Verifying Properties of Bit-vector Multiplication Using Cutting Planes Reasoning

Forskningsoutput: Kapitel i bok/rapport/Conference proceedingKonferenspaper i proceeding

Abstract

Systems mixing Boolean logic and arithmetic have been a long-standing challenge for verification tools such as SAT-based bit-vector solvers. Though SAT solvers can be highly efficient for Boolean reasoning, they scale poorly once multiplication is involved. Algebraic methods using Gröbner basis reduction have recently been used to efficiently verify multiplier circuits in isolation, but generally do not perform well on problems involving bit-level reasoning. We propose that pseudo-Boolean solvers equipped with cutting planes reasoning have the potential to combine the complementary strengths of the existing SAT and algebraic approaches while avoiding their weaknesses. Theoretically, we show that there are optimal-length cutting planes proofs for a large class of bit-level properties of some well known multiplier circuits. This scaling is significantly better than the smallest proofs known for SAT and, in some instances, for algebraic methods. We also show that cutting planes reasoning can extract bit-level consequences of word-level equations in exponentially fewer steps than methods based on Gröbner bases. Experimentally, we demonstrate that pseudo-Boolean solvers can verify the word-level equivalence of adder-based multiplier architectures, as well as commutativity of bit-vector multiplication, in times comparable to the best algebraic methods. We then go further than previous approaches and also verify these properties at the bit-level. Finally, we find examples of simple nonlinear bit-vector inequalities that are intractable for current bit-vector and SAT solvers but easy for pseudo-Boolean solvers.

Detaljer

Författare
Enheter & grupper
Externa organisationer
  • University of Washington
  • University of Copenhagen
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Datavetenskap (datalogi)

Nyckelord

Originalspråkengelska
Titel på värdpublikationProceedings of the 20th Conference on Formal Methods in Computer-Aided Design, FMCAD 2020
RedaktörerAlexander Ivrii, Ofer Strichman, Warren A. Hunt, Georg Weissenbacher
FörlagInstitute of Electrical and Electronics Engineers Inc.
Sidor194-204
Antal sidor11
ISBN (elektroniskt)9783854480426
StatusPublished - 2020
PublikationskategoriForskning
Peer review utfördJa
Evenemang20th International Conference on Formal Methods in Computer-Aided Design, FMCAD 2020 - Virtual, Haifa, Israel
Varaktighet: 2020 sep 212020 sep 24

Publikationsserier

NamnProceedings of the 20th Conference on Formal Methods in Computer-Aided Design, FMCAD 2020

Konferens

Konferens20th International Conference on Formal Methods in Computer-Aided Design, FMCAD 2020
LandIsrael
OrtVirtual, Haifa
Period2020/09/212020/09/24