System Description: GAPT 2.0

Ebner, Gabriel; Hetzl, Stefan; Reis, Giselle; Riener, Martin; Wolfsteiner, Simon; Zivota, Sebastian

doi:10.1007/978-3-319-40229-1_20

Cited by 22 publications

(22 citation statements)

References 18 publications

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“…In particular we show that the new method outperforms the old one (quadratic versus cubic) and that the complexity of the new method can never be higher than that of the old one. Finally we describe an implementation of the new method and the traditional one (both methods are implemented in the Gapt system [12]) and show how they can be used to extract expansion proofs from proofs. We compare the implementations of the two methods and it turns out that even for very small and simple proofs a visible speed-up in computing time can be obtained.…”

Section: Introductionmentioning

confidence: 89%

“…The algorithm EXP new is implemented in the Gapt-system 1 [12], which is a framework for implementing proof transformations written in the programming language Scala. Initially it was developed for the method CERES, but has been extended to other proof transformation algorithms (note that the methods described in this paper are available from version 2.5 on).…”

Section: Implementation and Experiments In Gaptmentioning

confidence: 99%

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Extraction of Expansion Trees

Leitsch

Lolić

2018

J Autom Reasoning

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We define a new method for proof mining by CERES (cut-elimination by resolution) that is concerned with the extraction of expansion trees in first-order logic (see Miller in Stud Log 46(4):347-370, 1987) with equality. In the original CERES method expansion trees can be extracted from proofs in normal form (proofs without quantified cuts) as a postprocessing of cut-elimination. More precisely they are extracted from an ACNF, a proof with at most atomic cuts. We define a novel method avoiding proof normalization and show that expansion trees can be extracted from the resolution refutation and the corresponding proof projections. We prove that the new method asymptotically outperforms the standard method (which first computes the ACNF and then extracts an expansion tree). Finally we compare an implementation of the new method with the old one; it turns out that the new method is also more efficient in our experiments.

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Section: Introductionmentioning

confidence: 89%

Section: Implementation and Experiments In Gaptmentioning

confidence: 99%

Extraction of Expansion Trees

Leitsch

Lolić

2018

J Autom Reasoning

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“…The first method [63] to address this problem introduced atomic cuts by using the resolution calculus, which is based on atomic cuts. A few years later, another method [34], based on discovering a grammar that could generate the Herbrand sequent of the proof to be compressed and then constructing a proof with cuts based on that grammar, was also proposed and implemented in GAPT [24,26,36,44,55].…”

Section: Related Workmentioning

confidence: 99%

“…All natural deduction, propositional and first-order resolution proof compression algorithms mentioned have been implemented by various people in Skeptik [12], whereas the sequent calculus algorithms have been implemented either in the CERes system [25] for cut-elimination by resolution, or in its successor GAPT [24,26,36,44,55] (the General Architecture for Proof Theory).…”

Section: Related Workmentioning

confidence: 99%

“…Secondly, whereas the main motivation for deletion information in the DRUP format was to speed up proof checking, the main concern here is memory consumption. And finally, whereas DRUP proofs are typically processed in a bottom-up way, here it is assumed that the proof consumer will do a top-down traversal of the proof, as usual for resolution [2,19,[24][25][26]36,44,55].…”

Section: Related Workmentioning

confidence: 99%

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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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Certification of Nonclausal Connection Tableaux Proofs

Färber

Kaliszyk

2019

Lecture Notes in Computer Science

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Nonclausal connection tableaux calculi enable proof search without performing clausification. We give a translation of nonclausal connection proofs to Gentzen's sequent calculus LK and compare it to an existing translation of clausal connection proofs. Furthermore, we implement the translation in the interactive theorem prover HOL Light, enabling certification of nonclausal connection proofs as well as a new, complementary automation technique in HOL Light.

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System Description: GAPT 2.0

Cited by 22 publications

References 18 publications

Extraction of Expansion Trees

Extraction of Expansion Trees

Greedy pebbling for proof space compression

Certification of Nonclausal Connection Tableaux Proofs

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