Crazy Credits. Alternate Versions. Rate This. Time has passed but they are still up for adventures and cruel jokes, and Director: Mario Monicelli. Added to Watchlist. Favourite Italian comedies. Use the HTML below.

You must be a registered user to use the IMDb rating plugin. Photos Add Image. Edit Cast Cast overview, first billed only: Ugo Tognazzi Conte Raffaello Mascetti Gastone Moschin Arch - Rambaldo Melandri Adolfo Celi Professor Alfeo Sassaroli Renzo Montagnani Guido Necchi Milena Vukotic Alice Mascetti Franca Tamantini Carmen Necchi Angela Goodwin Nora Perozzi Alessandro Haber Example — 2: A bag contains 10 red marbles, 10 white marbles, and 10 blue marbles.

What is the minimum no. Solution: Apply pigeonhole principle. Theorem: Let q 1 , q 2 ,. Application of this theorem is more important, so let us see how we apply this theorem in problem solving. Driving Engagement in the World's Leading Companies. An integrated platform for every communication need Crowdsource questions, brainstorm ideas, vote on decisions, collect feedback. Effective Communication in every context. Workshops Maintain participants' attention and test their understanding with Polls and Assessments.

The length of P is a constant that doesn't depend on D. So, there is at most a constant overhead, regardless of the object described. Therefore, the optimal language is universal up to this additive constant. Proof : By symmetry, it suffices to prove that there is some constant c such that for all strings s.

Now, suppose there is a program in the language L 1 which acts as an interpreter for L 2 :. The interpreter is characterized by the following property:. Thus, if P is a program in L 2 which is a minimal description of s , then InterpretLanguage P returns the string s.

The length of this description of s is the sum of. Algorithmic information theory is the area of computer science that studies Kolmogorov complexity and other complexity measures on strings or other data structures.

The concept and theory of Kolmogorov Complexity is based on a crucial theorem first discovered by Ray Solomonoff , who published it in , describing it in "A Preliminary Report on a General Theory of Inductive Inference" [3] as part of his invention of algorithmic probability. Andrey Kolmogorov later independently published this theorem in Problems Inform.

Transmission [6] in Gregory Chaitin also presents this theorem in J. The theorem says that, among algorithms that decode strings from their descriptions codes , there exists an optimal one. This algorithm, for all strings, allows codes as short as allowed by any other algorithm up to an additive constant that depends on the algorithms, but not on the strings themselves.

Solomonoff used this algorithm and the code lengths it allows to define a "universal probability" of a string on which inductive inference of the subsequent digits of the string can be based. Kolmogorov used this theorem to define several functions of strings, including complexity, randomness, and information.

When Kolmogorov became aware of Solomonoff's work, he acknowledged Solomonoff's priority. The general consensus in the scientific community, however, was to associate this type of complexity with Kolmogorov, who was concerned with randomness of a sequence, while Algorithmic Probability became associated with Solomonoff, who focused on prediction using his invention of the universal prior probability distribution. The broader area encompassing descriptional complexity and probability is often called Kolmogorov complexity.

The computer scientist Ming Li considers this an example of the Matthew effect : "…to everyone who has more will be given…" [9]. There are several other variants of Kolmogorov complexity or algorithmic information. The most widely used one is based on self-delimiting programs , and is mainly due to Leonid Levin An axiomatic approach to Kolmogorov complexity based on Blum axioms Blum was introduced by Mark Burgin in the paper presented for publication by Andrey Kolmogorov.

Theorem : There exist strings of arbitrarily large Kolmogorov complexity. Proof: Otherwise all of the infinitely many possible finite strings could be generated by the finitely many [note 2] programs with a complexity below n bits.

Theorem : K is not a computable function. In other words, there is no program which takes a string s as input and produces the integer K s as output. The following indirect proof uses a simple Pascal -like language to denote programs; for sake of proof simplicity assume its description i. Assume for contradiction there is a program. Now, consider the following program of length bits:. Using KolmogorovComplexity as a subroutine, the program tries every string, starting with the shortest, until it returns a string with Kolmogorov complexity at least 8 bits, [note 3] i.

However, the overall length of the above program that produced s is only 7 bits, [note 4] which is a contradiction. If the code of KolmogorovComplexity is shorter, the contradiction remains. If it is longer, the constant used in GenerateComplexString can always be changed appropriately.