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A New Approach to Formal Language Theory by Kolmogorov Complexity
 Preprint, SIAM J. Comput
, 1995
"... We present a new approach to formal language theory using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate deterministic contextfree languages and nondeterministic contextfree ..."
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We present a new approach to formal language theory using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate deterministic contextfree languages and nondeterministic contextfree languages. The use of the new ‘incompressibility arguments ’ is illustrated by many examples. The approach is also successful at the high end of the Chomsky hierarchy since one can quantify nonrecursiveness in terms of Kolmogorov complexity. (This is a preliminary uncorrected version. The final version is the one published in SIAM J. Comput., 24:2(1995), 398410.) 1
On superlinear lower bounds in complexity theory
 In Proc. 10th Annual IEEE Conference on Structure in Complexity Theory
, 1995
"... This paper first surveys the neartotal lack of superlinear lower bounds in complexity theory, for “natural” computational problems with respect to many models of computation. We note that the dividing line between models where such bounds are known and those where none are known comes when the mode ..."
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This paper first surveys the neartotal lack of superlinear lower bounds in complexity theory, for “natural” computational problems with respect to many models of computation. We note that the dividing line between models where such bounds are known and those where none are known comes when the model allows nonlocal communication with memory at unit cost. We study a model that imposes a “fair cost ” for nonlocal communication, and obtain modest superlinear lower bounds for some problems via a Kolmogorovcomplexity argument. Then we look to the larger picture of what it will take to prove really striking lower bounds, and pull from ours and others’ work a concept of information vicinity that may offer new tools and modes of analysis to a young field that rather lacks them.
Kolmogorov Complexity and a Triangle Problem of the Heilbronn Type
"... From among \Gamma n 3 \Delta triangles with vertices chosen from among n points in the unit square, U , let T be the one with the smallest area, and let A be the area of T . If the n points are chosen independently and at random (uniform distribution) then there exist positive c and C such tha ..."
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From among \Gamma n 3 \Delta triangles with vertices chosen from among n points in the unit square, U , let T be the one with the smallest area, and let A be the area of T . If the n points are chosen independently and at random (uniform distribution) then there exist positive c and C such that c=n 3 ! n ! C=n 3 for all large enough n, where n is the expectation of A. Moreover, with probability close to one c=n 3 ! A ! C=n 3 . Our proof uses the incompressibility method based on Kolmogorov complexity. The related Heilbronn problem asks for the maximum value assumed by A over all choices of n points. 1 Introduction From among \Gamma n 3 \Delta triangles with vertices chosen from among n points in the unit circle, let T be the one of least area, and let A be the area of T . Let \Delta n be the maximum assumed by A over all choices of n points. H.A. Heilbronn (19081975) 1 asked for the exact value or approximation of \Delta n . The list [1, 2, 3, 5, 8, 9, 10, 11,...
Licensed under a Creative Commons Attribution License
"... is essentially always possible to find a program solving any decision problem a factor of 2 faster. This result is a classical theorem in computing, but also one of the most debated. The main ingredient of the typical proof of the linear speedup theorem is tape compression, where a fast machine is c ..."
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is essentially always possible to find a program solving any decision problem a factor of 2 faster. This result is a classical theorem in computing, but also one of the most debated. The main ingredient of the typical proof of the linear speedup theorem is tape compression, where a fast machine is constructed with tape alphabet or number of tapes far greater than that of the original machine. In this paper, we prove that limiting Turing machines to a fixed alphabet and a fixed number of tapes rules out linear speedup. Specifically, we describe a language that can be recognized in linear time (e. g., 1.51n), and provide a proof, based on Kolmogorov complexity, that the computation cannot be sped up (e. g., below 1.49n). Without the tape and alphabet limitation, the linear speedup theorem does hold and yields machines of time complexity of the form (1 + ε)n for arbitrarily small ε> 0. Earlier results negating linear speedup in alternative models of computation have often been based on the existence of very efficient universal machines. In the vernacular of programming language theory: These models have very efficient selfinterpreters. As the second contribution of this paper, we define a class, PICSTI, of computation models that exactly captures this property, and we disprove the Linear Speedup Theorem for every model in this class, thus generalizing all similar, modelspecific proofs.
method
"... Background: Although a variety of methods and expensive kits are available, molecular cloning can be a timeconsuming and frustrating process. Results: Here we report a highly simplified, reliable, and efficient PCRbased cloning technique to insert any DNA fragment into a plasmid vector or into a ge ..."
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Background: Although a variety of methods and expensive kits are available, molecular cloning can be a timeconsuming and frustrating process. Results: Here we report a highly simplified, reliable, and efficient PCRbased cloning technique to insert any DNA fragment into a plasmid vector or into a gene (cDNA) in a vector at any desired position. With this method, the vector and insert are PCR amplified separately, with only 18 cycles, using a high fidelity DNA polymerase. The amplified insert has the ends with ~16base overlapping with the ends of the amplified vector. After DpnI digestion of the mixture of the amplified vector and insert to eliminate the DNA templates used in PCR reactions, the mixture is directly transformed into competent E. coli cells to obtain the desired clones. This technique has many advantages over other cloning methods. First, it does not need gel purification of the PCR product or linearized vector. Second, there is no need of any cloning kit or specialized enzyme for cloning. Furthermore, with reduced number of PCR cycles, it also decreases the chance of random mutations. In addition, this method is highly effective and reproducible. Finally, since this cloning method is also sequence independent, we demonstrated that it can be used for chimera construction, insertion, and multiple mutations spanning a stretch of DNA up to 120 bp.
A Complete Bibliography of Publications in Journal of Computational Chemistry: 1990–1999
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"... Abstract. In search of a single number like Shannon’s statesymbol product to compare the complicacy of Turing Machines including those with multiple tapes and tape heads, a number called TM index is proposed, using a generic definition for single and multi tape machines. Several examples are shown ..."
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Abstract. In search of a single number like Shannon’s statesymbol product to compare the complicacy of Turing Machines including those with multiple tapes and tape heads, a number called TM index is proposed, using a generic definition for single and multi tape machines. Several examples are shown together with their TM indices, including the recently rediscovered physical
Algorithmic Arguments in Physics of Computation
"... . We show the usefulness of incompressibility arguments based on Kolmogorov complexity in physics of computation by several examples. These include analysis of energy parsimonious `adiabatic' computation, and scalability of network architectures. 1 Introduction In [Shannon, 1948] C. Shannon fo ..."
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. We show the usefulness of incompressibility arguments based on Kolmogorov complexity in physics of computation by several examples. These include analysis of energy parsimonious `adiabatic' computation, and scalability of network architectures. 1 Introduction In [Shannon, 1948] C. Shannon formulated information theory dealing with the average number of bits required to communicate a message produced by a random source from a sender to a receiver who both agree on the ensemble of possible messages. In this theory, if the universe of messages consists of a two elements, a sentence "let's go drink a beer" and Homer's Illiad, both elements equally likely, then the Illiad can be transmitted by a single bit. This illustrates that, as Shannon points out, this theory does not say anything about the information content of individual objects, but only says something about the required information exchange for communication. In [Kolmogorov, 1965] A.N. Kolmogorov formulated a theory of informat...