Verifying identities

Rajagopalan, S.; Schulman, Leonard J.

doi:10.1109/sfcs.1996.548520

Cited by 4 publications

(8 citation statements)

References 3 publications

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“…In contrast, [RaS96] show that quadratic time is necessary and sufficient to test that a given cancellative operation is associative. This method yields a very efficient tester (over small domains) for all functions satisfying associative functional equations [Acz66].…”

mentioning

confidence: 90%

“…In this extended abstract we show the checker under the assumption that the input operation is cancellative and leave the general case for the full version of the paper. In contrast, [RaS96] show that quadratic time is necessary and sufficient to test that a given cancellative operation is associative. This method yields a very efficient tester (over small domains) for all functions satisfying associative functional equations [Acz66].…”

mentioning

confidence: 90%

“…Recently in a surprising and elegant result, [RaS96] show how to test that operation o is associative in O(]Dj2) steps, rather than the straightforward O(lD13). They also show that R(ID12) steps are necessary, even for cancellative operations.…”

Section: Introductionmentioning

confidence: 99%

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Spot-checkers

Ergün

Kannan

Kumar

et al. 1998

Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing - STOC '98

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On Labor Day Weekend, the highway patrol sets up spotchecka nt random points on the freeways with the intention of deterring a large fraction of motorists from driving incorrectly, WC explore a very similar idea in the context of program checking to ascertain with minimal overhead that a program output is reasonably correct. Our model of spotchecking requires that the spot-checker must run asymptotically much faster than the combined length of the input and output, We then show that the spot-checking model can be applied to problems in a wide range of areas, including problems regarding graphs, sets, and algebra. In particular, we present spot-checkers for sorting, element distinctness, set containment, set equality, total orders, and correctness of group operations. All of our spot-checkers are very simple to state and rely on testing that the input and/or output have certain simple properties that depend on very few bits.Our sorting spot-checker runs in O(logn) time to check the correctness of the output produced by a sorting algorithm on an input consisting of n numbers. We also show that there lo an O(1) spot-checker to check a program that determines whether a given relation is close to a total order. We present a technique for testing in almost linear time whether a given operation is close to an associative cancellative operation.In this extended abstract we show the checker under the assumption that the input operation is cancellative and leave the general case for the full version of the paper. In contrast, [RaS96] show that quadratic time is necessary and sufficient to test that a given cancellative operation is associative. This method yields a very efficient tester (over small domains) for all functions satisfying associative functional equations [Acz66]. We also extend this result to test in almost linear time whether the given operation is close to a group operation.

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confidence: 90%

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confidence: 90%

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Spot-checkers

Ergün

Kannan

Kumar

et al. 1998

Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing - STOC '98

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“…Before we finish, let us clarify an important difference between our work and the work on testing properties of relations, on group isomorphism, etc (see for example [5,13,15,20,26,28]). In that case the input is a multiplication table, of size O(|G| 2 ), while in our case we usually assume that k = O(log |G|).…”

Section: Introductionmentioning

confidence: 99%

Testing commutativity of a group and the power of randomization

Pak

2012

LMS J. Comput. Math.

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“…Given an n × n table of a binary operation • acting on a set S, deterministic and randomized algorithms have been given for testing if • represents an associative operation [21], if • is close to being associative and commutative [11], or if • is close to being cancellative, associative and commutative. Similarly, given a group G in the form of a multiplication table, we could ask if G is a special group.…”

Section: Introductionmentioning

confidence: 99%

Linear time algorithms for Abelian group isomorphism and related problems

Kavitha

2007

Journal of Computer and System Sciences

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We consider the problem of determining if two finite groups are isomorphic. The groups are assumed to be represented by their multiplication tables. We present an O(n) algorithm that determines if two Abelian groups with n elements each are isomorphic. This improves upon the previous upper bound of O(n log n) [Narayan Vikas, An O(n) algorithm for Abelian p-group isomorphism and an O(n log n) algorithm for Abelian group isomorphism, J. Comput. System Sci. 53 (1996) 1-9] known for this problem. We solve a more general problem of computing the orders of all the elements of any group (not necessarily Abelian) of size n in O(n) time. Our algorithm for isomorphism testing of Abelian groups follows from this result. We use the property that our order finding algorithm works for any group to design a simple O(n) algorithm for testing whether a group of size n, described by its multiplication table, is nilpotent. We also give an O(n) algorithm for determining if a group of size n, described by its multiplication table, is Abelian.

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Verifying identities

Cited by 4 publications

References 3 publications

Spot-checkers

Spot-checkers

Testing commutativity of a group and the power of randomization

Linear time algorithms for Abelian group isomorphism and related problems

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