Conformance analysis for context-free languages using abstract interpretation

Abstract

We design a string analysis within abstract interpretation framework. To this end, we invent novel predicates which are derived from the reference pushdown automaton. Using these predicates, we design a conjunctive domain whose element is a conjunction of the predicates. We establish the correctness relation by Galois connection and define a correct abstract concatenation operation on the domain. We also present a family of pushdown automata called $\epsilon$ bounded pushdown automata. This family covers all context-free languages. By using this family of pushdown automata, we can prevent abstract values from becoming infinite conjunctions and make sure that all the operations required in the analyzer are computable.

We also present a technique for embracing various string operations other than concatenation. We introduce small refinement to the conjunctive domain to design the abstract replace operation. Other various string operations that require more detailed information about the contents of the string are handled by grammar transformations. After all, these grammars are also accommodated to our analysis after abstracting the language of the grammar.

Our analysis can be used for any context-free reference language. Using our string analyzer designed in abstract interpretation framework, we can easily compose the string analysis with other analyses to improve the precision, and it is also possible to design modular string analyzer.