Knowledge compilation and theory approximation
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Incremental maintenance of recursive views using relational calculus/SQL
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Avoiding exponential explosion: generating compact verification conditions
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The pointer assertion logic engine
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Verifying reachability invariants of linked structures
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Mona: Monadic Second-Order Logic in Practice
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A semantics for procedure local heaps and its abstractions
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Back to the future: revisiting precise program verification using SMT solvers
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Deciding Effectively Propositional Logic Using DPLL and Substitution Sets
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Finite differencing of logical formulas for static analysis
ACM Transactions on Programming Languages and Systems (TOPLAS)
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Decidable logics combining heap structures and data
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Verification conditions for source-level imperative programs
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Accurate invariant checking for programs manipulating lists and arrays with infinite data
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Modular reasoning about heap paths via effectively propositional formulas
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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This paper proposes a novel method of harnessing existing SAT solvers to verify reachability properties of programs that manipulate linked-list data structures. Such properties are essential for proving program termination, correctness of data structure invariants, and other safety properties. Our solution is complete, i.e., a SAT solver produces a counterexample whenever a program does not satisfy its specification. This result is surprising since even first-order theorem provers usually cannot deal with reachability in a complete way, because doing so requires reasoning about transitive closure. Our result is based on the following ideas: (1) Programmers must write assertions in a restricted logic without quantifier alternation or function symbols. (2) The correctness of many programs can be expressed in such restricted logics, although we explain the tradeoffs. (3) Recent results in descriptive complexity can be utilized to show that every program that manipulates potentially cyclic, singly- and doubly-linked lists and that is annotated with assertions written in this restricted logic, can be verified with a SAT solver. We implemented a tool atop Z3 and used it to show the correctness of several linked list programs.