UnivTrevesV1, Main, Merge, bibRecord, 002755

Neither reading few bits twice nor reading illegally helps much

Identifieur interne : 002755 ( Main/Merge ); précédent : 002754; suivant : 002756

Neither reading few bits twice nor reading illegally helps much

Auteurs : S. Jukna [Allemagne, Lituanie] ; A. Razborov [Russie]

Source :

Discrete applied mathematics [ 0166-218X ] ; 1998.

RBID : Pascal:98-0504453

Descripteurs français

Pascal (Inist)
- Codage linéaire, Distance minimale, Machine abstraite, Machine Turing, Théorie programmation.

English descriptors

KwdEn :
- Abstract machine, Linear coding, Minimal distance, Programming theory, Turing machine.

Abstract

We first consider the so-called (1,+s)-branching programs in which along every consistent path at most s variables are tested more than once. We prove that any such program computing a characteristic function of a linear code C has size at least 2^Ω(min{d1^,d2^/s}), where d₁ and d2 are the minimal distances of C and its dual C⊥. We apply this criterion to explicit linear codes and obtain a super-polynomial lower bound for s=o(n/logn). Then we introduce a natural generalization of read-k-times and (1, +s)-branching programs that we call semantic branching programs. These programs correspond to corrupting Turing machines which, unlike eraser machines, are allowed to read input bits even illegally, i.e. in excess of their quota on multiple readings, but in that case they receive in response an unpredictably corrupted value. We generalize the above-mentioned bound to the semantic case, and also prove exponential lower bounds for semantic read-once nondeterministic branching programs.

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Pascal:98-0504453

Le document en format XML

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<front><div type="abstract" xml:lang="en">We first consider the so-called (1,+s)-branching programs in which along every consistent path at most s variables are tested more than once. We prove that any such program computing a characteristic function of a linear code C has size at least 2<sup>Ω(min{d</sup>
1<sup>,d</sup>
2<sup>/s})</sup>
, where d<sub>1</sub>
 and d2 are the minimal distances of C and its dual C⊥. We apply this criterion to explicit linear codes and obtain a super-polynomial lower bound for s=o(n/logn). Then we introduce a natural generalization of read-k-times and (1, +s)-branching programs that we call semantic branching programs. These programs correspond to corrupting Turing machines which, unlike eraser machines, are allowed to read input bits even illegally, i.e. in excess of their quota on multiple readings, but in that case they receive in response an unpredictably corrupted value. We generalize the above-mentioned bound to the semantic case, and also prove exponential lower bounds for semantic read-once nondeterministic branching programs.</div>
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Neither reading few bits twice nor reading illegally helps much

Neither reading few bits twice nor reading illegally helps much

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri