arXiv subjects

Diletta Rigo

Publications and source records attributed to Diletta Rigo.

2 recordsLinked to original sources

arXiv2026

A Program Logic for Abstract (Hyper)Properties

We introduce APPL (Abstract Program Property Logic), a unifying Hoare-style logic that subsumes standard Hoare logic, incorrectness logic, and several variants of Hyper Hoare logic. APPL provides a principled foundation for abstract program logics parameterised by an abstract domain, encompassing both existing and novel abstractions of properties and hyperproperties. The logic is grounded in a semantic framework where the meaning of commands is first defined on a lattice basis and then extended to the full lattice via additivity. Crucially, nondeterministic choice is interpreted by a monoidal operator that need not be idempotent nor coincide with the lattice join. This flexibility allows the framework to capture collecting semantics, various classes of abstract semantics, and hypersemantics. The APPL proof system is sound, and it is relatively complete whenever the property language is sufficiently expressive. When the property language is restricted to an abstract domain, the result is a sound abstract deduction system based on best correct approximations. Relative completeness with respect to a corresponding abstract semantics is recovered provided the abstract domain is complete, in the sense of abstract interpretation, for the monoidal operator.

cs.LO↗

arXiv2025

Model Checking as Program Verification by Abstract Interpretation (Extended Version)

Abstract interpretation offers a powerful toolset for static analysis, tackling precision, complexity and state-explosion issues. In the literature, state partitioning abstractions based on (bi)simulation and property-preserving state relations have been successfully applied to abstract model checking. Here, we pursue a different track in which model checking is seen as an instance of program verification. To this purpose, we introduce a suitable language-called MOKA (for MOdel checking as abstract interpretation of Kleene Algebras)-which is used to encode temporal formulae as programs. In particular, we show that (universal fragments of) temporal logics, such as ACTL or, more generally, universal mu-calculus can be transformed into MOKA programs. Such programs return all and only the initial states which violate the formula. By applying abstract interpretation to MOKA programs, we pave the way for reusing more general abstractions than partitions as well as for tuning the precision of the abstraction to remove or avoid false alarms. We show how to perform model checking via a program logic that combines under-approximation and abstract interpretation analysis to avoid false alarms. The notion of locally complete abstraction is used to dynamically improve the analysis precision via counterexample-guided domain refinement.

cs.LO↗