Levin, L.A. "Universal Search Problems," Problemy Peredaci Informacii 9 , pp. 115--116, 1973. Translated in Problems of Information Transmission 9 , pp. 265--266.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....gain ratio [18] or the Gini heuristic [2] are not useful for problems such as f( f( or f( g( with g being a function of the background knowledge. Another reason is that the guidance of the search by the MDL principle ensures a better use of computational resources [7, 22]. On the other hand, the majority of decision tree induction algorithms perform a greedy search in order to nd the best rst solution. We also perform a greedy search for each solution, but we are able to obtain N solutions and therefore the method is not so prone to getting In functional ....

L.A. Levin. Universal Search Problems. Problems Inform. Transmission, 9:265{ 266, 1973.

....a distribution to generate examples for testing to which class they belong, because probabilities, if uniformly distributed, would tend to 0. In order to solve this problem, we use an approach which is based on the universal distribution: Dx = 2 t(x) Specifically, we will use Levin s variant [11]. This variant is derived from the notion of age of a string, where age is dominated by the total time needed for a string to appear out of nothing, enumerated by a constant size program . The Levin variant is defined as Kt(X) log age(x) More formally: Definition 7. The Levin Length Time ....

L.A. Levin. Universal search problems. Probs. Inform. Transm., 9:265-266, 1973.

....space required for the program) We introduce a variant weighted on time. DEFINITION 4. 6 The Explanatory Complexity of a string x, denoted Et b (x) is defined as follows: Et b (x) min LT b (p) f b (p) x D(p) We have chosen LT b (p) l b (p) log cost b (p) the same weighing as [Levin 1973] s Kt because it provides a good compromise between space and time, but another relation could be tuned. But Et b is not computable in general, either. Thus, has definition 4.6 any utility We could have used a time bounded version to make it computable but the result is then a partial ....

Levin, L.A. "Universal search problems" Problems Inform. Transmission, 9:265-266, 1973.

.... is, soph c ( min fjpj : p is total, for all n exists dn such that jpj jd n j Km( 1:n ) c and dn 1 dn g Computational Depth The Kolmogorov complexity of a string x does not take into account the time necessary to produce the string from a description of length C(x) Levin [Lev73], introduced a useful variant weighing program size and running time. De nition 7. For any strings x; y, the Levin complexity of x given y is Ct(xjy) min fjpj log t : U(p; y) halts in at most t steps and outputs xg: After some attempts, Bennett [Ben88] formally de ned the s signi cant ....

Leonid A. Levin. Universal Search Problems. Problems Inform. Transmission, 9(1973), 265-266.

....of the information we have to solve the problem is in the probability distribution, and the only information we have about the time needed to generate and test a candidate is by experiment, then this search method is within a factor of 2 of the fastest way to solve the problem. In 1973 L. Levin [8], 16] used an algorithm much like this one to solve the same kinds of problems, but he did not postulate that all of the information needed to solve the problems was in the equivalent of the probability distribution. Lacking this strong postulate, his conclusion was weaker i.e. that the ....

Levin, L.A., "Universal Search Problems," Problemy Peredaci Informacii 9, pp. 115-116, 1973. Translated in Problems of Information Transmission 9, 265--266.

....Let A(p) be an optimal algorithm defining the Kolmogorov complexity K (x) K (x) min l(p) A(p) x , and let f ( p) A(p) l( p) Then for any x there is a p such that f ( p) x, K (x) An exhaustive search for such p takes exponential time, even when f ( p) is fast. Levin in [45] proposed the fastest algorithm for finding p. The corresponding complexity was defined by Levin in the beginning of the seventies and used in his optimal search algorithm, see [44, Section 1.3, 45] and [15] Section 7.5. Let A(p, y) be an optimal function (machine) and T A ( p, y) be the time ....

....its factorization. To solve the inverting problem naively often requires an exhaustive search through exponentially many candidates, that takes exponential time. Now we can present the main result of this section. The following theorem was proved by Levin in the beginning of the seventies (see [45]) THEOREM 23. An algorithm U (described below) exists such that the following holds. Let f be an arbitrary recursive function (not necessarily polynomial time computable) and assume that a self delimiting program q inverts the function f on any y and checks the result in time t (y) i.e. produces ....

Levin, L. A. (1973) Universal search problems. Prob. Inform. Transmission, 9, 265--266.

....in both measures and still low depth. Strings like initial segments of Chaitin s has high depth: It has high classical complexity but very small programs with access to the halting problem. To capture Bennet s notion of logical depth [Ben88] we consider the di erence of Levin s Kt complexity [Lev73b] and classical Kolmogorov complexity. The Kt complexity measures the logarithm of the age of a string the amount of time to produce the string when we run all programs in parallel. This nicely captures Bennet s intuition of considering the running time needed to produce a string. Bennet showed ....

....N N then KM [f(n) g(n) fx : 9y(jyj f(jxj) and M(y) x in time g(jxj)g This measure has the advantage of consider, not only, the program size, but also the time necessary to produce the string from it, however time and program length are disjoint, i.e. are not combined in any way. In [Lev73b] Levin introduced a useful variant of Kolmogorov complexity weighing space and time. De nition 2.3 ( Lev73b] Let M be a Turing machine. For any pair of strings x; y 2 f0; 1g ; the complexity of x relative to y with respect to M is de ned as KtM (xjy) minfjpj log t : M(p; y) x in at ....

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L.A. Levin. Universal search problems. Problems Inform. Transmission, 9:265-266, 1973.

....of comprehension, i.e. intelligence. The rst problem can be solved by incorporating time into the de nition of K. The most appropriate way 4 to weigh space and time of a program, the formula LT fi (p x ) l(p x ) log Cost fi (p x ) was introduced by Levin in the seventies (see e.g. Levin 1973). Then the next variant comes directly: De nition 4. The Levin s Length Time Complexity of an object x given y on a descriptional mechanism fi: Kt fi (xjy) minfLT fi (pjy) OE fi (hp; yi) x)g where LT fi (pjy) l(p) log Cost fi (hp; yi) This is a very practical alternative of ....

L. A. Levin. Universal search problems. Problems Inform. Transmission, 9:265-266, 1973.

....T 0 can be replaced with a subgroup of G, that also has the above property. 1 Introduction Tiling related problems are among the most anciently studied problems, but there is a renewed interest in them in computer science due to their role in proof checking and verification of Turing Machines [11] [12] 13] 1] Because of their expressive power tiling problems are usually hard. H. Wang has raised the following problem [20] Construct a tiling of the plain given infinitely many copies of finitely many different types of equal sized square tiles and a set of rules telling which type of ....

Levin, Leonid A, "Universal Search Problems," Problemy Peredachi Informatsii = Problems of Information Transmission. 9(3):265-266, 1973.

....1 Let F (w) x be a computable function from binary strings to binary strings. Say that an algorithm A conclusively inverts F if, given any x in the range of F , A computes an F witness w for x and then runs F to check that F (w) x. A diverges on inputs outside the range of F . Theorem 1 (L1, L2) For every computable function F (w) x from binary strings to binary strings, there exists a KU algorithm A such that A conclusively inverts F and (Time of A on x) O(Time of B on x) for every KU algorithm B that conclusively inverts F. For example, F may extract the theorem from a proof ....

Levin Leonid, "Universal Search Problems", Problems of Information Transmission 9:3 (1973), pages 265-266

....gain ratio [18] or the Gini heuristic [2] are not useful for functions that have a recursive de nition or that use concepts of the background knowledge. Another reason is that the guidance of the search by the MDL principle ensures a better use of computational resources following a Levin search [9]. We use the MDL principle as split criterion, as stopping criterion and also as solution tree selection criterion. In this way, we present a uniform framework based on the same measure for constructing the tree, selecting the split, selecting second best trees to explore and selecting or ....

....in accordance with space time resources. Therefore, we populate the tree up to a limit number of nodes or time. The result of this process behaves as a Levin search since solutions are found in a short to long fashion. The Levin search guarantees the optimal order of computational complexity [9] or, more precisely, it is the fastest method for inverting functions save for a large multiplicative constant [10] In what follows, we will introduce an approximation for K(Ejh) and for K(h) Notation Let S be a set of sorts , also called types. An S sorted signature is an S S sorted ....

L.A. Levin. Universal Search Problems. Problems Inform. Transmission, 9:265{ 266, 1973.

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Levin, L.A. "Universal Search Problems," Problemy Peredaci Informacii 9 , pp. 115--116, 1973. Translated in Problems of Information Transmission 9 , pp. 265--266.

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L. Levin, Universal search problems, Prob. Info. Trans., 9:265-266, 1973.

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L.A. Levin. Universal Search Problems. Problems Inform. Transmission, 9:265{ 266, 1973.

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Levin, L.A., "Universal Search Problems," Problemy Peredaci Informacii 9, pp. 115--116, 1973. Translated in Problems of Information Transmission 9, 265--266.

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L.A. Levin "Universal search problems" Problems Inform. Transmission, 9, 265-266, (1973).

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Levin, L.A., "Universal Search Problems", Problemy Peredaci Informacii 9, pp. 115--116, 1973. Translated in problems of Information Transmission 9, pp. 265--266.

No context found.

Levin, L.A. "Universal Search Problems," Problemy Peredaci Informacii 9, pp. 115--116, 1973. Translated in Problems of Information Transmission 9, pp. 265--266.

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