Lambalgen, M. (1987) Random Sequences. Academish Proefshri't, Amsterdam. Home/Search Document Not in Database Summary Related Articles Check |
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Algorithmic Complexity and Stochastic Properties of Finite Binary .. - V'Yugin (1999) (2 citations) (Correct)
....an additive constant, of encoding of finite objects (but he did not introduce complexity as an original notion) Similar ideas were published by Chaitin [5, 6] Since that time several surveys and books on related topics have been published. We note especially [7, 8, 9, 10, 11, 12] and monographs [13, 14, 15]. This paper contains wellknown results as well as results not covered by these publications. The concept of algorithmic entropy or complexity is applicable to finite objects, such as words in a finite alphabet, finite sequences of integer numbers, etc. The complexity K (x) of a finite object x ....
Lambalgen, M. (1987) Random Sequences. Academish Proefshri't, Amsterdam.
Choice Sequences: a Retrospect - Troelstra (1996) (Correct)
....same formal concept. Example 5. The notions of a random sequence and independency of random sequences. An analysis in our sense (not completely satisfactory) of this concept has been carried out by the probability theorist R. von Mises; in recent years M. van Lambalgen has published on this([6, 7, 8]. I shall not discuss any details here, since this would certainly carry us too far. Van Lambalgen argues that even if we can develop probability theory on an axiomatic basis, starting from the notion of a probability measure, instead of starting from the notion of random sequence, we still have ....
M. van Lambalgen (1987). Random Sequences. PhD thesis, Universiteit van Amsterdam.
How Much Can You Win When Your Adversary is Handicapped? - Staiger (2000) (5 citations) (Correct)
....Much Can You Win 3 It is well known that random sequences do not admit successful gambling strategies. Here we consider a game where a player bets at fixed odds, but with unlimited amount, on the tosses of a coin. We further agree on the fact that the player must have no debt. It was explained in [Sc71, vL87, LV93] that in such a game a player playing according a computable gambling strategy cannot have unlimited gain if the tosses of the coin follow a random zero one sequence. On the other hand, it is quite obvious that, if the zero one sequence follows partially a certain computable law, the player may ....
.... 0 and 0 , otherwise (4) yields a gambling strategy (W 0 ; W 1 ) which realizes the capital V (w) in the node w of the binary tree. Thus, in the sequel, it suffices to consider (computable) capital functions satisfying (1) and (3) Those functions are also called (computable) martingales (cf. [Sc71, vL87, LV93]) We conclude this section with two examples presenting gambling strategies for given constraints F 1 and F 2 . Example 1 As mentioned above in the introduction let our constrained satisfy F 1 : f00;11g w , that is, the adversary repeats its choice once. A reasonable betting strategy for the ....
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M. van Lambalgen, Random sequences, Ph. D. Thesis, Univ. of Amsterdam, 1987.
Kolmogorov Complexity and Hausdorff Dimension - Staiger (1989) (2 citations) (Correct)
.... via certain operations from classes of languages (sets of finite strings) Kolmogorov complexity We start with a brief account on the necessary prerequisites in Kolmogorov or program size complexity, for more detailed information see the book [Sc1] or the survey papers [ZL] and [LV] The thesis [vL] gives a nice recent survey of the work on random sequences. We conclude this section with a short presentation of our results. Program size complexity defines the complexity of a finite string to be the length of a shortest program which prints the string. Accordingly, the complexity of an ....
....take from the rest the q( th word 3 of length n. If j j log r s W (n) then the above enumeration process terminates. Hence K A (w j jwj) dlog r s W (jwj)e for every w 2 W . 2 This result, however, cannot be transferred to the next classes of the arithmetical hierarchy. 2. 6 Example ( Sc1] [vL]) There are sequences 2 X satisfying A( 2 Pi 2 Sigma 2 and K( n) n Gamma o(n) 4 Since s f g j 1, our assertion follows. 2 Our Theorem 2.5 leads to the following improvement of Theorem 1 of [S1] 2.7 Proposition If A(F ) 2 Sigma 1 [ Pi 1 then (F ) H F . 2 2.8 Proposition Let ....
van Lambalgen, M., Random sequences. Ph.D. Thesis, Univ. of Amsterdam, 1987.
Invariance Properties of Random Sequences - Hertling, Wang (Correct)
....is related to the independence properties of subsequences of a random sequence and is also related to the independent random sequences. A number of general independence properties for subsequences of a random sequence are established by Kautz [Kautz 1991] and van Lambalgen [van Lambalgen 1987b, van Lambalgen 1987a] et al. There are various applications of independence properties and independent random sequences. For example Lutz [Lutz 1992] used the independent random oracles to characterize complexity classes, and Kautz and Miltersen [Kautz and Miltersen 1994] used independence properties of Martin Lof ....
M. van Lambalgen: "Random Sequences"; PhD thesis, University of Amsterdam (1987).
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