A Quaternary Decision Diagram Machine and the Optimization of its Code

We show the advantage of Quarternary Decision Diagrams (QDDs) in representing and evaluating logic functions. That is, we show how QDDs are used to implement QDD machines, which yield high-speed implementations. We compare QDD machines with binary decision diagram (BDD) machines, and show a speed improvement of 1.28-2.02 times when QDDs are chosen. We consider 1-and 2-address BDD machines, and 3- and 4-address QDD machines, and we show a method to minimize the number of instructions.

[1]  Tiziano Villa,et al.  Multi-valued decision diagrams: theory and applications , 1998 .

[2]  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).

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

[4]  Raymond T. Boute,et al.  The binary decision machine as programmable controller , 1976 .

[5]  Tsutomu Sasao,et al.  Average path length of binary decision diagrams , 2005, IEEE Transactions on Computers.

[6]  Tsutomu Sasao,et al.  Implementation of multiple-output functions using PQMDDs , 2000, Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000).

[7]  Shinobu Nagayama,et al.  On the optimization of heterogeneous MDDs , 2005, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[8]  Wai-Kai Chen.  Logic Design , 2007 .

[9]  Paul J. Zsombor-Murray,et al.  Advances in binary decision based programmable controllers , 1988 .

[10]  Tsutomu Sasao,et al.  A hardware simulation engine based on decision diagrams , 2000, Proceedings 2000. Design Automation Conference. (IEEE Cat. No.00CH37106).

[11]  Tho Le-Ngoc,et al.  Binary-Decision-Based Programnmable Controllers , 1983, IEEE Micro.

[12]  Christopher R. Clare.  Designing logic systems using state machines , 1973 .

[13]  Tsutomu Sasao,et al.  A PC-Based Logic Simulator Using a Look-Up Table Cascade Emulator , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[14]  Tsutomu Sasao,et al.  Evaluation of multiple-output logic functions using decision diagrams , 2003, ASP-DAC '03.

[15]  David H. Green,et al.  Modern logic design , 1986 .

[16]  Jean-Pierre Deschamps,et al.  Digital systems, with algorithm implementation , 1983 .

[17]  Tsutomu Sasao,et al.  A Parallel Branching Program Machine for Emulation of Sequential Circuits , 2009, ARC.

[18]  Rajeev Murgai,et al.  Logic synthesis for a single large look-up table , 1995, Proceedings of ICCD '95 International Conference on Computer Design. VLSI in Computers and Processors.

[19]  Sharad Malik,et al.  Fast functional simulation using branching programs , 1995, ICCAD.

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

[21]  Shinobu Nagayama,et al.  Area-Time Complexities of Multi-Valued Decision Diagrams , 2004 .

[22]  Paul J. Zsombor-Murray,et al.  Binary- Decision -Based Programmable Controllers Part I , 1983 .

[23]  Shigeki Iwata.  Programs with Minimal Goto Statements , 1978, Inf. Control..

[24]  Nagisa Ishiura,et al.  Shared binary decision diagram with attributed edges for efficient Boolean function manipulation , 1990, 27th ACM/IEEE Design Automation Conference.

[25]  Daniel Mange,et al.  A High-Level-Language Programmable Controller , 1986, IEEE Micro.

[26]  Rolf Drechsler,et al.  Functional simulation using binary decision diagrams , 1997, 1997 Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[27]  A.L. Sangiovanni-Vincentelli,et al.  Fast discrete function evaluation using decision diagrams , 1995, Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[28]  Daniel Mange.  A High-Level-Language Programmable Controller, Part I-A Controller for Structured Microprogramming , 1986, IEEE Micro.

[29]  Nakahara Hiroki,et al.  Emulation of Sequential Circuits by a Parallel Branching Program Machine , 2009 .