99 research outputs found
Proof-Pattern Recognition and Lemma Discovery in ACL2
We present a novel technique for combining statistical machine learning for
proof-pattern recognition with symbolic methods for lemma discovery. The
resulting tool, ACL2(ml), gathers proof statistics and uses statistical
pattern-recognition to pre-processes data from libraries, and then suggests
auxiliary lemmas in new proofs by analogy with already seen examples. This
paper presents the implementation of ACL2(ml) alongside theoretical
descriptions of the proof-pattern recognition and lemma discovery methods
involved in it
Hipster: Integrating Theory Exploration in a Proof Assistant
This paper describes Hipster, a system integrating theory exploration with
the proof assistant Isabelle/HOL. Theory exploration is a technique for
automatically discovering new interesting lemmas in a given theory development.
Hipster can be used in two main modes. The first is exploratory mode, used for
automatically generating basic lemmas about a given set of datatypes and
functions in a new theory development. The second is proof mode, used in a
particular proof attempt, trying to discover the missing lemmas which would
allow the current goal to be proved. Hipster's proof mode complements and
boosts existing proof automation techniques that rely on automatically
selecting existing lemmas, by inventing new lemmas that need induction to be
proved. We show example uses of both modes
ENIGMA: Efficient Learning-based Inference Guiding Machine
ENIGMA is a learning-based method for guiding given clause selection in
saturation-based theorem provers. Clauses from many proof searches are
classified as positive and negative based on their participation in the proofs.
An efficient classification model is trained on this data, using fast
feature-based characterization of the clauses . The learned model is then
tightly linked with the core prover and used as a basis of a new parameterized
evaluation heuristic that provides fast ranking of all generated clauses. The
approach is evaluated on the E prover and the CASC 2016 AIM benchmark, showing
a large increase of E's performance.Comment: Submitted to LPAR 201
Development and validation of tools for the implementation of european air quality policy in Germany (Project VALIUM)
International audienceIn the framework of the German Atmospheric Research Program AFO-2000 a system of consistent coupled numerical models has been developed. The purpose of the model system is to serve as a tool for the execution of European urban air quality regulations. A consortium with the acronym VALIUM was formed, which consisted of German research institutes, environmental consultancies and an environmental agency. A substantial part of the VALIUM program was devoted to the generation of a set of high quality data for the validation of the numerical model system. The validation data are based on a combination of field studies, tracer experiments and corresponding wind tunnel experiments. The field experiments were carried out inside and around a street canyon in a city district of Hanover/Germany. After a brief introduction to the VALIUM project a summary of the main results will be given
Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
Smart premise selection is essential when using automated reasoning as a tool
for large-theory formal proof development. A good method for premise selection
in complex mathematical libraries is the application of machine learning to
large corpora of proofs. This work develops learning-based premise selection in
two ways. First, a newly available minimal dependency analysis of existing
high-level formal mathematical proofs is used to build a large knowledge base
of proof dependencies, providing precise data for ATP-based re-verification and
for training premise selection algorithms. Second, a new machine learning
algorithm for premise selection based on kernel methods is proposed and
implemented. To evaluate the impact of both techniques, a benchmark consisting
of 2078 large-theory mathematical problems is constructed,extending the older
MPTP Challenge benchmark. The combined effect of the techniques results in a
50% improvement on the benchmark over the Vampire/SInE state-of-the-art system
for automated reasoning in large theories.Comment: 26 page
Mining State-Based Models from Proof Corpora
Interactive theorem provers have been used extensively to reason about
various software/hardware systems and mathematical theorems. The key challenge
when using an interactive prover is finding a suitable sequence of proof steps
that will lead to a successful proof requires a significant amount of human
intervention. This paper presents an automated technique that takes as input
examples of successful proofs and infers an Extended Finite State Machine as
output. This can in turn be used to generate proofs of new conjectures. Our
preliminary experiments show that the inferred models are generally accurate
(contain few false-positive sequences) and that representing existing proofs in
such a way can be very useful when guiding new ones.Comment: To Appear at Conferences on Intelligent Computer Mathematics 201
Machine Learning for Mathematical Software
While there has been some discussion on how Symbolic Computation could be
used for AI there is little literature on applications in the other direction.
However, recent results for quantifier elimination suggest that, given enough
example problems, there is scope for machine learning tools like Support Vector
Machines to improve the performance of Computer Algebra Systems. We survey the
authors own work and similar applications for other mathematical software.
It may seem that the inherently probabilistic nature of machine learning
tools would invalidate the exact results prized by mathematical software.
However, algorithms and implementations often come with a range of choices
which have no effect on the mathematical correctness of the end result but a
great effect on the resources required to find it, and thus here, machine
learning can have a significant impact.Comment: To appear in Proc. ICMS 201
Improved cross-validation for classifiers that make algorithmic choices to minimise runtime without compromising output correctness
Our topic is the use of machine learning to improve software by making
choices which do not compromise the correctness of the output, but do affect
the time taken to produce such output. We are particularly concerned with
computer algebra systems (CASs), and in particular, our experiments are for
selecting the variable ordering to use when performing a cylindrical algebraic
decomposition of -dimensional real space with respect to the signs of a set
of polynomials.
In our prior work we explored the different ML models that could be used, and
how to identify suitable features of the input polynomials. In the present
paper we both repeat our prior experiments on problems which have more
variables (and thus exponentially more possible orderings), and examine the
metric which our ML classifiers targets. The natural metric is computational
runtime, with classifiers trained to pick the ordering which minimises this.
However, this leads to the situation were models do not distinguish between any
of the non-optimal orderings, whose runtimes may still vary dramatically. In
this paper we investigate a modification to the cross-validation algorithms of
the classifiers so that they do distinguish these cases, leading to improved
results.Comment: 16 pages. Accepted into the Proceedings of MACIS 2019. arXiv admin
note: text overlap with arXiv:1906.0145
- …