POLARIS

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

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.