Rigid tree automata and applications

Jacquemard, Florent; Klay, Francis; Vacher, Camille

doi:10.1016/j.ic.2010.11.015

Cited by 17 publications

(10 citation statements)

References 24 publications

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“…Many important notions, such as regular and context-free languages carry over from the setting of strings to that of trees. The class of rigid tree languages has been introduced in [25] with applications in verification in mind, see [26]. Rigid tree languages augment regular tree languages by the ability to carry out certain equality tests, a property that is very useful for applications.…”

Section: Proofs and Grammarsmentioning

confidence: 99%

Algorithmic introduction of quantified cuts

Hetzl

Leitsch

Reis

et al. 2014

Theoretical Computer Science

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We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computing a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize such a compression. Finally, a proof using these cut-formulas is constructed. This method allows an exponential compression of proof length. It can be applied to the output of automated theorem provers, which typically produce analytic proofs. An implementation is available on the web and described in this paper.

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Section: Proofs and Grammarsmentioning

confidence: 99%

Algorithmic introduction of quantified cuts

Hetzl

Leitsch

Reis

et al. 2014

Theoretical Computer Science

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“…of cryptographic protocols as in [JKV11]) as primary motivation. It will turn out that this class is appropriate for describing cut-elimination in classical first-order logic.…”

Section: Regular and Rigid Tree Grammarsmentioning

confidence: 99%

Herbrand-Confluence

Hetzl¹,

Straßburger²

2013

Logical Methods in Computer Science

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Abstract. We consider cut-elimination in the sequent calculus for classical first-order logic. It is well known that this system, in its most general form, is neither confluent nor strongly normalizing. In this work we take a coarser (and mathematically more realistic) look at cut-free proofs. We analyze which witnesses they choose for which quantifiers, or in other words: we only consider the Herbrand-disjunction of a cut-free proof. Our main theorem is a confluence result for a natural class of proofs: all (possibly infinitely many) normal forms of the non-erasing reduction lead to the same Herbrand-disjunction.

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“…Rigid tree languages have been introduced in [13] with applications in verification in mind (e.g. of cryptographic protocols as in [14]). A rigid tree grammar differs from a regular tree grammar (see e.g.…”

Section: Theoretical Foundationsmentioning

confidence: 99%

Project Presentation: Algorithmic Structuring and Compression of Proofs (ASCOP)

Hetzl

2012

Lecture Notes in Computer Science

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Computer-generated proofs are typically analytic, i.e. they essentially consist only of formulas which are present in the theorem that is shown. In contrast, mathematical proofs written by humans almost never are: they are highly structured due to the use of lemmas. The ASCOP-project aims at developing algorithms and software which structure and abbreviate analytic proofs by computing useful lemmas. These algorithms will be based on recent groundbreaking results establishing a new connection between proof theory and formal language theory. This connection allows the application of efficient algorithms based on formal grammars to structure and compress proofs.

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Rigid tree automata and applications

Cited by 17 publications

References 24 publications

Algorithmic introduction of quantified cuts

Algorithmic introduction of quantified cuts

Herbrand-Confluence

Project Presentation: Algorithmic Structuring and Compression of Proofs (ASCOP)

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