By Claire Kenyon (auth.), Volker Diekert, Michel Habib (eds.)

ISBN-10: 3540212361

ISBN-13: 9783540212362

ISBN-10: 3540247491

ISBN-13: 9783540247494

This e-book constitutes the refereed complaints of the twenty first Annual Symposium on Theoretical facets of machine technological know-how, STACS 2004, held in Montpellier, France, in March 2004.

The fifty four revised complete papers offered including invited contributions have been conscientiously reviewed and chosen from greater than 2 hundred submissions. The papers are prepared in topical sections on structural complexity, graph algorithms, quantum computing, satisfiability - constraint pride difficulties, scheduling, algorithms, networks, automata concept and phrases, course algorithms, cryptography, good judgment and formal languages, online game concept and complexity, and algorithmic details.

**Read or Download STACS 2004: 21st Annual Symposium on Theoretical Aspects of Computer Science, Montpellier, France, March 25-27, 2004. Proceedings PDF**

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**Extra info for STACS 2004: 21st Annual Symposium on Theoretical Aspects of Computer Science, Montpellier, France, March 25-27, 2004. Proceedings**

**Sample text**

Qn ∈ {∀, ∃} and i ∈ N with ∃ = Qi = Qi+1 = . . = Qn = ∀. It holds: Q1 · · · Qn F (x1 , . . , xn ) ∈ QAFaV if and only if Q1 a1 ∈ V · · · Qi ai ∈ V : F (a1 , . . , ai , xi+1 , . . , xn ) ∈ TAUTaV . After Theorem 5 we know TAUTaV ∈ ALOGTIME ⊆ P. Furthermore there is one alternation less in Q1 · · · Qi than in Q1 · · · Qn . 4 Distributive Lattices Distributivity is usually a property of a whole lattice, but we introduce distributive elements, too. An element a of a lattice V is called distributive, if ∀b, c ∈ V : a ∧ (b ∨ c) = (a ∧ b) ∨ (a ∧ c) and ∀b, c ∈ V : a ∨ (b ∧ c) = (a ∨ b) ∧ (a ∨ c).

Comparing Equation (6) to Equation (3) we see that for P CC we have a better upper bound than for T CC. It turns out that for some pairs (x, y) the communication complexity for totally correct (and even for partially correct) protocols is close to the upper bound n − α while the communication complexity for partial protocols is close to the lower bound C(y|x) − α n. 28 H. Buhrman et al. Theorem 6. For all α, n, x there are y of length n such that CCIα (x, y) ≥ n − α and C(y|x) ≤ α + O(1). Proof.

Consider, for instance, the winning condition ψ ∈ S1S that requires the number of zeroes occurring in a play to be odd on the completely 16 E. Gr¨ adel connected arenea with two positions 0, 1. When starting from position 1, Ego obviously has winning strategies for each of the games E ω (G, ψ), AE ω (G, ψ), and EAE ω (G, ψ), but no positional ones. Nevertheless, such games are always positionally determined for one of the players. Indeed, if a player wins a game γ(G, ψ) ﬁnally controlled by his opponent, he always has a positional winning strategy.

### STACS 2004: 21st Annual Symposium on Theoretical Aspects of Computer Science, Montpellier, France, March 25-27, 2004. Proceedings by Claire Kenyon (auth.), Volker Diekert, Michel Habib (eds.)

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