Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Information Science and Technology / Faculty of Information Science and Technology >
Peer-reviewed Journal Articles, etc >
Testable and untestable classes of first-order formulae
Title: | Testable and untestable classes of first-order formulae |
Authors: | Jordan, Charles Browse this author | Zeugmann, Thomas Browse this author |
Keywords: | Property testing | Logic | Randomized algorithms | Ackermann's class | Ramsey's class |
Issue Date: | Sep-2012 |
Publisher: | Elsevier |
Journal Title: | Journal of Computer and System Sciences |
Volume: | 78 |
Issue: | 5 |
Start Page: | 1557 |
End Page: | 1578 |
Publisher DOI: | 10.1016/j.jcss.2012.01.007 |
Abstract: | In property testing, the goal is to distinguish structures that have some desired property from those that are far from having the property, based on only a small, random sample of the structure. We focus on the classification of first-order sentences according to their testability. This classification was initiated by Alon et al. [2], who showed that graph properties expressible with prefix there exists*for all* are testable but that there is an untestable graph property expressible with quantifier prefix for all*there exists*. The main results of the present paper are as follows. We prove that all (relational) properties expressible with quantifier prefix there exists*for all there exists* (Ackermann's class with equality) are testable and also extend the positive result of Alon et al. [2] to relational structures using a recent result by Austin and Tao [8]. Finally, we simplify the untestable property of Alon et al. [2] and show that prefixes for all(3)there exists, for all(2)there exists for all, for all there exists for all(2) and for all there exists V there exists can express untestable graph properties when equality is allowed. |
Type: | article (author version) |
URI: | http://hdl.handle.net/2115/49938 |
Appears in Collections: | 情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
|
Submitter: Charles Jordan
|