Constraint-Based Relational Verification

Abstract

In recent years they have been numerous works that aim to automate relational verification. Meanwhile, although Constrained Horn Clauses ($$\mathrm {CHCs}$$ CHCs ) empower a wide range of verification techniques and tools, they lack the ability to express hyperproperties beyond k-safety such as generalized non-interference and co-termination.This paper describes a novel and fully automated constraint-based approach to relational verification. We first introduce a new class of predicate Constraint Satisfaction Problems called $$\mathrm {pfwCSP}$$ pfwCSP where constraints are represented as clauses modulo first-order theories over predicate variables of three kinds: ordinary, well-founded, or functional. This generalization over $$\mathrm {CHCs}$$ CHCs permits arbitrary (i.e., possibly non-Horn) clauses, well-foundedness constraints, functionality constraints, and is capable of expressing these relational verification problems. Our approach enables us to express and automatically verify problem instances that require non-trivial (i.e., non-sequential and non-lock-step) self-composition by automatically inferring appropriate schedulers (or alignment) that dictate when and which program copies move. To solve problems in this new language, we present a constraint solving method for $$\mathrm {pfwCSP}$$ pfwCSP based on stratified CounterExample-Guided Inductive Synthesis (CEGIS) of ordinary, well-founded, and functional predicates.We have implemented the proposed framework and obtained promising results on diverse relational verification problems that are beyond the scope of the previous verification frameworks.

Certified Verification of Relational Properties

“…We expect that user-provided coupling invariants and loop properties can avoid having to rely on code transformation methods. Moreover, we expect termination and co-termination [16], [34] to be used to extend the modularity of relational contracts. Recall that we consider a relational property R sw :…”

Software Verification of Hyperproperties Beyond k-Safety

“…We study the verification of such properties in infinite-state systems arising, e.g., in software. In contrast to k-safety, where a broad range of methods has been developed [38,26,39,10,40], no method for the automated verification of temporal ∀ * ∃ * properties in infinite-state systems exists (we discuss related approaches in Section 8).…”

“…Hyperproperties are system properties that relate multiple execution traces of a system [21] and commonly arise, e.g., in information-flow policies [34], the verification of code optimizations [6], and robustness of software [18]. Consequently, many methods for the automated verification of hyperproperties have been developed [38,40,26,39]. Almost all previous approaches verify a class of hyperproperties called k-safety, i.e., properties that stipulate the absence of a bad interaction between any k traces in the system.…”

An algebra of alignment for relational verification

“…Farzan and Vandikas [FV19] describe an approach to hypersafety verification of unary programs by discovering representative executions of a product program, whose correctness proofs are sufficient to prove the overall property. Unno et al [UTK21] work with transition systems and use a constraintsolving approach to automatically discover a "scheduler"-a form of alignment described as a function that directs which element of the -tuple (product of transition systems) should take the next step.…”