Classifying and Solving Horn Clauses for Verification [chapter]

Philipp Rümmer, Hossein Hojjat, Viktor Kuncak
<span title="">2014</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
As a promising direction to overcome difficulties of verification, researchers have recently proposed the use of Horn constraints as intermediate representation. Horn constraints are related to Craig interpolation, which is one of the main techniques used to construct and refine abstractions in verification, and to synthesise inductive loop invariants. We give a classification of the different forms of Craig interpolation problems found in literature, and show that all of them correspond to
more &raquo; ... ral fragments of (recursion-free) Horn constraints. For a logic that has the binary interpolation property, all of these problems are solvable, but have different complexity. In addition to presenting the theoretical classification and solvability results, we present a publicly available collection of benchmarks to evaluate solvers for Horn constraints, categorized according to our classification. The benchmarks are derived from real-world verification problems. The behavior with our tools as well as with Z3 prover indicates the importance of Horn clause solving as distinct from the general problem of solving quantified constraints by quantifier instantiation.
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