Loosely speaking, a proximity-oblivious (property) tester is a randomized algorithm that makes a constant number of queries to a tested object and distinguishes objects that have a predetermined property from those that lack it. Specifically, for some threshold probability $c$, objects having the property are accepted with probability at least $c$, whereas objects that are $\e$-far from having the property are accepted with probability at most $c-F(\e)$, where $F:(0,1] \to(0,1]$ is some fixed monotone function. (We stress that, in contrast to standard testers, a proximity-oblivious tester is not given the proximity parameter.)
The foregoing notion, introduced by Goldreich and Ron (STOC 2009), was originally defined with respect to $c=1$, which corresponds to one-sided error (proximity-oblivious) testing. Here we study the two-sided error version of proximity-oblivious testers; that is, the (general) case of arbitrary $c\in(0,1]$. We show that, in many natural cases, two-sided error proximity-oblivious testers are more powerful than one-sided error proximity-oblivious testers; that is, many
natural properties that have no one-sided error proximity-oblivious testers do have a two-sided error proximity-oblivious tester.
Mainly revising the introduction so to include a more elaborate account of the main results.
Loosely speaking, a proximity-oblivious (property) tester is a randomized algorithm that makes a constant number of queries to a tested object and distinguishes objects that have a predetermined property from those that lack it. Specifically, for some threshold probability $c$, objects having the property are accepted with probability at least $c$, whereas objects that are $\e$-far from having the property are accepted with probability at most $c-F(\e)$, where $F:(0,1] \to(0,1]$ is some fixed monotone function. (We stress that, in contrast to standard testers, a proximity-oblivious tester is not given the proximity parameter.)
The foregoing notion, introduced by Goldreich and Ron (STOC 2009), was originally defined with respect to $c=1$, which corresponds to one-sided error (proximity-oblivious) testing. Here we study the two-sided error version of proximity-oblivious testers; that is, the (general) case of arbitrary $c\in(0,1]$. We show that, in many natural cases, two-sided error proximity-oblivious testers are more powerful than one-sided error proximity-oblivious testers; that is, many
natural properties that have no one-sided error proximity-oblivious testers do have a two-sided error proximity-oblivious tester.
Minor corrections.
Loosely speaking, a proximity-oblivious (property) tester is a randomized algorithm that makes a constant number of queries to a tested object and distinguishes objects that have a predetermined property from those that lack it. Specifically, for some threshold probability $c$, objects having the property are accepted with probability at least $c$, whereas objects that are $\e$-far from having the property are accepted with probability at most $c-F(\e)$, where $F:(0,1] \to(0,1]$ is some fixed monotone function. (We stress that, in contrast to standard testers, a proximity-oblivious tester is not given the proximity parameter.)
The foregoing notion, introduced by Goldreich and Ron (STOC 2009), was originally defined with respect to $c=1$, which corresponds to one-sided error (proximity-oblivious) testing. Here we study the two-sided error version of proximity-oblivious testers; that is, the (general) case of arbitrary $c\in(0,1]$. We show that, in many natural cases, two-sided error proximity-oblivious testers are more powerful than one-sided error proximity-oblivious testers; that is, many
natural properties that have no one-sided error proximity-oblivious testers do have a two-sided error proximity-oblivious tester.
New material included in a new Sec 3.3.
Loosely speaking, a proximity-oblivious (property) tester is a randomized algorithm that makes a constant number of queries to a tested object and distinguishes objects that have a predetermined property from those that lack it. Specifically, for some threshold probability $c$, objects having the property are accepted with probability at least $c$, whereas objects that are $\e$-far from having the property are accepted with probability at most $c-F(\e)$, where $F:(0,1] \to(0,1]$ is some fixed monotone function. (We stress that, in contrast to standard testers, a proximity-oblivious tester is not given the proximity parameter.)
The foregoing notion, introduced by Goldreich and Ron (STOC 2009), was originally defined with respect to $c=1$, which corresponds to one-sided error (proximity-oblivious) testing. Here we study the two-sided error version of proximity-oblivious testers; that is, the (general) case of arbitrary $c\in(0,1]$. We show that, in many natural cases, two-sided error proximity-oblivious testers are more powerful than one-sided error proximity-oblivious testers; that is, many
natural properties that have no one-sided error proximity-oblivious testers do have a two-sided error proximity-oblivious tester.
The 2nd author's name was omitted due to system fault. The PDF is identical to the original.
Loosely speaking, a proximity-oblivious (property) tester is a randomized algorithm that makes a constant number of queries to a tested object and distinguishes objects that have a predetermined property from those that lack it. Specifically, for some threshold probability $c$, objects having the property are accepted with probability at least $c$, whereas objects that are $\e$-far from having the property are accepted with probability at most $c-F(\e)$, where $F:(0,1] \to(0,1]$ is some fixed monotone function. (We stress that, in contrast to standard testers, a proximity-oblivious tester is not given the proximity parameter.)
The foregoing notion, introduced by Goldreich and Ron (STOC 2009), was originally defined with respect to $c=1$, which corresponds to one-sided error (proximity-oblivious) testing. Here we study the two-sided error version of proximity-oblivious testers; that is, the (general) case of arbitrary $c\in(0,1]$. We show that, in many natural cases, two-sided error proximity-oblivious testers are more powerful than one-sided error proximity-oblivious testers; that is, many
natural properties that have no one-sided error proximity-oblivious testers do have a two-sided error proximity-oblivious tester.