Advancing Polynomial and Logical Approaches for Trusted Automated Reasoning over Integrated Systems

Objetivo

In today's digital world, the correctness of systems is not
optional; it is essential. From hardware circuits in medical devices and
aircraft to cryptographic protocols securing our data, the systems that
underpin society demand absolute precision down to the level of individual
bits. Formal verification employs rigorous mathematical techniques and logical
reasoning to guarantee that such systems behave exactly as intended.

A wide range of central verification tasks, including proving the correctness
of hardware circuits, analyzing cryptographic encodings, and reasoning about
bit-vectors that model computer memory, can be naturally encoded as non-linear
polynomials over finite variable domains. State-of-the-art reasoning
approaches, such as satisfiability modulo theory solvers, however, reduce these
tasks to propositional reasoning on the bit-level and apply satisfiability
solving, which becomes infeasible when confronted with the complexity of modern
systems involving non-linear arithmetic and large state spaces.

POLARIS addresses this bottleneck by developing a new generation of trusted
verification techniques that operate directly on polynomial representations
while preserving bit-level accuracy. Central to this vision is the tight
integration of algebraic methods for word-level reasoning with established
bit-level approaches, combined with proof logging that produces
machine-checkable certificates. This ensures that every verification result is
both scalable and independently trustworthy.

Reaching this ambitious goal will enable verification capabilities that are
currently unattainable, in particular for complex arithmetic circuits,
cryptographic protocols, and low-level memory models with high arithmetic
complexity. By advancing the theoretical foundations and practical algorithms
for bit-precise reasoning, the project will extend the frontier of formal
verification and decisively strengthen the reliability and trustworthiness of
future digital systems.