Algorithms on Strings, Trees and Sequences - Computer by Dan Gusfield

By Dan Gusfield

Typically a space of research in desktop technology, string algorithms have, in recent times, develop into an more and more vital a part of biology, rather genetics. This quantity is a complete examine laptop algorithms for string processing. as well as natural machine technology, Gusfield provides huge discussions on organic difficulties which are solid as string difficulties and on equipment built to unravel them. this article emphasizes the elemental rules and methods relevant to cutting-edge functions. New methods to this complicated fabric simplify tools that during the past were for the expert by myself. With over four hundred workouts to augment the fabric and improve extra issues, the booklet is acceptable as a textual content for graduate or complicated undergraduate scholars in machine technology, computational biology, or bio-informatics.

Show description

Read Online or Download Algorithms on Strings, Trees and Sequences - Computer Science and Computational Biology PDF

Similar discrete mathematics books

Smooth Particle Applied Mechanics: The State of the Art (Advanced Series in Nonlinear Dynamics) (Advanced Series in Nonlinear Dynamics)

This booklet takes readers via the entire steps priceless for fixing difficult difficulties in continuum mechanics with tender particle tools. Pedagogical difficulties make clear the new release of preliminary stipulations, the therapy of boundary stipulations, the mixing of the equations of movement, and the research of the consequences.

Surveys in Combinatorics 2011

This quantity comprises 9 survey articles in line with the invited lectures given on the twenty third British Combinatorial convention, held at Exeter in July 2011. This biennial convention is a well-established overseas occasion, with audio system from around the globe. through its nature, this quantity presents an up to date review of present study task in numerous components of combinatorics, together with extremal graph thought, the cyclic sieving phenomenon and transversals in Latin squares.

Aspects of Infinite Groups: A Festschrift in Honor of Anthony Gaglione (Algebra and Discrete Mathematics)

This booklet is a festschrift in honor of Professor Anthony Gaglione's 60th birthday. This quantity offers a superb mixture of examine and expository articles on quite a few facets of endless staff idea. The papers provide a vast evaluate of current learn in limitless team concept normally, and combinatorial staff conception and non-Abelian group-based cryptography particularly.

Extra info for Algorithms on Strings, Trees and Sequences - Computer Science and Computational Biology

Example text

Es gibt einfache, praktische Verfahren, um große Primzahlen zu erzeugen. Man baut große Primzahlen iterativ aus kleinen Primzahlen zusammen. 17 Seien p1 , . . , pr prim und p = 1 + (p−1)/pi ai =1 (mod p), r ei i=1 pi . ap−1 =1 i Aus (mod p) f¨ ur i = 1, 2, . . , r folgt, daß p prim ist. (p−1)/pi Beweis. ai Nach CRT folgt prim. = 1 (mod p), ap−1 = 1 (mod p) impliziert pei i ord(ai ). i r ei i=1 pi |ord(ai ), und somit ϕ(p) = p − 1. Damit ist p ✷ F¨ ur prime p, p − 1 = r ei i=1 pi gilt andererseits f¨ ur zuf¨allige a ∈ Z∗p Ws a(p−1)/pi = 1 (mod p) = 1 − 1 pi .

Wir zeigen, daß ordpe (y) = ϕ(pe ) bereits ordpe+1 (y) = ϕ(pe+1 ) ¨ impliziert. Zur Ubung beweist man die Behauptung: z = 1 mod pe , z = 1 mod pe+1 =⇒ e z p = 1 mod pe+1 , z p = 1 mod pe+2 e Sei ordpe (y) = ϕ(pe ) und z = y ϕ(p )/p , wobei ϕ(pp ) = ϕ(pe−1 ). Dann gilt e z = 1 mod pe−1 , aber z = 1 mod pe . Diese Behauptung liefert y ϕ(p ) = 1 (mod pe+1 ) und folglich ordpe+1 (y) = ϕ(pe+1 ). KAPITEL 4. RSA UND STRUKTUR VON Z∗N 38 2. 1) (mod 2r ) : j = 1, 2, . . 2) folgt jetzt aus −1 = 5j (mod 2r ) f¨ ur j = 1, 2, .

R . Beweis. 4 schließt man: λ(N ) = kgV {λ(pei i ) : i = 1, 2, . . 8. ✷ Man w¨ ahlt den RSA-Modul N = P1 ·P2 so, daß ggT(P1 − 1, P2 − 1) = 2. Dann gilt λ(N ) = 21 ϕ(N ). 3 ∈ {0, 1, . . , ϕ(N ) − 1} ∗ Pseudoprimzahlen und Carmichael-Zahlen Zum RSA-Schema ben¨ otigt man große zuf¨allige Primzahlen. Weil die Primzahlen ≤ N etwa die Dichte log1N haben, gen¨ ugt ein effektiver Primheitstest. 3. ∗ PSEUDOPRIMZAHLEN UND CARMICHAEL-ZAHLEN 39 F¨ ur jede Primzahl p gilt die Fermat-Identit¨ at ap−1 = 1 mod p f¨ ur alle ∗ a ∈ Zp .

Download PDF sample

Rated 4.30 of 5 – based on 43 votes