By Bruno Courcelle (auth.), Luca Aceto, Ivan Damgård, Leslie Ann Goldberg, Magnús M. Halldórsson, Anna Ingólfsdóttir, Igor Walukiewicz (eds.)
The two-volume set LNCS 5125 and LNCS 5126 constitutes the refereed court cases of the thirty fifth foreign Colloquium on Automata, Languages and Programming, ICALP 2008, held in Reykjavik, Iceland, in July 2008.
The 126 revised complete papers offered including four invited lectures have been rigorously reviewed and chosen from a complete of 407 submissions. The papers are grouped in 3 significant tracks on algorithms, automata, complexity and video games, on common sense, semantics, and idea of programming, and on safety and cryptography foundations. LNCS 5125 comprises 70 contributions of tune a particular from 269 submissions in addition to 2 invited lectures. The papers are geared up in topical sections on complexity: boolean features and circuits, information buildings, random walks and random constructions, layout and research of algorithms, scheduling, codes and coding, coloring, randomness in computation, on-line and dynamic algorithms, approximation algorithms, estate checking out, parameterized algorithms and complexity, graph algorithms, computational complexity, video games and automata, workforce checking out, streaming, and quantum, algorithmic video game thought, and quantum computing.
Read or Download Automata, Languages and Programming: 35th International Colloquium, ICALP 2008, Reykjavik, Iceland, July 7-11, 2008, Proceedings, Part I PDF
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Additional info for Automata, Languages and Programming: 35th International Colloquium, ICALP 2008, Reykjavik, Iceland, July 7-11, 2008, Proceedings, Part I
Now, since we are assuming that D came from a negative instance of MSSC, we know that D rejects some assignment to its variables other than the all-true assignment. On the other hand E accepts this assignment when the z variable is true. This implies that E depends on z and that F (the w -expanded version of E) depends on each zi . So some zi occurs exactly once. Fix an i for which zi occurs exactly once. Now, let ρ be the restriction that restricts all zj for j = i to true, and leaves all other variables free.
When discussing constant-depth formulas, as usual, we allow arbitrary fanin AND and OR gates and we use the convention that all NOT gates occur at the variable level. 3 (minimum equivalent depth d expression (MEEd )). Given a depth d Boolean formula F and an integer k, is there an equivalent depth d formula of size at most k? While distributing the NOT gates to the variable level clearly does not aﬀect formula size, it’s not as clear that ﬁnding the minimum depth-d formula is equivalent to ﬁnding the minimum depth-d formula with an OR gate at the root.
N} with |I| ≤ k and D ∨ i∈I xi ≡ 1? This can be seen as a succinct version of Set Cover, in which the sets are implicitly speciﬁed by the ones of the formulas D, x1 , x2 , . . , because it covers some point not covered by any of the other sets). Throughout this paper, we assume that the formula D accepts the all-true assignment, as it only requires polynomial time to check this and the SSC instance is trivially false otherwise. Our reductions exploit the special structure of this “succinct” set cover instance.