285 research outputs found
A Deep Reinforcement Learning Approach to First-Order Logic Theorem Proving
Automated theorem provers have traditionally relied on manually tuned
heuristics to guide how they perform proof search. Deep reinforcement learning
has been proposed as a way to obviate the need for such heuristics, however,
its deployment in automated theorem proving remains a challenge. In this paper
we introduce TRAIL, a system that applies deep reinforcement learning to
saturation-based theorem proving. TRAIL leverages (a) a novel neural
representation of the state of a theorem prover and (b) a novel
characterization of the inference selection process in terms of an
attention-based action policy. We show through systematic analysis that these
mechanisms allow TRAIL to significantly outperform previous
reinforcement-learning-based theorem provers on two benchmark datasets for
first-order logic automated theorem proving (proving around 15% more theorems)
Learning to Prove Theorems by Learning to Generate Theorems
We consider the task of automated theorem proving, a key AI task. Deep
learning has shown promise for training theorem provers, but there are limited
human-written theorems and proofs available for supervised learning. To address
this limitation, we propose to learn a neural generator that automatically
synthesizes theorems and proofs for the purpose of training a theorem prover.
Experiments on real-world tasks demonstrate that synthetic data from our
approach improves the theorem prover and advances the state of the art of
automated theorem proving in Metamath. Code is available at
https://github.com/princeton-vl/MetaGen
Learning to Find Proofs and Theorems by Learning to Refine Search Strategies: The Case of Loop Invariant Synthesis
We propose a new approach to automated theorem proving where an
AlphaZero-style agent is self-training to refine a generic high-level expert
strategy expressed as a nondeterministic program. An analogous teacher agent is
self-training to generate tasks of suitable relevance and difficulty for the
learner. This allows leveraging minimal amounts of domain knowledge to tackle
problems for which training data is unavailable or hard to synthesize. As a
specific illustration, we consider loop invariant synthesis for imperative
programs and use neural networks to refine both the teacher and solver
strategies
Conjectures, tests and proofs: An overview of theory exploration
A key component of mathematical reasoning is the ability to formulate interesting conjectures about a problem domain at hand. In this paper, we give a brief overview of a theory exploration system called QuickSpec, which is able to automatically discover interesting conjectures about a given set of functions. QuickSpec works by interleaving term generation with random testing to form candidate conjectures. This is made tractable by starting from small sizes and ensuring that only terms that are irreducible with respect to already discovered conjectures are considered. QuickSpec has been successfully applied to generate lemmas for automated inductive theorem proving as well as to generate specifications of functional programs. We give an overview of typical use-cases of QuickSpec, as well as demonstrating how to easily connect it to a theorem prover of the user’s choice
ML + FV = ? A Survey on the Application of Machine Learning to Formal Verification
Formal Verification (FV) and Machine Learning (ML) can seem incompatible due
to their opposite mathematical foundations and their use in real-life problems:
FV mostly relies on discrete mathematics and aims at ensuring correctness; ML
often relies on probabilistic models and consists of learning patterns from
training data. In this paper, we postulate that they are complementary in
practice, and explore how ML helps FV in its classical approaches: static
analysis, model-checking, theorem-proving, and SAT solving. We draw a landscape
of the current practice and catalog some of the most prominent uses of ML
inside FV tools, thus offering a new perspective on FV techniques that can help
researchers and practitioners to better locate the possible synergies. We
discuss lessons learned from our work, point to possible improvements and offer
visions for the future of the domain in the light of the science of software
and systems modeling.Comment: 13 pages, no figures, 3 table
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