Towards Realizability Checking of Contracts using Theories

TL;DR

This paper introduces a novel approach for checking the realizability of system contracts involving theories, addressing a gap in existing methods for infinite theories, and demonstrates its effectiveness through multiple examples.

Contribution

It presents a new method for realizability checking of contracts with theories, extending beyond propositional cases and applicable to complex system architectures.

Findings

The approach successfully verifies realizability on several example contracts.

It extends realizability checking to contracts involving infinite theories.

The method enhances early design validation for complex embedded systems.

Abstract

Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate architectural descriptions and compositional reasoning rules, these techniques can be used to prove important safety properties about the architecture prior to system construction. Such proofs build from "leaf-level" assume/guarantee component contracts through architectural layers towards top-level safety properties. The proofs are built upon the premise that each leaf-level component contract is realizable; i.e., it is possible to construct a component such that for any input allowed by the contract assumptions, there is some output value that the component can produce that satisfies the contract guarantees. Without engineering support it is all too easy to write leaf-level components that can't be realized. Realizability checking for propositional contracts has been well-studied for many years, both for component synthesis and checking correctness of temporal logic requirements. However, checking realizability for contracts involving infinite theories is still an open problem. In this paper, we describe a new approach for checking realizability of contracts involving theories and demonstrate its usefulness on several examples.