A Faithful Semantics for Generalised Symbolic Trajectory Evaluation

TL;DR

This paper introduces a new faithful semantics for Generalised Symbolic Trajectory Evaluation (GSTE), ensuring that the semantics accurately reflect the proving capabilities of GSTE algorithms for hardware verification.

Contribution

It provides a simple formal theory that aligns the semantics with GSTE's proving power, proving soundness and completeness of the GSTE algorithm relative to this semantics.

Findings

The semantics are faithful to GSTE's proving power.

GSTE algorithm is proven sound and complete with respect to the new semantics.

Enhances understanding of GSTE's capabilities in hardware verification.

Abstract

Generalised Symbolic Trajectory Evaluation (GSTE) is a high-capacity formal verification technique for hardware. GSTE uses abstraction, meaning that details of the circuit behaviour are removed from the circuit model. A semantics for GSTE can be used to predict and understand why certain circuit properties can or cannot be proven by GSTE. Several semantics have been described for GSTE. These semantics, however, are not faithful to the proving power of GSTE-algorithms, that is, the GSTE-algorithms are incomplete with respect to the semantics. The abstraction used in GSTE makes it hard to understand why a specific property can, or cannot, be proven by GSTE. The semantics mentioned above cannot help the user in doing so. The contribution of this paper is a faithful semantics for GSTE. That is, we give a simple formal theory that deems a property to be true if-and-only-if the property can be proven by a GSTE-model checker. We prove that the GSTE algorithm is sound and complete with respect to this semantics.