STABLE: A new QF-BV SMT solver for hard verification problems combining Boolean reasoning with computer algebra

Groebner basis based formal verification of large arithmetic circuits using Gaussian elimination and cone-based polynomial extraction

“…This approach, however, is not applicable to integer multipliers due to carry propagation issues. The authors of [7] have proposed a formal verification technique in which ABL components [18] are modeled by polynomials over unique ring and their normal forms are computed with respect to the Groebner basis over rings Z 2 k using computer algebra techniques. In order to overcome the expensive Groebner basis computation problem, they have proposed a technique to directly generate individual output polynomials in terms of primary inputs.…”

“…On the other hand, recently some techniques for verification of bit-level implementations using the theory of Groebner basis have been proposed [6,7,9]. However, these techniques are computationally intensive and are not scalable to large arithmetic circuits.…”

Function Extraction from Arithmetic Bit-Level Circuits

“…The literature related to this subject addresses extraction of arithmetic bit-level structure from gate-level implementations, [2], [3], without being concerned with the arithmetic function it implements. Automated techniques for extracting arithmetic bit level (ABL) information from gate level netlists have been proposed in the context of property and equivalence checking [2] but they do not address the issue of the function implemented by the network.…”

“…In our view this model is unnecessarily complicated and not scalable to practical designs. A simplified version of this technique replaces the expensive Grobner base computation with a direct generation of polynomials representing circuit components [3]. However, no practical method for deriving such large polynomials and no systematic comparison against the specification have been proposed.…”

Arithmetic Bit-Level Verification Using Network Flow Model

“…In our view this model is unnecessarily complicated and not scalable to practical designs. A simplified version of this technique replaces the expensive Grobner base computation with a direct generation of polynomials representing circuit components [15]. However, no practical method for deriving such large polynomials and no systematic comparison against the specification have been proposed.…”