Formally Verified Algorithms for Upper-Bounding State Space Diameters

Formally Verified Algorithms for Upper-Bounding State Space Diameters A completeness threshold is required to guarantee the completeness of planning as satisfiability, and bounded model checking of safety properties. We investigate completeness thresholds related to the diameter of the underlying transition system. A valid threshold, the diameter is the maximum element in the set of lengths of all shortest paths between pairs of states. The diameter is not calculated exactly in our setting, where the transition system is succinctly described using a (propositionally) factored representation. Rather, an upper bound on the diameter is calculated compositionally, by bounding the diameters of small abstract subsystems, and then composing those. We describe our formal verification in HOL4 of compositional algorithms for computing a relatively tight upper bound on the system diameter. Existing compositional algorithms are characterised in terms of the problem structures they exploit, including acyclicity in state-variable dependencies, and acyclicity in the state space. Such algorithms are further distinguished by: (1) whether the bound calculated for abstractions is the diameter, sublist diameter or recurrence diameter, and (2) the “direction” of traversal of the compositional structure, either top-down or bottom-up. As a supplement, we publish our library—now over 14k lines—of HOL4 proof scripts about transition systems. That shall be of use to future related mechanisation efforts, and is carefully designed for compatibility with hybrid systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Automated Reasoning Springer Journals

Formally Verified Algorithms for Upper-Bounding State Space Diameters

Loading next page...
 
/lp/springer_journal/formally-verified-algorithms-for-upper-bounding-state-space-diameters-dDtw3KyMhB
Publisher
Springer Netherlands
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Computer Science; Mathematical Logic and Formal Languages; Artificial Intelligence (incl. Robotics); Mathematical Logic and Foundations; Symbolic and Algebraic Manipulation
ISSN
0168-7433
eISSN
1573-0670
D.O.I.
10.1007/s10817-018-9450-z
Publisher site
See Article on Publisher Site

Abstract

A completeness threshold is required to guarantee the completeness of planning as satisfiability, and bounded model checking of safety properties. We investigate completeness thresholds related to the diameter of the underlying transition system. A valid threshold, the diameter is the maximum element in the set of lengths of all shortest paths between pairs of states. The diameter is not calculated exactly in our setting, where the transition system is succinctly described using a (propositionally) factored representation. Rather, an upper bound on the diameter is calculated compositionally, by bounding the diameters of small abstract subsystems, and then composing those. We describe our formal verification in HOL4 of compositional algorithms for computing a relatively tight upper bound on the system diameter. Existing compositional algorithms are characterised in terms of the problem structures they exploit, including acyclicity in state-variable dependencies, and acyclicity in the state space. Such algorithms are further distinguished by: (1) whether the bound calculated for abstractions is the diameter, sublist diameter or recurrence diameter, and (2) the “direction” of traversal of the compositional structure, either top-down or bottom-up. As a supplement, we publish our library—now over 14k lines—of HOL4 proof scripts about transition systems. That shall be of use to future related mechanisation efforts, and is carefully designed for compatibility with hybrid systems.

Journal

Journal of Automated ReasoningSpringer Journals

Published: Feb 3, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off