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Neither reading few bits twice nor reading illegally helps much

Identifieur interne : 002253 ( Main/Exploration ); précédent : 002252; suivant : 002254

Neither reading few bits twice nor reading illegally helps much

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

Source :

Discrete Applied Mathematics [ 0166-218X ] ; 1998.

RBID : ISTEX:1A543866482F7A94762EE0F8C9766AFC57C63F34

Descripteurs français

Pascal (Inist)
- Codage linéaire, Distance minimale, Machine Turing, Machine abstraite, 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 2Ω(min/s 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.

Url:

https://api.istex.fr/document/1A543866482F7A94762EE0F8C9766AFC57C63F34/fulltext/pdf

DOI: 10.1016/S0166-218X(98)00042-0

Affiliations:

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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 2Ω(min/s 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.</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

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