Space Complexity vs. Query Complexity

Abstract. 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) log n there is a language with space complexity O(s(n)) and query complexity 2(s(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 ...

• Type: Conference
• Year: 2006
• Where: APPROX
• Authors: Oded Lachish, Ilan Newman, Asaf Shapira
• Keywords: Algorithms, APPROX 2006, Constant Number, Query Complexity, Space Complexity