## Testing membership in languages that have small width branching programs

Venue: | SIAM Journal on Computing |

Citations: | 19 - 5 self |

### BibTeX

@ARTICLE{Newman_testingmembership,

author = {Ilan Newman},

title = {Testing membership in languages that have small width branching programs},

journal = {SIAM Journal on Computing},

year = {},

volume = {31},

pages = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. Combinatorial property testing, initiated formally by Goldreich, Goldwasser, and

### Citations

2352 | Computational Complexity
- Papadimitriou
- 1994
(Show Context)
Citation Context ...amples of functions that are, say, in uniform SP ACE(log log n) but not regular and hence do not belong to SP ACE(o(log log n)). One such interesting example is the following example of Papadimitriou =-=[14]-=-:Let b be a binary string without leading 0’s. We denote by n(b) the natural number whose binary representation is b. Let L = {b1$b2$ ...$bk| n(bi) =i}. Clearly L ∈ SP ACE(log log n). It is also not h... |

721 | Proof verification and the hardness of approximation problems - Arora, Lund, et al. - 1998 |

429 | Property testing and its connection to learning and approximation
- Goldreich, Goldwasser, et al.
- 1996
(Show Context)
Citation Context ...lgorithms, branching programs AMS subject classifications. 68Q15, 68Q10 PII. S009753970038211X 1. Introduction. Combinatorial property testing, initiated formally by Goldreich, Goldwasser, and Ron in =-=[11]-=- and inspired by Rubinfeld and Sudan [16], deals with the following relaxation of decision problems:Given a fixed property and an input x, one wants to decide whether x has the property or is “far” fr... |

348 | Self-testing/correcting with applications to numerical problems
- Blum, Luby, et al.
- 1993
(Show Context)
Citation Context ...rt from being a natural relaxation of the standard decision problem, combinatorial property testing emerges naturally in the context of probably approximately correct (PAC) learning, program checking =-=[10, 6, 16]-=-, probabilistically checkable proofs [3], and approximation algorithms [11]. In [11], the authors mainly consider graph properties and show (among other ∗ Received by the editors December 5, 2000; acc... |

332 | Robust characterizations of polynomials with applications to program testing
- Rubinfeld, Sudan
- 1996
(Show Context)
Citation Context ... classifications. 68Q15, 68Q10 PII. S009753970038211X 1. Introduction. Combinatorial property testing, initiated formally by Goldreich, Goldwasser, and Ron in [11] and inspired by Rubinfeld and Sudan =-=[16]-=-, deals with the following relaxation of decision problems:Given a fixed property and an input x, one wants to decide whether x has the property or is “far” from having the property. A property here i... |

213 | Bounded-width polynomial-size branching programs recognize exactly those languages in nc1
- Barrington
(Show Context)
Citation Context ...evel query the same variable), and each variable appears in at most one level. BPs have been extensively studied as a model of computation for Boolean functions. ([7] contains a survey text; see also =-=[4, 5, 13]-=- for a partial list of different aspects involving BPs and read-once BPs.) The size of a BP (and a read-once BP) is tightly related to the space complexity of the function it computes:If a language is... |

179 |
The complexity of finite functions
- Boppana, Sipser
- 1990
(Show Context)
Citation Context ...ted with a variable (all nodes in a level query the same variable), and each variable appears in at most one level. BPs have been extensively studied as a model of computation for Boolean functions. (=-=[7]-=- contains a survey text; see also [4, 5, 13] for a partial list of different aspects involving BPs and read-once BPs.) The size of a BP (and a read-once BP) is tightly related to the space complexity ... |

160 | Efficient testing of large graphs
- Alon, Fischer, et al.
- 2000
(Show Context)
Citation Context ...btaining general results identifying classes of properties that are testable. Some interesting examples are given in [11], and several additional ones can be obtained by applying the regularity lemma =-=[1]-=-. Alon et. al. [2] proved that membership in any regular language is testable, hence obtaining a general result identifying a nontrivial class of properties, each being testable. Here we further pursu... |

79 | Regular languages are testable with a constant number of queries
- Alon, Krivelevich, et al.
- 2001
(Show Context)
Citation Context ...esults identifying classes of properties that are testable. Some interesting examples are given in [11], and several additional ones can be obtained by applying the regularity lemma [1]. Alon et. al. =-=[2]-=- proved that membership in any regular language is testable, hence obtaining a general result identifying a nontrivial class of properties, each being testable. Here we further pursue this direction:W... |

44 | Time-space tradeoffs for branching programs
- Beame, Saks, et al.
- 1998
(Show Context)
Citation Context ...evel query the same variable), and each variable appears in at most one level. BPs have been extensively studied as a model of computation for Boolean functions. ([7] contains a survey text; see also =-=[4, 5, 13]-=- for a partial list of different aspects involving BPs and read-once BPs.) The size of a BP (and a read-once BP) is tightly related to the space complexity of the function it computes:If a language is... |

42 |
The recognition problem for the set of perfect squares
- Cobham
- 1966
(Show Context)
Citation Context ...once BPs.) The size of a BP (and a read-once BP) is tightly related to the space complexity of the function it computes:If a language is in SP ACE(s), then it has a BP of total size at most n · 2O(s) =-=[8]-=- and also a read-once BP of width 2O(2s ) [12]. However, the inverse of the last assertion is not true even for computable languages. The result of [2] and the result here, in its uniform manifestatio... |

25 | Functions that have read-twice constant width branching programs are not necessarily testable, Random Structures and Algorithms
- Fischer, Newman, et al.
(Show Context)
Citation Context ... However, in [2], examples of such functions that require θ( √ n) queries are presented. Hence, instead, one may ask whether constant width linear size BPs are testable. A negative answer is given in =-=[9]-=-:They show that there is a Boolean function g : {0, 1} n −→ {0, 1} that is computed by a read-twice constant width oblivious BP and that is not ɛ-testable for some fixed ɛ>0 (a read-k-times BP is a BP... |

25 |
Selftesting /correcting for polynomials and for approximate functions
- Gemmell, Lipton, et al.
- 1991
(Show Context)
Citation Context ...rt from being a natural relaxation of the standard decision problem, combinatorial property testing emerges naturally in the context of probably approximately correct (PAC) learning, program checking =-=[10, 6, 16]-=-, probabilistically checkable proofs [3], and approximation algorithms [11]. In [11], the authors mainly consider graph properties and show (among other ∗ Received by the editors December 5, 2000; acc... |

14 |
On P versus NP ∩ co-NP for decision trees and read-once branching programs
- Jukna, Razborov, et al.
- 1999
(Show Context)
Citation Context ...evel query the same variable), and each variable appears in at most one level. BPs have been extensively studied as a model of computation for Boolean functions. ([7] contains a survey text; see also =-=[4, 5, 13]-=- for a partial list of different aspects involving BPs and read-once BPs.) The size of a BP (and a read-once BP) is tightly related to the space complexity of the function it computes:If a language is... |

6 |
Hierarchies of memory-limited computations
- Stearns, Hartmanis, et al.
- 1965
(Show Context)
Citation Context ...BP) is tightly related to the space complexity of the function it computes:If a language is in SP ACE(s), then it has a BP of total size at most n · 2O(s) [8] and also a read-once BP of width 2O(2s ) =-=[12]-=-. However, the inverse of the last assertion is not true even for computable languages. The result of [2] and the result here, in its uniform manifestation, may be viewed as asserting that “very small... |

4 | Testing parenthesis languages
- Parnas, Ron, et al.
- 2001
(Show Context)
Citation Context ...nctive normal form (DNF), O(1)clauses conjunctive normal form (CNF), and some other interesting examples (see section 4). Finally, we note that SP ACE(O(log n)) functions are not testable in general; =-=[2, 11, 15]-=- contain lower bounds showing that some functions in SP ACE(O(log n)) are not ɛ-testable and sometimes not even (ɛ, nδ )-testable for some fixed ɛ, δ < 1. However, the question of whether properties i... |