By Sanjeev Arora (auth.), Andrzej Lingas, Bengt J. Nilsson (eds.)

This booklet constitutes the refereed court cases of the 14th foreign Symposium basics of Computation idea, FCT 2003, held in Malm?, Sweden in August 2003.

The 36 revised complete papers provided including an invited paper and the abstracts of two invited talks have been conscientiously reviewed and chosen from seventy three submissions. The papers are prepared in topical sections on approximibility, algorithms, networks and complexity, computational biology, computational geometry, computational types and complexity, structural complexity, formal languages, and logic.

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Extra info for Fundamentals of Computation Theory: 14th International Symposium, FCT 2003, Malmö, Sweden, August 12-15, 2003. Proceedings

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Enumerate all 2n assignments of x1 , . . , xn and output an optimal solution. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. : The Probabilistic Method. John Wiley and Sons 1992. : A Gap in Average Proof Complexity. ECCC 003 (2002). : Spectral Graph Theory. American Mathematical Society 1997. : The Lovasz number of random graphs. Hamburger Beitr¨ age zur Mathematik 169. : Colouring random graphs in expected polynomial time. Proc. STACS 2003, Springer LNCS 2607 487–498. : Relations between average case complexity and approximation complexity.

X3k }. The union of gadgets Ax (over all x ∈ V (G)) contains already all nodes of our consistency 3k-amplifier H, and some of its edges. Now we identify the remaining edges of H. For each edge {x, y} of G we connect corresponding gadgets Ax , Ay with a pair of edges in H, as follows: if {x, y} ∈ M, we connect X0 with Y1 and X1 with Y0 ; if {x, y} ∈ E(G) \ M, we connect x0 with y1 , and x1 with y0 . Having this done, one after another for each edge {x, y} ∈ E(G), we obtain the consistency 3k-amplifier H = (V (H), E(H)) with contact nodes xij determined by contact nodes xi of G, for j ∈ {0, 1}, i ∈ {1, 2, .

Applied to Form+ n,k,m , DecideSAT runs in polynomial expected time. DecideSAT exploits the following connection between the k-SAT problem and the maximum independent set problem. Let V = {1, . . , n}k/2 , and ν = nk/2 . Given any k-SAT instance F over Varn we define two graphs GF = (V, EF ), GF = (V, EF ) as follows. We let {(v1 , . . , vk/2 ), (w1 , . . , wk/2 )} ∈ EF iff the k-clause xv1 ∨ · · · ∨ xvk/2 ∨ xw1 ∨ · · · ∨ xwk/2 occurs in F . Similarly, {(v1 , . . , vk/2 ), (w1 , . . , wk/2 )} ∈ EF iff the k-clause ¬xv1 ∨· · ·∨¬xvk/2 ∨¬xw1 ∨ · · · ∨ ¬xwk/2 occurs in F.

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