Computing and Combinatorics: 8th Annual International by Gene Myers Ph.D (auth.), Oscar H. Ibarra, Louxin Zhang

By Gene Myers Ph.D (auth.), Oscar H. Ibarra, Louxin Zhang (eds.)

This booklet constitutes the refereed complaints of the eighth Annual foreign Computing and Combinatorics convention, COCOON 2002, held in Singapore in August 2002.
The 60 revised complete papers provided including 3 invited contributions have been conscientiously reviewed and chosen from 106 submissions. The papers are equipped in topical sections on complexity idea, discrete algorithms, computational biology and studying conception, radio networks, automata and formal languages, net networks, computational geometry, combinatorial optimization, and quantum computing.

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Additional info for Computing and Combinatorics: 8th Annual International Conference, COCOON 2002 Singapore, August 15–17, 2002 Proceedings

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22. P. Sos´ık, D0L Systems + Watson-Crick Complement = Universal Computation. Springer LNCS 2055 (2001) 308–320. On Higher Arthur-Merlin Classes Jin-Yi Cai1, , Denis Charles2, , A. edu Abstract. We study higher Arthur-Merlin classes defined via several natural probabilistic operators BP, R and coR. We investigate the complexity classes they define, and a number of interactions between these operators and the standard polynomial time hierarchy. We prove a hierarchy theorem for these higher Arthur-Merlin classes involving interleaving operators, and a theorem giving non-trivial upper bounds to the intersection of the complementary classes in the hierarchy.

Firstly, if m0 > n0 , we add 32 (m0 − n0 ) new variables and use them to construct a formula Φ1 which contains 12 (m0 − n0 ) clauses, in which each of all those 32 (m0 − n0 ) new variables appears once and only once. This means that Φ1 is always satisfiable. Let Φ = Φ1 ∧ Φ0 then we get the instance of 3-ESAT since m0 + 12 (m0 − n0 ) = n0 + 32 (m0 − n0 ), and Φ is satisfiable if and only if Φ0 is satisfiable, and the reduction can be done in polynomial time of n0 . Note that m0 + 12 (m0 − n0 ) < 2m0 .

Proof. We prove the first equality, by induction on n, the number of levels. Our base case is ΣkBP·Σl ⊆ ZPPΣk+l , for k ≥ 1, l ≥ 0, which we shall prove by induction on k. We know, by Theorem 1, that NPBP·Σl ⊆ ZPPΣl+1 . So when k = 1 the base case is true. Now consider the BP·Σl case k ≥ 2. Assume Σk−1 ⊆ ZPPΣk+l−1 , for k ≥ 2. Now, BP·Σl ΣkBP·Σl = NPΣk−1 Σk+l−1 ⊆ NPZPP = Σk+l ⊆ ZPPΣk+l The second inclusion is by assumption and the last equality is by Lemma 2. Let us assume that, for k2 , . . , kn ≥ 1 and l2 , .

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