Automata, Languages and Programming: 35th International by Ran Canetti (auth.), Luca Aceto, Ivan Damgård, Leslie Ann

By Ran Canetti (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 lawsuits 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 provided including four invited lectures have been conscientiously 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 protection and cryptography foundations. LNCS 5126 includes fifty six contributions of tune B and song C chosen from 208 submissions and a pair of invited lectures. The papers for music B are geared up in topical sections on bounds, dispensed computation, real-time and probabilistic platforms, common sense and complexity, phrases and bushes, nonstandard types of computation, reasoning approximately computation, and verification. The papers of song C conceal themes in safety and cryptography resembling conception, safe computation, two-party protocols and zero-knowledge, encryption with exact properties/quantum cryptography, quite a few kinds of hashing, in addition to public-key cryptography and authentication.

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2 3 This will be no surprise for the reader acquainted with monotone frameworks or abstract interpretation, but the examples will be used throughout the paper. Abstract interpretation provides a general recipe to define these operators. 18 J. Esparza, S. Kiefer, and M. Luttenberger Probabilistic interpretations. Assume that the choices between actions are stochastic. For instance, actions a and b are chosen with probability p and (1 − p), respectively. The probability of termination is given by the least solution of (1) when interpreted over the following semiring (the real semiring) [8, 9].

Consider the following family of equation systems. Newton’s Method for ω-Continuous Semirings 25 X1 = 1/2 + 1/2 · X12 X2 = 1/4 · X12 + 1/2 · X1 X2 + 1/4 · X22 .. 2 Xn = 1/4 · Xn−1 + 1/2 · Xn−1 Xn + 1/4 · Xn2 (14) Its least solution is (1, . . , 1). We show in [14,6] that at least i · 2n−1 iterations of Newton’s method are needed to obtain i bits. More precisely, we show that after i · 2n−1 iterations no more than i · 2n−1 bits of accuracy have been obtained for the first component (cf. the convergence behaviour of (13) above) and that the number of accurate bits of the (k + 1)-th component is at most one half of the number of accurate bits of the k-th component, for all k < n.

Consider the (very abstractly defined) program consisting of three procedures X1 , X2 , X3 , and associate to it a system of equations. For our discussion it is not relevant which is the main procedure. The flow graphs of the procedures are shown in Figure 1. For instance, procedure X1 can either execute the abstract action b and terminate, or execute a, call itself recursively, and, after the call has terminated, call procedure X2 . proc X1 proc X2 a call X1 call X2 c b call X2 call X3 proc X3 f d call X2 e call X1 call X1 h g Fig.

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