3,854 research outputs found
Learning-Assisted Automated Reasoning with Flyspeck
The considerable mathematical knowledge encoded by the Flyspeck project is
combined with external automated theorem provers (ATPs) and machine-learning
premise selection methods trained on the proofs, producing an AI system capable
of answering a wide range of mathematical queries automatically. The
performance of this architecture is evaluated in a bootstrapping scenario
emulating the development of Flyspeck from axioms to the last theorem, each
time using only the previous theorems and proofs. It is shown that 39% of the
14185 theorems could be proved in a push-button mode (without any high-level
advice and user interaction) in 30 seconds of real time on a fourteen-CPU
workstation. The necessary work involves: (i) an implementation of sound
translations of the HOL Light logic to ATP formalisms: untyped first-order,
polymorphic typed first-order, and typed higher-order, (ii) export of the
dependency information from HOL Light and ATP proofs for the machine learners,
and (iii) choice of suitable representations and methods for learning from
previous proofs, and their integration as advisors with HOL Light. This work is
described and discussed here, and an initial analysis of the body of proofs
that were found fully automatically is provided
The use of data-mining for the automatic formation of tactics
This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques
Defining an approximation to formally verify cryptographic protocols
Electronic forms of communication are abundant in todays world, and much emphasis is placed on these methods of communication in every day life. In order to guarantee the secrecy and authenticity of information exchanged, it is vital to formally verify the cryptographic protocols used in these forms of communications. This verification does, however, present many challenges. The systems to verify are infinite, with an infinite number of sessions and of p articipants. As if this was not enough, there is also a reactive element to deal with: th e intruder. The intruder will attack the protocol to achieve his goal: usurping identity, stealing confidential information, etc. His behavior is unpredictable!
This thesis describes a method of verification based 011 the verification of systems by approximation. Starting from an initial configuration of the network, an overapproximation of the set of messages exchanged is automatically computed. Secrecy and authentication properties can then be checked on the approximated system. Starting from an existing semi-automatic proof method developed by Genet and Klay, an automatic solution is developed.
Starting from an existing semi-automatic proof method developed by Genet and Klay, an automatic solution is developed. This thesis defines a particular approximation function that can be generated automatically and that guarantees that the computation of the approximated system terminates.
Th e verification by approximation only tells if properties are verified. When the verification fails no conclusion can be drawn on the property. Thus, this thesis also shows how the approximation technique can easily be combined with another verification technique to combine the strengths of both approaches.
Finally, the tool developed to validate these developments and the results of cryptographic protocol verifications carried out in the course of this research are included
HOL(y)Hammer: Online ATP Service for HOL Light
HOL(y)Hammer is an online AI/ATP service for formal (computer-understandable)
mathematics encoded in the HOL Light system. The service allows its users to
upload and automatically process an arbitrary formal development (project)
based on HOL Light, and to attack arbitrary conjectures that use the concepts
defined in some of the uploaded projects. For that, the service uses several
automated reasoning systems combined with several premise selection methods
trained on all the project proofs. The projects that are readily available on
the server for such query answering include the recent versions of the
Flyspeck, Multivariate Analysis and Complex Analysis libraries. The service
runs on a 48-CPU server, currently employing in parallel for each task 7 AI/ATP
combinations and 4 decision procedures that contribute to its overall
performance. The system is also available for local installation by interested
users, who can customize it for their own proof development. An Emacs interface
allowing parallel asynchronous queries to the service is also provided. The
overall structure of the service is outlined, problems that arise and their
solutions are discussed, and an initial account of using the system is given
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