Invariant Elimination of Definite Iterations over Arrays in C Programs Verification

Abstract

Abstract. This work represents the further development of the method for definite iteration verification [7]. It extends the mixed axiomatic semantics method [1] suggested for C-light program verification. This extension includes a verification method for definite iteration over unchangeable arrays with a loop exit in C-light programs. The method includes an inference rule for the iteration without invariants, which uses a special function that expresses loop body. This rule was implemented in verification conditions generator, which is the part of our C-light verification system. To prove generated verification conditions an induction is applied which is a challenge for SMT-solvers. At proof stage the SMT-solver CVC4 is used in our verification system. To overcome mentioned difficulty a rewriting strategy for verification conditions is suggested. A method based on theory extension by new theorems to prove verification conditions is suggested. An example, which illustrates the application of these methods, is considered. The article is published in the authors' wording.Keywords: C-light, loop invariants, mixed axiomatic semantics, definite iteration, arrays, CVC4, specification, verification, Hoare logic

Towards Automated Error Localization in C Programs With Loops

“…These strategies are the new contribution relative to previous research [6][7][8]11]. Based on these methods, we conducted some experiments on error localization.…”

“…Function rep is defined in Appendix B. Semantic label ass_pre denotes hypothesis from precondition, ass_pre denotes hypothesis from postcondition, ens_post denotes goal from postcondition, rep_iter denotes substitution of replacement function [7]. As expected, vc-1 cannot be proved by SAT strategies, like those from [8,11]. It is time to use our UNSAT strategy.…”

“…Since all variables in ACL2 are implicitly universally quantified, the existence quantifier appears in the negated VC. Thus, our previous strategies [8,11] fail here and we need revised ones. Another requirement the unsat strategies must work for loops with abrupt termination (i.e.…”

“…At the moment, the main theorem prover for C-light is ACL2 [5]. The classic induction in ACL2 is not powerful enough to handle VCs with replacement function rep, so the proof strategies are proposed in [8,11].…”

Методы Комплексного Подхода К Автоматизации Дедуктивной Верификации Программ С Финитными Итерациями

“…Этот способ основан на классической идее доказательства шага индукции и доказательстве индукционного перехода. Однако, для автоматизации доказательства УК такой тактики недостаточно [144,171]. Рейнольдс и Кунчак (Reynolds, Kuncak) [171] предложили набор стратегий автоматизации доказательства по индукции для SMT-решателя CVC4 [43].…”