UnivTrevesV1, PascalFrancis, Curation, bibRecord, 001726

Neither reading few bits twice nor reading illegally helps much

Identifieur interne : 001726 ( PascalFrancis/Curation ); précédent : 001725; suivant : 001727

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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A03		`1`		`@0 Discrete appl. math.`
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A06				`@2 3`
A08	`01`	`1`	`ENG`	`@1 Neither reading few bits twice nor reading illegally helps much`
A11	`01`	`1`		`@1 JUKNA (S.)`
A11	`02`	`1`		`@1 RAZBOROV (A.)`
A14	`01`			`@1 Department of Computer Science, University of Trier @2 54286 Trier @3 DEU @Z 1 aut.`
A14	`02`			`@1 Institute of Mathematics, Akademijos 4 @2 2600 Vilnius @3 LTU @Z 1 aut.`
A14	`03`			`@1 Steklov Mathematical Institute, Gubkina 8, GSP-1 @2 117966, Moscow @3 RUS @Z 2 aut.`
A20				`@1 223-238`
A21				`@1 1998`
A23	`01`			`@0 ENG`
A43	`01`			`@1 INIST @2 18287 @5 354000077123500040`
A44				`@0 0000 @1 © 1998 INIST-CNRS. All rights reserved.`
A45				`@0 20 ref.`
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A64		`1`		`@0 Discrete applied mathematics`
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C01	`01`		`ENG`	@0 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.
C02	`01`	`X`		`@0 001D02A03`
C02	`02`	`X`		`@0 001D02A07`
C03	`01`	`X`	`FRE`	`@0 Codage linéaire @5 01`
C03	`01`	`X`	`ENG`	`@0 Linear coding @5 01`
C03	`01`	`X`	`SPA`	`@0 Codificación lineal @5 01`
C03	`02`	`X`	`FRE`	`@0 Distance minimale @5 02`
C03	`02`	`X`	`ENG`	`@0 Minimal distance @5 02`
C03	`02`	`X`	`SPA`	`@0 Distancia mínima @5 02`
C03	`03`	`X`	`FRE`	`@0 Machine abstraite @5 03`
C03	`03`	`X`	`ENG`	`@0 Abstract machine @5 03`
C03	`03`	`X`	`SPA`	`@0 Máquina abstracta @5 03`
C03	`04`	`X`	`FRE`	`@0 Machine Turing @5 04`
C03	`04`	`X`	`ENG`	`@0 Turing machine @5 04`
C03	`04`	`X`	`SPA`	`@0 Máquina Turing @5 04`
C03	`05`	`1`	`FRE`	`@0 Théorie programmation @5 05`
C03	`05`	`1`	`ENG`	`@0 Programming theory @5 05`
N21				`@1 327`

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Neither reading few bits twice nor reading illegally helps much

Neither reading few bits twice nor reading illegally helps much

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Descripteurs français

English descriptors

Abstract

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