1. What are the contributions in "Model checking recursive programs with exact predicate abstraction" ?
The authors propose an approach for analyzing non-termination and reachability properties of recursive programs using a combination of overand underapproximating abstractions.. Second, the authors combine this algorithm with abstraction by following classical fixpoint abstraction techniques.. This makes their approach parametrized by different approximating semantics of predicate abstraction and enables a uniform solution for overand under-approximating semantics.. The algorithm is implemented in YASM, and the authors show that it can establish non-termination of non-trivial C programs completely automatically.
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2. What are the future works in "Model checking recursive programs with exact predicate abstraction" ?
Although the authors specialize their approach to predicate abstraction, they believe that it can be extended to other abstract domains as well.. In the future, the authors plan to investigate how the strengths of the two approaches can be combined in a single algorithm.. The authors hope to extend their approach to a more general class of properties, e. g., the ones expressible in CARET [ 2 ].. Their reachability algorithm can be seen as a pre-image-based variant of the RHS algorithm [ 23 ], as implemented in BEBOP [ 6 ].
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![Table 2.The rules of operational and mixed semanics.U is the set of local variables in the scope of the function call;[[f ]] is natural semantics,pf are the formals, andrf are the returns off .](/figures/table-2-the-rules-of-operational-and-mixed-semanics-u-is-the-9azw4th1.png)


