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Certifying Algorithms
, 2010
"... A certifying algorithm is an algorithm that produces, with each output, a certificate or witness (easytoverify proof) that the particular output has not been compromised by a bug. A user of a certifying algorithm inputs x, receives the output y and the certificate w, and then checks, either manual ..."
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Cited by 24 (6 self)
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A certifying algorithm is an algorithm that produces, with each output, a certificate or witness (easytoverify proof) that the particular output has not been compromised by a bug. A user of a certifying algorithm inputs x, receives the output y and the certificate w, and then checks, either manually or by use of a program, that w proves that y is a correct output for input x. In this way, he/she can be sure of the correctness of the output without having to trust the algorithm. We put forward the thesis that certifying algorithms are much superior to noncertifying algorithms, and that for complex algorithmic tasks, only certifying algorithms are satisfactory. Acceptance of this thesis would lead to a change of how algorithms are taught and how algorithms are researched. The widespread use of certifying algorithms would greatly enhance the reliability of algorithmic software. We survey the state of the art in certifying algorithms and add to it. In particular, we start a
A Proof Planning Framework for Isabelle
, 2005
"... Proof planning is a paradigm for the automation of proof that focuses on encoding intelligence to guide the proof process. The idea is to capture common patterns of reasoning which can be used to derive abstract descriptions of proofs known as proof plans. These can then be executed to provide fully ..."
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Cited by 14 (9 self)
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Proof planning is a paradigm for the automation of proof that focuses on encoding intelligence to guide the proof process. The idea is to capture common patterns of reasoning which can be used to derive abstract descriptions of proofs known as proof plans. These can then be executed to provide fully formal proofs. This thesis concerns the development and analysis of a novel approach to proof planning that focuses on an explicit representation of choices during search. We embody our approach as a proof planner for the generic proof assistant Isabelle and use the Isar language, which is humanreadable and machinecheckable, to represent proof plans. Within this framework we develop an inductive theorem prover as a case study of our approach to proof planning. Our prover uses the difference reduction heuristic known as rippling to automate the step cases of the inductive proofs. The development of a flexible approach to rippling that supports its various modifications and extensions is the second major focus of this thesis. Here, our inductive theorem prover provides a context in which to evaluate rippling experimentally. This work results in an efficient and powerful inductive theorem prover for Isabelle as well as proposals for further improving the efficiency of rippling. We also draw observations in order
AUTOMATIC PROOF OF GRAPH NONISOMORPHISM
"... Abstract. We describe automated methods for constructing nonisomorphism proofs for pairs of graphs. The proofs can be humanreadable or machinereadable. We have developed a proof generator for graph nonisomorphism, which allows users to input graphs and construct a proof of (non)isomorphism. 1. ..."
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Abstract. We describe automated methods for constructing nonisomorphism proofs for pairs of graphs. The proofs can be humanreadable or machinereadable. We have developed a proof generator for graph nonisomorphism, which allows users to input graphs and construct a proof of (non)isomorphism. 1.
On the Comparison of Proof Planning Systems λCLAM
 ΩMEGA and ISAPLANNER. Electronic Notes in Theoretical Computer Sci. 151
, 2005
"... We present a framework for describing proof planners. This framework is based around a decomposition of proof planners into planning states, proof language, proof plans, proof methods, proof revision, proof control and planning algorithms. We use this framework to motivate the comparison of three re ..."
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We present a framework for describing proof planners. This framework is based around a decomposition of proof planners into planning states, proof language, proof plans, proof methods, proof revision, proof control and planning algorithms. We use this framework to motivate the comparison of three recent proof planning systems, λCLaM, Ωmega and IsaPlanner, and demonstrate how the framework allows us to discuss and illustrate both their similarities and differences in a consistent fashion. This analysis reveals that proof control and the use of contextual information in planning states are key areas in need of further investigation. Key words: Proof Planning
System Description: Multi A MultiStrategy Proof Planner
"... The CASC competitions among automated theorem provers show that there is no single system that outperforms all other systems in all domains. One reaction to this observation is the combination of several systems in a competitive (e.g., the SSCPA system) or cooperative manner (e.g., the CSSCPA and TE ..."
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The CASC competitions among automated theorem provers show that there is no single system that outperforms all other systems in all domains. One reaction to this observation is the combination of several systems in a competitive (e.g., the SSCPA system) or cooperative manner (e.g., the CSSCPA and TECHS systems).
Calculemus 2005 Preliminary Version On the Comparison of Proof Planning Systems
"... We present a framework for describing proof planners. This framework is based around a decomposition of proof planners into planning states, proof language, proof plans, proof methods, proof revision, proof control and planning algorithms. We use this framework to motivate the comparison of three re ..."
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We present a framework for describing proof planners. This framework is based around a decomposition of proof planners into planning states, proof language, proof plans, proof methods, proof revision, proof control and planning algorithms. We use this framework to motivate the comparison of three recent proof planning systems, λCLaM, Ωmega and IsaPlanner, and demonstrate how the framework allows us to discuss and illustrate both their similarities and differences in a consistent fashion. This analysis reveals that proof control and the use of contextual information in planning states are key areas in need of further investigation. Key words: Proof Planning 1
Project Title Systems for ComputerSupported Mathematical Knowledge Evolution Specific Programme Structuring the European Research Area Activity Human Resources and Mobility Activities
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On the Comparison of Proof Planning Systems
"... We present a framework for describing proof planners. This framework is based around a decomposition of proof planners into planning states, proof language, proof plans, proof methods, proof revision, proof control and planning algorithms. We use this framework to motivate the comparison of three re ..."
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We present a framework for describing proof planners. This framework is based around a decomposition of proof planners into planning states, proof language, proof plans, proof methods, proof revision, proof control and planning algorithms. We use this framework to motivate the comparison of three recent proof planning systems, λCLaM, Ωmega and IsaPlanner, and demonstrate how the framework allows us to discuss and illustrate both their similarities and differences in a consistent fashion. This analysis reveals that proof control and the use of contextual information in planning states are key areas in need of further investigation. Key words: Proof Planning 1