Towards a Semantics of Unsatisfiability Proofs with Inprocessing

Philipp, Tobias; Rebola-Pardo, Adrián

doi:10.29007/7jgq

Cited by 6 publications

(22 citation statements)

References 39 publications

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“…The parsimony of the resolution calculus also makes checking a resolution proof conceptually simpler and implementable in fewer lines of trusted code. The extra information contained in resolution proofs is essential for further manipulation and compression of the proof [3,13,21,29,57] and for applications that rely, for instance, on interpolants extracted from proofs [23,38,51]. And finally, although alternative detailed proof systems for conflict-driven clause learning, mixing resolution and natural deduction have recently been proposed [60], resolution remains the primary format chosen by major SMT-solvers [4,5,14] and conversion from DRUP to resolution is possible for SAT-solvers that are not able to output resolution proofs directly [37].…”

Section: Introductionmentioning

confidence: 99%

Greedy pebbling for proof space compression

Fellner

Paleo

2017

Int J Softw Tools Technol Transfer

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Automated reasoning tools for the verification and synthesis of software often produce proofs to allow independent certification of the correctness of the produced solutions. As proofs can be large, this paper considers the problem of compressing proofs with respect to their space, which is approximately proportional to the memory necessary to check them. Proof checking with a small amount of available memory is analogous to playing a pebbling game with a small number of pebbles. This paper exploits this analogy and describes novel algorithms for playing a pebbling game. The sequence of moves executed in the pebbling game then corresponds to an improved topological ordering of the nodes of the proof, leading to smaller memory consumption when the proof is checked. Because the number of possible pebbling strategies and topological orderings is too large, brute-force approaches to find optimal solutions are impractical, and hence, the new pebbling algorithms proposed here are based on heuristics for finding good, though not necessarily optimal, solutions. The algorithms are evaluated on the task of compressing the space of thousands of propositional resolution proofs generated by SAT-and SMT-solvers.

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Section: Introductionmentioning

confidence: 99%

Greedy pebbling for proof space compression

Fellner

Paleo

2017

Int J Softw Tools Technol Transfer

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“…Contributions One way to understand DPR proofs is to look for semantic invariants preserved throughout proofs. In truth-preserving proof systems this is straightforward, but previous results imply that no such invariants exist for DPR proofs [29]. In this paper, we argue that DPR can be construed as operating over a more general logic, called overwrite logic, which derives expressions that generalize clauses.…”

Section: Introductionmentioning

confidence: 87%

“…Interference has practical implications beyond SAT solving, especially when one considers the use of proofs with aims other than certifying the solvers' results. For example, no method exists in the literature to generate Craig interpolants [5] from DRAT proofs that can be used in model checking [27], and the allowed inferences lack of some of the intuitive features familiar from other proof systems such as resolution [29]. The issues of interference all boil down to the allowed inferences being just satisfiability-preserving, rather than truth-preserving [29].…”

Section: Introductionmentioning

confidence: 99%

“…For example, no method exists in the literature to generate Craig interpolants [5] from DRAT proofs that can be used in model checking [27], and the allowed inferences lack of some of the intuitive features familiar from other proof systems such as resolution [29]. The issues of interference all boil down to the allowed inferences being just satisfiability-preserving, rather than truth-preserving [29]. For example, methods to obtain interpolants from other proof systems work by recursively constructing partial interpolants throughout the proof tree [26,40,8,33], but the invariants ensuring the correctness of this procedure rely strongly on the proof being truth-preserving, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…For example, methods to obtain interpolants from other proof systems work by recursively constructing partial interpolants throughout the proof tree [26,40,8,33], but the invariants ensuring the correctness of this procedure rely strongly on the proof being truth-preserving, i.e. the conclusion of every inference being a consequence of its premises [29]. Even worse, DRAT and DPR proofs are not even tree-shaped.…”

Section: Introductionmentioning

confidence: 99%

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A Theory of Satisfiability-Preserving Proofs in SAT Solving

Rebola-Pardo¹,

Suda²

EPiC Series in Computing

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We study the semantics of propositional interference-based proof systems such as DRAT and DPR. These are characterized by modifying a CNF formula in ways that preserve satisfiability but not necessarily logical truth. We propose an extension of propositional logic called overwrite logic with a new construct which captures the meta-level reasoning behind interferences. We analyze this new logic from the point of view of expressivity and complexity, showing that while greater expressivity is achieved, the satisfiability problem for overwrite logic is essentially as hard as SAT, and can be reduced in a way that is well-behaved for modern SAT solvers. We also show that DRAT and DPR proofs can be seen as overwrite logic proofs which preserve logical truth. This much stronger invariant than the mere satisfiability preservation maintained by the traditional view gives us better understanding on these practically important proof systems. Finally, we showcase this better understanding by finding intrinsic limitations in interference-based proof systems.

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Simulating Strong Practical Proof Systems with Extended Resolution

et al. 2020

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Proof systems for propositional logic provide the basis for decision procedures that determine the satisfiability status of logical formulas. While the well-known proof system of extended resolution—introduced by Tseitin in the sixties—allows for the compact representation of proofs, modern SAT solvers (i.e., tools for deciding propositional logic) are based on different proof systems that capture practical solving techniques in an elegant way. The most popular of these proof systems is likely DRAT, which is considered the de-facto standard in SAT solving. Moreover, just recently, the proof system DPR has been proposed as a generalization of DRAT that allows for short proofs without the need of new variables. Since every extended-resolution proof can be regarded as a DRAT proof and since every DRAT proof is also a DPR proof, it was clear that both DRAT and DPR generalize extended resolution. In this paper, we show that—from the viewpoint of proof complexity—these two systems are no stronger than extended resolution. We do so by showing that (1) extended resolution polynomially simulates DRAT and (2) DRAT polynomially simulates DPR. We implemented our simulations as proof-transformation tools and evaluated them to observe their behavior in practice. Finally, as a side note, we show how Kullmann’s proof system based on blocked clauses (another generalization of extended resolution) is related to the other systems.

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Towards a Semantics of Unsatisfiability Proofs with Inprocessing

Cited by 6 publications

References 39 publications

Greedy pebbling for proof space compression

Greedy pebbling for proof space compression

A Theory of Satisfiability-Preserving Proofs in SAT Solving

Simulating Strong Practical Proof Systems with Extended Resolution

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