ALU Constraint Verification

Concept

ALU Constraint Verification refers to the use of constrained-random verification techniques to model and check the behavior of an Arithmetic Logic Unit (ALU) at various operand bit widths. It is presented in the CRAVE framework as a benchmark demonstrating how constraint solvers scale (or fail to scale) with ALU width, and is used comparatively against the SystemC Verification (SCV) library.

First seen 7/2/2026

Last seen 7/2/2026

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Overview

ALU Constraint Verification describes the application of declarative, constraint-based modeling to an Arithmetic Logic Unit (ALU) design, in order to automatically generate stimulus vectors that respect the ALU's operational semantics. In the CRAVE constrained-random verification framework, the ALU is encoded as a randomized object whose fields — an opcode and two operands — are bound by conditional constraints that express valid ALU behavior for each supported operation.

CRAVE ALU Encoding (16-bit example)

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CITATIONS

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[1] The 16-bit ALU is encoded in CRAVE with a 2-bit opcode `op` and two 16-bit operands `a` and `b`, with overflow-free constraints for add/sub/mul and a non-zero-divisor constraint for division, expressed via `IF_THEN` implications. CRAVE: An Advanced Constrained RAndom Verification Environment for SystemC

[2] A scalability comparison (Table III) reports that SCV fails with MO at ALU16 and TO at ALU24/ALU32, while CRAVE completes all ALU widths up to ALU32 with sub-second first-solution times and finished times of 0.14–0.49 seconds. CRAVE: An Advanced Constrained RAndom Verification Environment for SystemC

[3] SCV's failure at ALU16 is attributed to a 32-bit memory restriction caused by representing all solutions as a BDD in order to give each solution equal probability via weighted paths in a reduced ordered BDD. CRAVE: An Advanced Constrained RAndom Verification Environment for SystemC

[4] CRAVE's backend exposes multiple constraint solvers including SWORD, Z3, Boolector, MiniSAT, PicoSAT, CUDD, and AIGER, against which ALU constraint models can be evaluated. CRAVE: An Advanced Constrained RAndom Verification Environment for SystemC