In the presence of 5 mol% Pd(OAc)(2), 1 equiv. of norbornene, and K2CO3, the reaction of 4-iodo-2-quinolones with tertiary o-bromobenzylic alcohols produced the desired benzopyran-fused 2-quinolones in moderate to hig...
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In the presence of 5 mol% Pd(OAc)(2), 1 equiv. of norbornene, and K2CO3, the reaction of 4-iodo-2-quinolones with tertiary o-bromobenzylic alcohols produced the desired benzopyran-fused 2-quinolones in moderate to high yields. A Catellani-type mechanism involving vinylic C-H cleavage is proposed based on the results of control experiments and density functional theory calculations.
Circumscription is a popular common-sense reasoning technique, used in the fields of Artificial Intelligence, Databases and Logic Programming. In this paper we investigate the size of representations (formulae, data s...
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Circumscription is a popular common-sense reasoning technique, used in the fields of Artificial Intelligence, Databases and Logic Programming. In this paper we investigate the size of representations (formulae, data structures) equivalent to the circumscription of a propositional formula T, taking into account three different definitions of equivalence. We find necessary and sufficient conditions for the existence of polynomial-size representations (formulae, data structures) equivalent to the circumscription of T in the three cases. All such conditions imply the collapse of the polynomial hierarchy. In particular, we prove that - unless the polynomial hierarchy collapses at the second level - the size of the shortest propositional formula T' logically equivalent to the circumscription of T grows faster than any polynomial as the size of T increases. The significance of this result in the related held of closed-world reasoning is then analyzed.
Founded by J.F. Ritt, Differential Algebra is a true part of Algebra so that constructive and algorithmic problems and methods appear in this field. In this talk, I do nor intend to give an exhaustive survey of algori...
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Founded by J.F. Ritt, Differential Algebra is a true part of Algebra so that constructive and algorithmic problems and methods appear in this field. In this talk, I do nor intend to give an exhaustive survey of algorithmic aspects of Differential Algebra but I only propose some examples to give an insight of the stare of knowledge in this domain. Some problems are known to have an effective solution, others have an efficient effective solution which is implemented in recent computer algebra systems, and the decidability of some others is still an open question, which does not prevent computations from leading to interesting results. Liouville's theory of integration in finite terms and Risch's theorem are examples of problems that computer algebra systems now deal with very efficiently (implementation work by M. Bronstein). In what concerns Linear differential equations of arbitrary order, a basis for the vector space of all liouvillian solutions can ''in principle'' be computed effectively thanks to a theorem of Singer's [17, 22];the complexity bound is actually awful and a lot of work is done or in progress, especially by M. Singer and F, Ulmer, to give realistic algorithms [20, 21] for third-order linear differential equations. Existence of liouvillian first integrals is a way to make precise the notion of integrability of vector fields. Even in the simplest case of three-dimensional polynomial vector fields, no decision procedure is known for this existence. Nevertheless, explicit computations with computer algebra yield interesting solutions for special examples. In this case, the process of looking for so-called Darboux curves can only be called a method but not an algorithm;for a given degree, this search is a classical algebraic elimination process but no bound is known on the degree of the candidate polynomials. This paper insists on the search of liouvillian first integrals of polynomial vector fields and a new result is given: the generic absence of such
In this paper, we are concerned with finite p-s-composed codes, that is with codes obtained by composition of finite prefix and suffix codes. We give a method to decompose a finite prefix-suffix composed code in a min...
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In this paper, we are concerned with finite p-s-composed codes, that is with codes obtained by composition of finite prefix and suffix codes. We give a method to decompose a finite prefix-suffix composed code in a minimal number of prefix and suffix codes. Using this method, we establish that every prefix-suffix composed n-word code (n greater than or equal to 3) can be expressed as the composition of at most 2n - 3 prefix and suffix codes. We show that for all n, this limit is reached, that is, there exists a ps-composed n-word code that cannot be expressed as the composition of less than 2n - 3 prefix and suffix codes. Then we give an example of a three-word code which is not prefix-suffix composed, refuting a conjecture proposed by Restive et al. in 1989.
The function class #P lacks an important closure property: it is not closed under subtraction. To remedy this problem, we introduce the function class GapP as a natural alternative to #P. GapP is the closure of #P und...
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The function class #P lacks an important closure property: it is not closed under subtraction. To remedy this problem, we introduce the function class GapP as a natural alternative to #P. GapP is the closure of #P under subtraction and has all the other useful closure properties of #P as well. We show that most previously studied counting classes, including PP, C=P, and ModkP, are “gap-definable,” i.e., definable using the values of GapP functions alone. We show that there is a smallest gap-definable class, SPP, which is still large enough to contain Few. We also show that SPP consists of exactly those languages low for GapP, and thus SPP languages are low for any gap-definable class. These results unify and improve earlier disparate results of J. Cai and L. Hemachandra (Math. Systems theory23, No. 2 (1990), 95–106) and J. Köbler et al. (J. Comput. System Sci.44, No. 2 (1992), 272–286). We show further that any countable collection of languages is contained in a unique minimum gap-definable class, which implies that the gap-definable classes form a lattice under inclusion. Subtraction seems necessary for this result, since nothing similar is known for the #P-definable classes.
The first analysis of approximate counting is due to Flajolet (1985), whereas the first satisfactory analysis of the average path length in digital search trees has been performed by Knuth (1973). Both authors have us...
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The first analysis of approximate counting is due to Flajolet (1985), whereas the first satisfactory analysis of the average path length in digital search trees has been performed by Knuth (1973). Both authors have used the Mellin integral transform, but in rather different ways. It was shown by Kirschenhofer and Prodinger (1991) that both problems are very similar. (This note contains also an "explanation" of this phenomenon.) It is amusing to figure out what Flajolet and Knuth would have done by considering the exchanged problems. The aim of this note is to perform these analyses.
Computing the maximum bichromatic discrepancy is an interesting theoretical problem with important applications in computational learning theory, computational geometry and computer graphics. In this paper we give alg...
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Computing the maximum bichromatic discrepancy is an interesting theoretical problem with important applications in computational learning theory, computational geometry and computer graphics. In this paper we give algorithms to compute the maximum bichromatic discrepancy for simple geometric ranges, including rectangles and halfspaces. In addition, we give extensions to other discrepancy problems. (C) 1996 Academic Press, Inc.
We consider one-dimensional and multidimensional vector covering with variable sized bins In the one-dimensional case, we consider variable sized bin covering with bounded item sizes, For every finite set of bins B, a...
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We consider one-dimensional and multidimensional vector covering with variable sized bins In the one-dimensional case, we consider variable sized bin covering with bounded item sizes, For every finite set of bins B, and upper bound l/m on the size of item, for some integer m, we define a ratio r(B, m). We prove this is the best possible competitive ratio for the set of bin, B and the parameter m by giving both an algorithm with competitive ratio r(B, m) and an upper bound of r( B, m) on the competitive ratio of any online deterministic or randomized algorithm. The ratio satisfies r(B, m) greater than or equal to m/(m + 1) and equals this number if all bins are of size 1. For multidimensional vector covering we consider the case,there each bin is a binary d-dimensional hector, It was shown by N. Alon, Y, Azar, J. Csirik L. Epstein, S. V. Sevastianov, A. P. A. Vestjens. and G. J. Woeginger (1998, Algorithmica 21, 104-118) that if B contains a single bin which is all 1, then the best competitive ratio is Theta(1/d). We show an upper bound of 1/2(d(1-sigma(1))) for the general problem. and consider four special case variants, We show an algorithm with optimal competitive ratio 1/2 for die model where each bin in B is a standard basis vector. We consider the model where B consists of all unit prefix vector, A unit prefix vector has i leftmost components of 1. and all other components are 0. We show that this model is harder than the case of standard basis vector bins by giving an upper hound of 0(1/log d) on die competitive ratio of an deterministic or randomized algorithm. Next, we discuss the model where B contains all binary vectors, We show this model is easier than the model of one bin type which is all I by giving an algorithm with competitive ratio Omega(1/log d). The most interesting multidimensional case is d = 2. The results of N. Alon et al give a 0.25-competitive algorithm for B = {( 1. 1)} and an upper bound of 0,4 on the competitive ratio of an algorithm, I
We consider the problem of efficient and reliable computing on EREW PRAM whose processors are subject to random independent stop-failures with constant probability p < 1. An algorithm for such a fault-prone machine...
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We consider the problem of efficient and reliable computing on EREW PRAM whose processors are subject to random independent stop-failures with constant probability p < 1. An algorithm for such a fault-prone machine is called safe if it solves a problem of size n with probability exceeding 1 - d/n, for some constant d independent of n. Our main contribution is a safe algorithm for the well-known list ranking problem, working in time O(log n) on an O(n log n)-processor EREW PRAM. We also show an optimal safe algorithm for computing prefix sums, which works in time O(log n) on an O(nl log n)-processor EREW PRAM. The methods presented in this paper can be applied to a wide class of EREW PRAM algorithms making them safe and simultaneously preserving their complexity.
This review focuses on the computational aspects of Si-29 NMR chemical shifts and spin +/- spin coupling constants involving the Si-29 nucleus. It concentrates on the electronic and stereochemical effects manifesting ...
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This review focuses on the computational aspects of Si-29 NMR chemical shifts and spin +/- spin coupling constants involving the Si-29 nucleus. It concentrates on the electronic and stereochemical effects manifesting in these parameters, calculated at different levels of theory with a special emphasis on their practical applications. For (29)SiNMRchemical shifts, a good deal of interest is focused on the less common solid state studies, in addition to more popular liquid state data. For spin +/- spin coupling constants, the main interest is concentrated on the mostly common Si-29 +/- 1H and Si-29 +/- C-13 couplings. The review is written in memory of the Full Member of the Russian Academy of Sciences, Professor Mikhail G. Voronkov in view of his invaluable contribution to the field of organosilicon chemistry and Si-29 NMR. The bibliography includes 93 references.
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