Differentiating the Free Exercise and Establishment Clauses

The Relationship between Craig Interpolation and Recursion-Free Horn Clauses

Despite decades of research, there are still a number of concepts commonly found in software programs that are considered challenging for verification: among others, such concepts include concurrency, and the compositional analysis of programs with procedures. As a promising direction to overcome such difficulties, recently the use of Horn constraints as intermediate representation of software ...

On recursion-free Horn clauses and Craig interpolation

One of the main challenges in software verification is efficient and precise analysis of programs with procedures and loops. Interpolation methods remain among the most promising techniques for such verification. To accommodate the demands of various programming language features, over the past years several extended forms of interpolation have been introduced. We give a precise ontology of suc...

The Free Exercise Thereof

Free Exercise Is Dead, Long Live Free Exercise: Smith, Lukumi and and the General Applicability Requirement

Function-Free Horn Clauses Are Hard to Approximate

In this paper, we show two hardness results for approximating the best function-free Horn clause by an element of the same class. Our first result shows that for some constant k > 0, the error rate of the best k-Horn clause cannot be approximated in polynomial time to within any constant factor by an element of the same class. Our second result is much stronger. Under some frequently encountere...