Efficient representation and validation of proofs

Necula, George C.; Lee, P.

doi:10.1109/lics.1998.705646

Cited by 52 publications

(33 citation statements)

References 11 publications

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“…Existing first-order provers, that embody the results of years of research on data structures and algorithms for deduction, could be applied, or at least their code could be reused, offering a higher degree of assurance about soundness and completeness of the procedure. Furthermore, theorem-proving strategies support proof generation and model generation, that are two more desiderata of satisfiability procedures (e.g., [Necula and Lee 1998;Lahiri and Musuvathi 2005a]), in a theory-independent way. Indeed, if the input is unsatisfiable, the strategy generates a proof with no additional effort.…”

Section: Introductionmentioning

confidence: 99%

New results on rewrite-based satisfiability procedures

Armando

Bonacina

Ranise

et al. 2009

ACM Trans. Comput. Logic

133

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Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T . If a sound and complete inference system for first-order logic is guaranteed to terminate on T -satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T -satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.

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Section: Introductionmentioning

confidence: 99%

New results on rewrite-based satisfiability procedures

Armando

Bonacina

Ranise

et al. 2009

ACM Trans. Comput. Logic

133

View full text Add to dashboard Cite

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“…Foundational PCC [2,18] attempts to reduce the trusted computing base of PCC to solely the foundations of mathematical logic. Bernard and Lee [5] propose a new temporal logic to express PCC policies for machine code.Non-SAT-based techniques for minimizing PCC proof sizes [29,32] and formalizing machine code semantics [24] have also been proposed. Our work uses proofs to certify software but is applicable to safety as well as liveness specifications, and at the source code level.…”

Section: Related Workmentioning

confidence: 99%

SAT-Based Software Certification

Chaki

2006

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. We formalize a notion of witnesses for satisfaction of linear temporal logic specifications by infinite state programs. We show how such witnesses may be constructed via predicate abstraction, and validated by generating verification conditions and proving them. We propose the use of SAT-based theorem provers and resolution proofs in proving these verification conditions. In addition to yielding extremely compact proofs, a SAT-based approach overcomes several limitations of conventional theorem provers when applied to the verification of programs written in real-life programming languages. We also formalize a notion of witnesses of simulation conformance between infinite state programs and finite state machine specifications. We present algorithms to construct simulation witnesses of minimal size by solving pseudo-Boolean constraints. We present experimental results on several non-trivial benchmarks which suggest that a SAT-based approach can yield extremely compact proofs, in some cases by a factor of over 10 5 , when compared to existing non-SAT-based theorem provers.

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“…Initial PCC works used as certificates a lambda-term encoding of proofs [Nec97] to be type-checked by the Logical Framework (LF). To optimise the size of these proofs, Necula and Lee proposed LF i a compressed proof format for LF terms [NL98]. For a weaker logic, Necula and Rahul transmit as certificate an oracle (a stream of bits) that guides a higher-order logic interpreter in its proof search [NR01].…”

Section: Introductionmentioning

confidence: 99%

Small Witnesses for Abstract Interpretation-Based Proofs

Besson

Jensen

Turpin

2007

Programming Languages and Systems

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Abstract. Abstract interpretation-based proof carrying code uses post-fixpoints of abstract interpretations to witness that a program respects a safety policy. Some witnesses carry more information than needed and are therefore unnecessarily large. We introduce a notion of size of a witness and propose techniques for reducing the size of such certificates. For distributive analyses, we show that a smallest witness exist and we give an iterative algorithm for computing it. For non-distributive analyes we propose a technique for pruning a witness and illustrate this pruning on a relational, polyhedra-based analysis. Finally, only the existence of a witness is needed to assure the code consumer of the safety of a given program. This makes possible a compression technique of witnesses where only part of a witness is sent together with an encoding of the iterative steps necessary to prove that it is part of a post-fixpoint.

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Efficient representation and validation of proofs

Cited by 52 publications

References 11 publications

New results on rewrite-based satisfiability procedures

New results on rewrite-based satisfiability procedures

SAT-Based Software Certification

Small Witnesses for Abstract Interpretation-Based Proofs

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