By Laura Kovács, Andrei Voronkov (auth.), Natasha Sharygina, Helmut Veith (eds.)

This booklet constitutes the completely refereed court cases of the twenty fifth overseas convention on laptop Aided Verification, CAV 2013 held in St. Petersburg, Russia in July 2013. The fifty four normal and sixteen device papers provided have been conscientiously chosen from 209 submissions. The papers are equipped in topical sections on biology, concurrency, undefined, hybrid platforms, interpolation, loops and termination, new domain names, likelihood and records, SAT and SMZ, protection, form research, synthesis, and time.

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**Extra info for Computer Aided Verification: 25th International Conference, CAV 2013, Saint Petersburg, Russia, July 13-19, 2013. Proceedings**

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The pioneering works [25,13], an interpolant is typically defined as a reverse interpolant. The use of interpolation in hardware and software verification requires deriving (reverse) interpolants from refutations. A local derivation [13,19] is a derivation in which no inference contains both red and blue symbols. An inference with at least one coloured premise and a grey conclusion is called a symbol-eliminating inference. It turns out that one can extract interpolants from local proofs. For example, in [19] we gave an algorithm for extracting a reverse interpolant of R and B from a local refutation of {R, B}.

5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Select a relevant subset of formulas (optional). Add theory axioms (optional). Rectify the formula. If the formula contains any occurrence of or ⊥, simplify the formula. Remove if-then-else and let-in connectives. Flatten the formula. Apply pure predicate elimination. Remove unused predicate definitions (optional). Convert the formula into equivalence negation normal form (ennf). Use a naming technique to replace some subformulas by their names.

There are more complex equational tautologies, for example, a = b ∨ b = c ∨ a = c. Equational tautology checking can be implemented using congruence closure. It is implemented in VAMPIRE and the number of removed tautologies appears in the statistics. Subsumption. We say that a clause C subsumes a clause D if D can be obtained from C by two operations: application of a substitution θ and adding zero or more literals. In other words, Cθ is a submultiset of D if we consider clauses as multisets of their literals.