@conference {403,
	title = {Unsatisfiability Proofs for Horn Solving},
	booktitle = {TACAS},
	year = {2025},
	abstract = {Many verification tools currently rely on logic solvers as backend reasoning engines. Despite playing such a pivotal role, bugs are not uncommon in the complex codebases of these solvers. Validating their results is thus critical, with correctness witnesses often being used for this end. Output validation for constrained Horn clauses (CHC) solvers is not a well explored topic though, especially in regards to unsatisfiability results. This is a significant issue, given that CHC solvers are being increasingly employed in verification tooling. To address it, we propose an approach to validate CHC unsatisfiability results based on independently checkable proofs. Our approach is generic in regards to the solving algorithm, preprocessing steps, and exact proof format used, and works by first producing a coarse-grained proof during solving and then instantiating it into a suitable proof format by adding missing details, at which point the instantiated proof can be checked by an independent proof checker. We instrumented a state-of-the-art CHC solver to generate proofs in the Alethe format and performed a large-scale evaluation. Our results indicate that proofs can be produced with minimal overhead, can be efficiently checked, and have tractable sizes.
},
	doi = {10.1007/978-3-031-90653-4_4},
	author = {Rodrigo Otoni and Martin Blicha and Matias Barandiaran Rivera and Patrick Eugster and Jan Kofron and Natasha Sharygina}
}
@article {356,
	title = {Using linear algebra in decomposition of Farkas interpolants},
	journal = {International Journal on Software Tools for Technology Transfer},
	year = {2021},
	type = {Journal},
	abstract = {<p>The use of propositional logic and systems of linear inequalities over reals is a common means to model software for formal verification. Craig interpolants constitute a central building block in this setting for over-approximating reachable states, e.g. as candidates for inductive loop invariants. Interpolants for a linear system can be efficiently computed from a Simplex refutation by applying the Farkas{\textquoteright} lemma. However, these interpolants do not always suit the verification task{\textemdash}in the worst case, they can even prevent the verification algorithm from converging. This work introduces the decomposed interpolants, a fundamental extension of the Farkas interpolants, obtained by identifying and separating independent components from the interpolant structure, using methods from linear algebra. We also present an efficient polynomial algorithm to compute decomposed interpolants and analyse its properties. We experimentally show that the use of decomposed interpolants in model checking results in immediate convergence on instances where state-of-the-art approaches diverge. Moreover, since being based on the efficient Simplex method, the approach is very competitive in general.</p>
},
	url = {https://link.springer.com/article/10.1007/s10009-021-00641-z},
	author = {Martin Blicha and Antti E. J. Hyv{\"a}rinen and Jan Kofron and Natasha Sharygina}
}
@conference {159,
	title = {Using Cross-Entropy for Satisfiability},
	booktitle = {ACM Symposium on Applied Computing (SAC)},
	year = {2013},
	author = {Chockler, H. and Ivrii, A. and Matsliah, A. and Rollini, S.F. and Natasha Sharygina}
}
