William "Velvel" Morton Kahan born June 5, is a Canadian mathematician and computer scientist , who received the Turing Award in for " his fundamental contributions to numerical analysis ",  was named an ACM Fellow in ,  and inducted into the National Academy of Engineering in Born to a Canadian Jewish family,  he attended the University of Toronto , where he received his bachelor's degree in , his master's degree in , and his Ph. Kahan is now emeritus professor of mathematics and of electrical engineering and computer sciences EECS at the University of California, Berkeley. In the s he developed the program "paranoia", a benchmark that tests for a wide range of potential floating-point bugs. He also developed the Kahan summation algorithm , an important algorithm for minimizing error introduced when adding a sequence of finite-precision floating-point numbers.
Research papers on dijkstra's algorithm - ashleysixto.com
Dijkstra's Shortest Path Algorithm - A Detailed and Visual Introduction
He graduated at King's College, Cambridge with a degree in mathematics. Whilst he was a fellow at Cambridge, he published a proof demonstrating that some purely mathematical yes—no questions can never be answered by computation and defined a Turing machine , and went on to prove the halting problem for Turing machines is undecidable. For a time he led Hut 8 , the section that was responsible for German naval cryptanalysis. Here, he devised a number of techniques for speeding the breaking of German ciphers , including improvements to the pre-war Polish bombe method, an electromechanical machine that could find settings for the Enigma machine. Turing played a crucial role in cracking intercepted coded messages that enabled the Allies to defeat the Nazis in many crucial engagements, including the Battle of the Atlantic. The Automatic Computing Engine was one of the first designs for a stored-program computer. In , Turing joined Max Newman 's Computing Machine Laboratory , at the Victoria University of Manchester , where he helped develop the Manchester computers  and became interested in mathematical biology.
Dijkstra's algorithm revisited: the dynamic programming connexion
He is a co-inventor of the Rivest—Shamir—Adleman RSA algorithm along with Ron Rivest and Len Adleman , a co-inventor of the Feige—Fiat—Shamir identification scheme along with Uriel Feige and Amos Fiat , one of the inventors of differential cryptanalysis and has made numerous contributions to the fields of cryptography and computer science. After a year as a postdoctoral researcher at the University of Warwick , he did research at Massachusetts Institute of Technology MIT from — before returning to be a member of the faculty of Mathematics and Computer Science at the Weizmann Institute. Together with Eli Biham , he discovered differential cryptanalysis in the late s, a general method for attacking block ciphers.