Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Regular Languages are Testable with a Constant Number of Queries
SIAM Journal on Computing
Some 3CNF properties are hard to test
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Testing of function that have small width branching programs
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Three theorems regarding testing graph properties
Random Structures & Algorithms
Functions that have read-twice constant width branching programs are not necessarily testable
Random Structures & Algorithms
A Characterization of the (natural) Graph Properties Testable with One-Sided Error
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Deterministic one-counter automata
Journal of Computer and System Sciences
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Combinatorial property testing deals with the following relaxation of decision problems: Given a fixed property and an input x, one wants to decide whether x satisfies the property or is “far” from satisfying it. The main focus of property testing is in identifying large families of properties that can be tested with a certain number of queries to the input. Unfortunately, there are nearly no general results connecting standard complexity measures of languages with the hardness of testing them. In this paper we study the relation between the space complexity of a language and its query complexity. Our main result is that for any space complexity s(n)≤logn there is a language with space complexity O(s(n)) and query complexity 2$^{\Omega({\it s}({\it n}))}$. We conjecture that this exponential lower bound is best possible, namely that the query complexity of a languages is at most exponential in its space complexity. Our result has implications with respect to testing languages accepted by certain restricted machines. Alon et al. [FOCS 1999] have shown that any regular language is testable with a constant number of queries. It is well known that any language in space o(loglogn) is regular, thus implying that such languages can be so tested. It was previously known that there are languages in space O(logn) which are not testable with a constant number of queries and Newman [FOCS 2000] raised the question of closing the exponential gap between these two results. A special case of our main result resolves this problem as it implies that there is a language in space O(loglogn) that is not testable with a constant number of queries, thus showing that the o(loglogn) bound is best possible. It was also previously known that the class of testable properties cannot be extended to all context-free languages. We further show that one cannot even extend the family of testable languages to the class of languages accepted by single counter machines which is perhaps the weakest (uniform) computational model that is strictly stronger than finite automata.