al.  Ternary Decision Diagrams and their Applications , 1996 .

[61]  R. Stankovic,et al.  Calculation of the Gibbs derivatives on finite Abelian groups through the decision diagrams , 1998 .

[62]  H. E. Chrestenson.  A class of generalized Walsh functions , 1955 .

[63]  Radomir S. Stankovic,et al.  Fibonacci Decision Diagrams , 2005 .

[64]  E. C. Tan,et al.  Fast tabular technique for fixed-polarity Reed-Muller logic with inherent parallel processes , 1998 .

[65]  Claudio Moraga,et al.  From Fourier Expansions to Arithmetic-Haar Expressions on Quaternion Groups , 2001, Applicable Algebra in Engineering, Communication and Computing.

[66]  Claudio Moraga,et al.  Spectral Transform Decision Diagrams , 1996 .

[67]  Fabio Somenzi,et al.  Efficient manipulation of decision diagrams , 2001, International Journal on Software Tools for Technology Transfer.

[68]  Tsutomu Sasao.  An application of multiple-valued logic to a design of programmable logic arrays , 1978, MVL '78.

[69]  Rolf Drechsler,et al.  BDD Minimization by Linear Transformations , 1998 .

[70]  Tsutomu Sasao,et al.  Representations of Logic Functions Using EXOR Operators , 1996 .

[71]  R.S. Stankovic.  Matrix-valued EXOR-TDDs in decomposition of switching functions , 1999, Proceedings 1999 29th IEEE International Symposium on Multiple-Valued Logic (Cat. No.99CB36329).

[72]  Marek Perkowski,et al.  One more way to calculate generalized Reed-Muller expansions of boolean functions , 1991 .

[73]  David E. Muller,et al.  Application of Boolean algebra to switching circuit design and to error detection , 1954, Trans. I R E Prof. Group Electron. Comput..

[74]  Susanto Rahardja,et al.  Fast Linearly Independent Arithmetic Expansions , 1999, IEEE Trans. Computers.

[75]  Tsutomu Sasao.  Optimization of Pseudo-Kronecker Expressions Using Multiple-Place Decision Diagrams , 1993 .

[76]  Liu Zhihua,et al.  Introduction to Bridge Functions , 1983, IEEE Transactions on Electromagnetic Compatibility.

[77]  Tsutomu Sasao,et al.  Exact Minimization of FPRMs Using Multi-Terminal Exor TDDs , 1996 .

[78]  R. Bryant,et al.  Verification of Arithmetic Functions with Binary Moment Diagrams , 1994 .

[79]  Jaakko Astola,et al.  On Generalized Fibonacci Cubes and Unitary Transforms , 1997, Applicable Algebra in Engineering, Communication and Computing.

[80]  Mark G. Karpovsky,et al.  Finite Orthogonal Series in the Design of Digital Devices: Analysis, Synthesis and Optimization , 1976 .

[81]  Henning F. Harmuth,et al.  A generalized concept of frequency and some applications , 1968, IEEE Trans. Inf. Theory.

[82]  Enrico Macii,et al.  Predicting the functional complexity of combinational circuits by symbolic spectral analysis of Boolean functions , 1995, Proceedings of EURO-DAC. European Design Automation Conference.

[83]  Tsutomu Sasao,et al.  Optimization of multiple-valued AND-EXOR expressions using multiple-place decision diagrams , 1992, [1992] Proceedings The Twenty-Second International Symposium on Multiple-Valued Logic.

[84]  Jaakko Astola,et al.  Some remarks on linear transform of variables in representation of adders by word-level expressions and spectral transform decision diagrams , 2002, Proceedings 32nd IEEE International Symposium on Multiple-Valued Logic.

[85]  Fabio Somenzi,et al.  Symmetry detection and dynamic variable ordering of decision diagrams , 1994, ICCAD '94.

[86]  Radomir S. Stankovic,et al.  Spectral Interpretation and Applications of Decision Diagrams , 2000, VLSI Design.

[87]  T Kozlowski,et al.  Unified decision diagrams: a representation for mixed AND-OR/EXOR combinational networks , 1995 .

[88]  Zhang Qishan,et al.  Ordering of Walsh Functions , 1983, IEEE Transactions on Electromagnetic Compatibility.

[89]  Claudio Moraga,et al.  Calculation of Reed-Muller-Fourier coefficients of multiple-valued functions through multiple-place decision diagrams , 1994, Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94).

[90]  W. Rudin,et al.  Fourier Analysis on Groups. , 1965 .

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

[92]  Tsutomu Sasao,et al.  Ternary decision diagrams. Survey , 1997, Proceedings 1997 27th International Symposium on Multiple- Valued Logic.

[93]  Jiunn-Chern Chen,et al.  Equivalence checking of integer multipliers , 2001, Proceedings of the ASP-DAC 2001. Asia and South Pacific Design Automation Conference 2001 (Cat. No.01EX455).

[94]  Ingo Wegener,et al.  Worst case examples for operations on OBDDs , 2000, Inf. Process. Lett..

[95]  Kenneth George Beauchamp,et al.  Applications of Walsh and related functions : with an introduction to sequency theory , 1985 .

[96]  Robert K. Brayton,et al.  BDD minimization by truth table permutations , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[97]  Rolf Drechsler,et al.  Dynamic re-encoding during MDD minimization , 2000, Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000).

[98]  Bogdan J. Falkowski,et al.  Walsh-like functions and their relations , 1996 .

[99]  Claudio Moraga,et al.  Design of Haar wavelet transforms and Haar spectral transform decision diagrams for multiple-valued functions , 2001, Proceedings 31st IEEE International Symposium on Multiple-Valued Logic.

[100]  Rolf Drechsler,et al.  Ternary and quaternary lattice diagrams for linearly-independent logic, multiple-valued logic, and analog synthesis , 1997, Proceedings of ICICS, 1997 International Conference on Information, Communications and Signal Processing. Theme: Trends in Information Systems Engineering and Wireless Multimedia Communications (Cat..

[101]  Sheldon B. Akers,et al.  Binary Decision Diagrams , 1978, IEEE Transactions on Computers.

[102]  Susanto Rahardja,et al.  Application of linearly independent arithmetic transform in testing of digital circuits , 1999 .

[103]  Jochen Bern,et al.  Boolean manipulation with free BDD's. First experimental results , 1994, Proceedings of European Design and Test Conference EDAC-ETC-EUROASIC.

[104]  E. Clarke,et al.  Multi-Terminal Binary Decision Diagrams and Hybrid Decision Diagrams , 1996 .

[105]  J. E. Gibbs.  'Instant' Fourier transform , 1977 .

[106]  Radomir S. Stankovic,et al.  Spectral interpretation of the fast tabular technique for fixed-polarity Reed-Muller expressions , 2000 .

[107]  Claudio Moraga,et al.  Reed-Muller-Fourier versus Galois field representations of four-valued logic functions , 1998, Proceedings. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138).

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

[109]  Chip-Hong Chang,et al.  Forward and Inverse Transformations Between Haar Spectra and Ordered Binary Decision Diagrams of Boolean Functions , 1997, IEEE Trans. Computers.

[110]  Chip-Hong Chang,et al.  Adaptive exact optimisation of minimally testable FPRM expansions , 1998 .

[111]  Takayasu Ito,et al.  A Note on a General Expansion of Functions of Binary Variables , 1968, Inf. Control..

[112]  J. Astola,et al.  Binary polynomial transforms and nonlinear digital filters , 1995 .

[113]  Detlef Sieling.  On the Existence of Polynomial Time Approximation Schemes for OBDD Minimization (Extended Abstract) , 1998, STACS.

[114]  R. Rudell.  Dynamic variable ordering for ordered binary decision diagrams , 1993, Proceedings of 1993 International Conference on Computer Aided Design (ICCAD).

[115]  Marek Perkowski,et al.  A family of all essential Radix-2 addition/subtraction multi-polarity transforms: algorithms and interpretations in Boolean domain , 1990, IEEE International Symposium on Circuits and Systems.

[116]  J.P. Hansen,et al.  Decision diagram based techniques for the Haar wavelet transform , 1997, Proceedings of ICICS, 1997 International Conference on Information, Communications and Signal Processing. Theme: Trends in Information Systems Engineering and Wireless Multimedia Communications (Cat..

[117]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[118]  R. Drechsler,et al.  Generic implementation of DD packages in MVL , 1999, Proceedings 25th EUROMICRO Conference. Informatics: Theory and Practice for the New Millennium.

[119]  Tsutomu Sasao,et al.  An exact minimization algorithm for generalized Reed-Muller expressions , 1994, Proceedings of APCCAS'94 - 1994 Asia Pacific Conference on Circuits and Systems.

[120]  R. S. Stankovic.  Fourier decision diagrams on finite non-Abelian groups with preprocessing , 1997, Proceedings 1997 27th International Symposium on Multiple- Valued Logic.

[121]  Rolf Drechsler,et al.  Minimization of free BDDs , 2002, Integr..

[122]  C. R. Edwards.  The Gibbs Dyadic differentiator and its relationship to the Boolean difference , 1978 .

[123]  Rolf Drechsler,et al.  Decision Diagram Method for Calculation of Pruned Walsh Transform , 2001, IEEE Trans. Computers.

[124]  Radomir S. Stankovic,et al.  FFT and decision diagrams based methods for calculation of spectral transforms , 1997, Proceedings of ICICS, 1997 International Conference on Information, Communications and Signal Processing. Theme: Trends in Information Systems Engineering and Wireless Multimedia Communications (Cat..

[125]  Irving S. Reed,et al.  A class of multiple-error-correcting codes and the decoding scheme , 1954, Trans. IRE Prof. Group Inf. Theory.

[126]  R. Drechsler,et al.  Ordered and shared, linearly-independent, variable-pair decision diagrams , 1997, Proceedings of ICICS, 1997 International Conference on Information, Communications and Signal Processing. Theme: Trends in Information Systems Engineering and Wireless Multimedia Communications (Cat..

[127]  Elena Dubrova,et al.  Generalized Reed-Muller Canonical Form for a Multiple-Valued Algebra , 1996 .

[128]  Kozo Kinoshita,et al.  Conservative Logic Elements and Their Universality , 1979, IEEE Transactions on Computers.

[129]  B. J. Falkowski,et al.  Properties and ways of calculation of multi-polarity generalized Walsh transforms , 1994 .

[130]  Rolf Drechsler,et al.  Circuit design from Kronecker Galois field decision diagrams for multiple-valued functions , 1997, Proceedings 1997 27th International Symposium on Multiple- Valued Logic.

[131]  F. Somenzi,et al.  Who are the variables in your neighbourhood , 1995, Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[132]  Bogdan J. Falkowski,et al.  Algorithm for identifying skew symmetries through Walsh transform , 2000 .

[133]  Philipp W. Besslich.  Determination of the irredundant forms of a Boolean function using Walsh-Hadamard analysis and dyadic groups , 1978 .

[134]  N. Ahmed,et al.  Sequency Theory: Foundations and Applications , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[135]  R. Bryant.  Graph-Based Algorithms for Boolean Function Manipulation12 , 1986 .

[136]  Martin Cohn.  Walsh Functions, Sequency, and Gray Codes , 1971 .

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

[138]  Susanto Rahardja,et al.  Classification and properties of fast linearly independent logic transformations , 1997 .

[139]  Tsutomu Sasao,et al.  On properties of Kleene TDDs , 1997, Proceedings of ASP-DAC '97: Asia and South Pacific Design Automation Conference.

[140]  Radomir S. Stankovic.  Functional decision diagrams for multiple-valued functions , 1995, Proceedings 25th International Symposium on Multiple-Valued Logic.

[141]  C. Moraga.  A decade of spectral techniques , 1991, [1991] Proceedings of the Twenty-First International Symposium on Multiple-Valued Logic.

[142]  Bogdan J. Falkowski,et al.  Complex spectral decision diagrams , 1996, Proceedings of 26th IEEE International Symposium on Multiple-Valued Logic (ISMVL'96).

[143]  D. Michael Miller,et al.  Multiple-valued decision diagrams with symmetric variable nodes , 1996, Proceedings of 26th IEEE International Symposium on Multiple-Valued Logic (ISMVL'96).

[144]  Claudio Moraga,et al.  Spectral techniques in binary and multiple-valued switching theory. A review of results in the decade 1991-2000 , 2001, Proceedings 31st IEEE International Symposium on Multiple-Valued Logic.

[145]  Robert K. Brayton,et al.  Algorithms for discrete function manipulation , 1990, 1990 IEEE International Conference on Computer-Aided Design. Digest of Technical Papers.

[146]  Massoud Pedram,et al.  Edge Valued Binary Decision Diagrams , 1996 .

[147]  S. C. Kleene,et al.  Introduction to Metamathematics , 1952 .

[148]  Rolf Drechsler,et al.  Efficient graph based representation of multi-valued functions with an application to genetic algorithms , 1994, Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94).

[149]  Irving John Good,et al.  The Interaction Algorithm and Practical Fourier Analysis , 1958 .

[150]  Marek A. Perkowski,et al.  Free Kronecker decision diagrams and their application to Atmel 6000 series FPGA mapping , 1994, EURO-DAC '94.

[151]  Tsutomu Sasao,et al.  Switching Theory for Logic Synthesis , 1999, Springer US.

[152]  Randal E. Bryant,et al.  An efficient graph representation for arithmetic circuitverification , 2001, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[153]  Rolf Drechsler,et al.  Efficient manipulation algorithms for linearly transformed BDDs , 1999, 1999 IEEE/ACM International Conference on Computer-Aided Design. Digest of Technical Papers (Cat. No.99CH37051).

[154]  Shin-ichi Minato,et al.  Zero-Suppressed BDDs for Set Manipulation in Combinatorial Problems , 1993, 30th ACM/IEEE Design Automation Conference.

[155]  Chip-Hong Chang,et al.  Generation of quasi-optimal FBDDs through paired Haar spectra , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

[156]  N. M. Blachman.  Sinusoids versus Walsh functions , 1974 .

[157]  Mark G. Karpovsky,et al.  Fast Fourier Transforms on Finite Non-Abelian Groups , 1977, IEEE Transactions on Computers.

[158]  N. Fine.  On the Walsh functions , 1949 .

[159]  Klaus D. Heidtmann,et al.  Arithmetic Spectrum Applied to Fault Detection for Combinational Networks , 1991, IEEE Trans. Computers.

[160]  Rolf Drechsler,et al.  Polynomial Formal Verification of Multipliers , 2003, Formal Methods Syst. Des..

[161]  Glenn Jennings,et al.  Symbolic incompletely specified functions for correct evaluation in the presence of indeterminate input values , 1995, Proceedings of the Twenty-Eighth Annual Hawaii International Conference on System Sciences.

[162]  Rolf Drechsler,et al.  Binary decision diagrams in theory and practice , 2001, International Journal on Software Tools for Technology Transfer.

[163]  Radomir S. Stankovic.  Non-Abelian Groups in Optimization of Decision Diagrams Representations of Discrete Functions , 2001, Formal Methods Syst. Des..

[164]  F. Somenzi,et al.  Linear Sifting Of Decision Diagrams , 1997, Proceedings of the 34th Design Automation Conference.

[165]  Tsutomu Sasao.  Application of multiple-valued logic to a serial decomposition of PLAs , 1989, Proceedings. The Nineteenth International Symposium on Multiple-Valued Logic.

[166]  Bogdan J. Falkowski,et al.  Complex decision diagrams , 1996 .

[167]  E.M. Clarke,et al.  Hybrid decision diagrams. Overcoming the limitations of MTBDDs and BMDs , 1995, Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[168]  Beate Bollig,et al.  Improving the Variable Ordering of OBDDs Is NP-Complete , 1996, IEEE Trans. Computers.

[169]  Rolf Drechsler,et al.  On the construction of multiple-valued decision diagrams , 2002, Proceedings 32nd IEEE International Symposium on Multiple-Valued Logic.

[170]  Sarma Vrudhula,et al.  EVBDD-based algorithms for integer linear programming, spectral transformation, and function decomposition , 1994, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[171]  Jaakko Astola,et al.  Fibonacci decision diagrams and spectral Fibonacci decision diagrams , 2000, Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000).

[172]  Dragomir Z. Dokovic.  Two Hadamard Matrices of Order 956 of Goethals-Seidel Type , 1994, Comb..