Algorithmic Compression of Finite Tree Languages by Rigid Acyclic Grammars

Eberhard, Sebastian; Ebner, Gabriel; Hetzl, Stefan

doi:10.1145/3127401

Cited by 4 publications

(6 citation statements)

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“…In [12], the authors propose an algorithm for the compression of a finite set of terms by reducing the problem (in polynomial time) to Max-SAT. This is another method for finding a decomposition.…”

Section: The Maxsat-algorithmmentioning

confidence: 99%

“…We evaluated our lemma generation method on the remaining 35480 proofs and several different methods to generate decompositions: the Δ-table algorithm for a single variable, and many variables with and without row merging, as well as the so-called MaxSAT-algorithm of [12] for different parameters.…”

Section: Large-scale Experimentsmentioning

confidence: 99%

“…3.2. The MaxSAT-algorithm from [12], finding a single cut with 2 quantifiers, came in as a close second, although with a much higher constant overhead. Additional modifications to the Δtable algorithm (single variable, row merging) did not increase the number of decompositions that could be computed.…”

Section: Large-scale Experimentsmentioning

confidence: 99%

“…In this paper we extend the method to predicate logic with equality and to the introduction of an arbitrary number of Π 1 -cuts, each of which has an arbitrary number of quantifiers. We present an implementation based on a new (and efficient) algorithm for computing a decomposition of a Herbrand-disjunction [12]. We carry out a comprehensive empirical evaluation of the implementation and describe a case study demonstrating how our algorithm generates the notion of a partial order from a proof about a lattice.…”

Section: Introductionmentioning

confidence: 99%

“…Comparison of the different algorithms used to generate decompositions. The label 2_2_maxsat refers to the algorithm of[12] with |ᾱ 1 | = 2 and |ᾱ 2 | = 2, many_dtable is the one from Sect. 3.2, many_dtable_ss includes the row-merging modification, and 1_dtable is the variant of the Δ-table algorithm that uses the Δ 1 -vector…”

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On the Generation of Quantified Lemmas

et al. 2018

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In this paper we present an algorithmic method of lemma introduction. Given a proof in predicate logic with equality the algorithm is capable of introducing several universal lemmas. The method is based on an inversion of Gentzen's cut-elimination method for sequent calculus. The first step consists of the computation of a compact representation (a so-called decomposition) of Herbrand instances in a cut-free proof. Given a decomposition the problem of computing the corresponding lemmas is reduced to the solution of a secondorder unification problem (the solution conditions). It is shown that that there is always a solution of the solution conditions, the canonical solution. This solution yields a sequence of lemmas and, finally, a proof based on these lemmas. Various techniques are developed to simplify the canonical solution resulting in a reduction of proof complexity. Moreover, the paper contains a comprehensive empirical evaluation of the implemented method and gives an application to a mathematical proof.

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Section: The Maxsat-algorithmmentioning

confidence: 99%

Section: Large-scale Experimentsmentioning

confidence: 99%

Section: Large-scale Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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