@MISC{WALLACE.MIZ,
  AUTHOR = {Wasaki, Katsumi},
 TITLE = {Stability of the 7-3 Compressor Circuit for {W}allace Tree. Part {I}},
  NOTE = {This work has been partially supported by the JSPS KAKENHI Grant Number
   19K11821, Japan.},
  SECTION1 = {Properties of `Intermediate' STC Circuit Structure (LAYER-I)},
  SECTION2 = {Properties of `Intermediate' STC Circuit Structure (LAYER-II)},
  SECTION3 = {Properties of STC Circuit Structure (LAYER-III)},
  DAY = {30},
  MONTH = {December},
  YEAR = {2019},
  ADDRESS1 = {Shinshu University, Nagano, Japan},
  SUMMARY = {To evaluate our formal verification method on a real-size
  calculation circuit, in this article, we continue to formalize the
  concept of the 7-3 Compressor (STC) Circuit \cite{Mehta:1991} for Wallace
  Tree \cite{Wallace:1964}, to define the structures of calculation units
  for a very fast multiplication algorithm for VLSI implementation
  \cite{Vuillemin:1983}. We define the circuit structure of the tree
  constructions of the Generalized Full Adder Circuits (GFAs). We then
  successfully prove its circuit stability of the calculation outputs
  after four and six-steps. The motivation for this research is to establish
  a technique based on formalized mathematics and its applications for
  calculation circuits with high reliability, and to implement the
  applications of the reliable logic synthesizer and hardware compiler
  \cite{Iwasaki:2008}}}

@inproceedings{Mehta:1991,
 author={Mayur Mehta and Vijay Parmar and Earl Swartzlander},
 booktitle={Proceedings 10th IEEE Symposium on Computer Arithmetic},
 title={High-speed Multiplier Design using Multi-input Counter and Compressor Circuits},
 year={1991},
 volume={},
 number={},
 pages={43-50},
 doi={10.1109/ARITH.1991.145532},
 ISSN={},
 month={June},
}

@article{Wallace:1964,
 author={Christopher Stewart Wallace},
 journal={IEEE Transactions on Electronic Computers},
 title={A Suggestion for a Fast Multiplier},
 year={1964},
 volume={EC-13},
 number={1},
 pages={14-17},
 doi={10.1109/PGEC.1964.263830},
 ISSN={},
 month={Feb},
}

@article{Vuillemin:1983,
 author = "Jean Vuillemin",
 title = "A Very Fast Multiplication Algorithm for VLSI Implementation",
 journal = "Integration",
 volume = "1",
 number = "1",
 pages = "39--52",
 year = "1983",
 issn = "0167-9260",
 doi = "10.1016/0167-9260(83)90005-6",
}

@inproceedings{Iwasaki:2008,
 author    = {Naoki Iwasaki and Katsumi Wasaki},
 title     = {A Meta Hardware Description Language Melasy for Model-Checking Systems},
 booktitle = {Proceedings 5th International Conference on Information Technology: New Generations
              {(ITNG} 2008)},
 pages     = {273--278},
 year      = {2008},
 doi       = {10.1109/ITNG.2008.135},
}
