• Skip to primary navigation
  • Skip to main content
SRI logo
  • About
    • Press room
    • Our history
  • Expertise
    • Advanced imaging systems
    • Artificial intelligence
    • Biomedical R&D services
    • Biomedical sciences
    • Computer vision
    • Cyber & formal methods
    • Education and learning
    • Innovation strategy and policy
    • National security
    • Ocean & space
    • Quantum
    • Robotics, sensors & devices
    • Speech & natural language
    • Video test & measurement
  • Ventures
  • NSIC
  • Careers
  • Contact
  • 日本支社
Search
Close
Publication June 1, 2011

Synthesizing Geometry Constructions

Citation

Copy to clipboard


Gulwani, S., Korthikanti, V. A., & Tiwari, A. (2011). Synthesizing geometry constructions. ACM SIGPLAN Notices, 46(6), 50-61.

Abstract

In this paper, we study the problem of automatically solving ruler/compass based geometry construction problems. We first introduce a logic and a programming language for describing such constructions and then phrase the automation problem as a program synthesis problem. We then describe a new program synthesis technique based on three key insights: (i) reduction of symbolic reasoning to concrete reasoning (based on a deep theoretical result that reduces verification to random testing), (ii) extending the instruction set of the programming language with higher level primitives (representing basic constructions found in textbook chapters, inspired by how humans use their experience and knowledge gained from chapters to perform complicated constructions), and (iii) pruning the forward exhaustive search using a goal-directed heuristic (simulating backward reasoning performed by humans). Our tool can successfully synthesize constructions for various geometry problems picked up from high-school textbooks and examination papers in a reasonable amount of time. This opens up an amazing set of possibilities in the context of making classroom teaching interactive.

↓ View online

Share this

How can we help?

Once you hit send…

We’ll match your inquiry to the person who can best help you.

Expect a response within 48 hours.

Career call to action image

Make your own mark.

Search jobs

Our work

Case studies

Publications

Timeline of innovation

Areas of expertise

Institute

Leadership

Press room

Media inquiries

Compliance

Careers

Job listings

Contact

SRI Ventures

Our locations

Headquarters

333 Ravenswood Ave
Menlo Park, CA 94025 USA

+1 (650) 859-2000

Subscribe to our newsletter


日本支社
SRI International
  • Contact us
  • Privacy Policy
  • Cookies
  • DMCA
  • Copyright © 2023 SRI International
Manage Cookie Consent
To provide the best experiences, we use technologies like cookies to store and/or access device information. Consenting to these technologies will allow us to process data such as browsing behavior or unique IDs on this site. Not consenting or withdrawing consent, may adversely affect certain features and functions.
Functional Always active
The technical storage or access is strictly necessary for the legitimate purpose of enabling the use of a specific service explicitly requested by the subscriber or user, or for the sole purpose of carrying out the transmission of a communication over an electronic communications network.
Preferences
The technical storage or access is necessary for the legitimate purpose of storing preferences that are not requested by the subscriber or user.
Statistics
The technical storage or access that is used exclusively for statistical purposes. The technical storage or access that is used exclusively for anonymous statistical purposes. Without a subpoena, voluntary compliance on the part of your Internet Service Provider, or additional records from a third party, information stored or retrieved for this purpose alone cannot usually be used to identify you.
Marketing
The technical storage or access is required to create user profiles to send advertising, or to track the user on a website or across several websites for similar marketing purposes.
Manage options Manage services Manage vendors Read more about these purposes
View preferences
{title} {title} {title}