The Certification Problem Format

Sternagel, Christian; Thiemann, René

doi:10.4204/eptcs.167.8

Cited by 24 publications

(15 citation statements)

References 33 publications

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“…However, a typical termination proof has 10-100 proof witnesses and totals a few KB to a few MB of data, and recent work [16] mentions problems were encountered when dealing with proofs using "several hundred megabytes" of oracle data. In contrast, our target proof of size-optimality of sorting networks with 9 inputs requires dealing with nearly 70 million proof witnesses, totalling 27 GB of oracle data.…”

Section: Related Workmentioning

confidence: 99%

Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker

Cruz-Filipe

Schneider–Kamp

2015

Interactive Theorem Proving

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Abstract. Since the proof of the four color theorem in 1976, computergenerated proofs have become a reality in mathematics and computer science. During the last decade, we have seen formal proofs using verified proof assistants being used to verify the validity of such proofs. In this paper, we describe a formalized theory of size-optimal sorting networks. From this formalization we extract a certified checker that successfully verifies computer-generated proofs of optimality on up to 8 inputs. The checker relies on an untrusted oracle to shortcut the search for witnesses on more than 1.6 million NP-complete subproblems.

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Section: Related Workmentioning

confidence: 99%

Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker

Cruz-Filipe

Schneider–Kamp

2015

Interactive Theorem Proving

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“…In order to deal with this problem, trusted proof checkers for rewrite tools have been implemented in the course of the last decade. To that end, a vast amount of rewriting theory has been formalized and proved correct in Isabelle/HOL in the Isabelle Formalization of Rewriting (IsaFoR) project [30,33]. 8 From this formalization the proof checker CeTA is generated automatically, which can validate certificates for the respective properties (like termination, confluence of completeness) output by T T T 2 , CSI, KBCV, mkbTT, FORT, or T C T. Even though many techniques are already supported by IsaFoR/CeTA, some of the methods implemented in tools remain to be added.…”

Section: Resultsmentioning

confidence: 99%

Tools in Term Rewriting for Education

Winkler

Middeldorp

2020

Electron. Proc. Theor. Comput. Sci.

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Term rewriting is a Turing complete model of computation. When taught to students of computer science, key properties of computation as well as techniques to analyze programs on an abstract level are conveyed. This paper gives a swift introduction to term rewriting and presents several automatic tools to analyze term rewrite systems which were developed by the Computational Logic Group at the University of Innsbruck. These include the termination tool T T T 2 , the confluence prover CSI, the completion tools mkbTT and KBCV, the complexity tool TcT, the strategy tool AutoStrat, as well as FORT, an implementation of the decision procedure for the first-order theory for a decidable class of rewrite systems. Besides its applications in research, this software pool has also proved invaluable for teaching, e.g., in multiple editions of the International Summer School on Rewriting.

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“…Certification is the answer to this question. Tools that participate in certified categories are required to produce their justifications in a common format, the certification problem format, or CPF [46] for short. Justifications in this format are usually called certificates.…”

Section: Categoriesmentioning

confidence: 99%

The Termination and Complexity Competition

Giesl

Rubio

Sternagel

et al. 2019

Tools and Algorithms for the Construction and Analysis of Systems

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The termination and complexity competition (termCOMP) focuses on automated termination and complexity analysis for various kinds of programming paradigms, including categories for term rewriting, integer transition systems, imperative programming, logic programming, and functional programming. In all categories, the competition also welcomes the participation of tools providing certifiable output. The goal of the competition is to demonstrate the power and advances of the stateof-the-art tools in each of these areas.

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The Certification Problem Format

Cited by 24 publications

References 33 publications

Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker

Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker

Tools in Term Rewriting for Education

The Termination and Complexity Competition

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