17,312 research outputs found
Robust Computer Algebra, Theorem Proving, and Oracle AI
In the context of superintelligent AI systems, the term "oracle" has two
meanings. One refers to modular systems queried for domain-specific tasks.
Another usage, referring to a class of systems which may be useful for
addressing the value alignment and AI control problems, is a superintelligent
AI system that only answers questions. The aim of this manuscript is to survey
contemporary research problems related to oracles which align with long-term
research goals of AI safety. We examine existing question answering systems and
argue that their high degree of architectural heterogeneity makes them poor
candidates for rigorous analysis as oracles. On the other hand, we identify
computer algebra systems (CASs) as being primitive examples of domain-specific
oracles for mathematics and argue that efforts to integrate computer algebra
systems with theorem provers, systems which have largely been developed
independent of one another, provide a concrete set of problems related to the
notion of provable safety that has emerged in the AI safety community. We
review approaches to interfacing CASs with theorem provers, describe
well-defined architectural deficiencies that have been identified with CASs,
and suggest possible lines of research and practical software projects for
scientists interested in AI safety.Comment: 15 pages, 3 figure
Towards the Formal Reliability Analysis of Oil and Gas Pipelines
It is customary to assess the reliability of underground oil and gas
pipelines in the presence of excessive loading and corrosion effects to ensure
a leak-free transport of hazardous materials. The main idea behind this
reliability analysis is to model the given pipeline system as a Reliability
Block Diagram (RBD) of segments such that the reliability of an individual
pipeline segment can be represented by a random variable. Traditionally,
computer simulation is used to perform this reliability analysis but it
provides approximate results and requires an enormous amount of CPU time for
attaining reasonable estimates. Due to its approximate nature, simulation is
not very suitable for analyzing safety-critical systems like oil and gas
pipelines, where even minor analysis flaws may result in catastrophic
consequences. As an accurate alternative, we propose to use a
higher-order-logic theorem prover (HOL) for the reliability analysis of
pipelines. As a first step towards this idea, this paper provides a
higher-order-logic formalization of reliability and the series RBD using the
HOL theorem prover. For illustration, we present the formal analysis of a
simple pipeline that can be modeled as a series RBD of segments with
exponentially distributed failure times.Comment: 15 page
Applying Formal Methods to Networking: Theory, Techniques and Applications
Despite its great importance, modern network infrastructure is remarkable for
the lack of rigor in its engineering. The Internet which began as a research
experiment was never designed to handle the users and applications it hosts
today. The lack of formalization of the Internet architecture meant limited
abstractions and modularity, especially for the control and management planes,
thus requiring for every new need a new protocol built from scratch. This led
to an unwieldy ossified Internet architecture resistant to any attempts at
formal verification, and an Internet culture where expediency and pragmatism
are favored over formal correctness. Fortunately, recent work in the space of
clean slate Internet design---especially, the software defined networking (SDN)
paradigm---offers the Internet community another chance to develop the right
kind of architecture and abstractions. This has also led to a great resurgence
in interest of applying formal methods to specification, verification, and
synthesis of networking protocols and applications. In this paper, we present a
self-contained tutorial of the formidable amount of work that has been done in
formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial
Variations on a Theme: A Bibliography on Approaches to Theorem Proving Inspired From Satchmo
This articles is a structured bibliography on theorem provers,
approaches to theorem proving, and theorem proving applications inspired
from Satchmo, the model generation theorem prover developed
in the mid 80es of the 20th century at ECRC, the European Computer-
Industry Research Centre. Note that the bibliography given in this article
is not exhaustive
Formal representation and proof for cooperative games
In this contribution we present some work we have been doing in representing and proving theorems from the area of economics, and mainly we present work we will do in a project in which we will apply mechanised theorem proving tools to a class of economic problems for which very few general tools currently exist. For mechanised theorem proving, the research introduces the field to a new application domain with a large user base; more specifically, the researchers are collaborating with developers working on state-of-the-art theorem provers. For economics, the research will provide tools for handling a hard class of problems; more generally, as the first application of mechanised theorem proving to centrally involve economic theorists, it aims to properly introduce mechanised theorem proving techniques to the discipline.\u
Proving soundness of combinatorial Vickrey auctions and generating verified executable code
Using mechanised reasoning we prove that combinatorial Vickrey auctions are
soundly specified in that they associate a unique outcome (allocation and
transfers) to any valid input (bids). Having done so, we auto-generate verified
executable code from the formally defined auction. This removes a source of
error in implementing the auction design. We intend to use formal methods to
verify new auction designs. Here, our contribution is to introduce and
demonstrate the use of formal methods for auction verification in the familiar
setting of a well-known auction
Edit and verify
Automated theorem provers are used in extended static checking, where they
are the performance bottleneck. Extended static checkers are run typically
after incremental changes to the code. We propose to exploit this usage pattern
to improve performance. We present two approaches of how to do so and a full
solution
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
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