SAT, Computer Algebra, Multipliers

18 pages•Published: March 11, 2020

Daniela Kaufmann, Armin Biere and Manuel Kauers

Abstract

Verifying multiplier circuits is an important problem which in practice still requires substantial manual effort. The currently most effective approach uses polynomial reasoning. However parts of a multiplier, i.e., complex final stage adders are hard to verify using computer algebra. In our approach we combine SAT and computer algebra to substantially improve automated verification of integer multipliers. In this paper we focus on the implementation details of our new dedicated reduction engine, which not only allows fully automated adder substitution, but also employs polynomial re- duction efficiently. Our tool is furthermore able to generate proof certificates in the practical algebraic calculus and we also investigate the size of these proofs for one specific multiplier architecture.

Keyphrases: computer algebra, multiplier circuits, polynomial reasoning, proof certificates, sat

In: Laura Kovacs and Andrei Voronkov (editors). Vampire 2018 and Vampire 2019. The 5th and 6th Vampire Workshops, vol 71, pages 1-18.

Links:	https://easychair.org/publications/paper/bpc4
	https://doi.org/10.29007/j8cm

BibTeX entry

@inproceedings{Vampire2019:SAT_Computer_Algebra_Multipliers,
  author    = {Daniela Kaufmann and Armin Biere and Manuel Kauers},
  title     = {SAT, Computer Algebra, Multipliers},
  booktitle = {Vampire 2018 and Vampire 2019. The 5th and 6th Vampire Workshops},
  editor    = {Laura Kovacs and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {71},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/bpc4},
  doi       = {10.29007/j8cm},
  pages     = {1-18},
  year      = {2020}}

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