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In this paper, by employing bivariate cubic C-1 B-splines, a bivariate B-spline finite element method is presented to solve bending problems of rectangular plates. In comparison with analytical solutions, it is found that, for various boundary conditions and different loading conditions, the accuracy of the present numerical method is very satisfactory.
Error correction is an effective way to mitigate fault attacks in cryptographic hardware. It is also an effective solution to soft errors in deep sub-micron technologies. To this end, we present a systematic method for designing single error correcting (SEC) and double error detecting (DED) finite field (Galoisfield) multipliers over GF(2m). The detection and correction are done on-line. We use multiple...
In this paper, we present a systematic method for the designing fault tolerant reversible arithmetic circuits for finite field or Galois fields of the form GF(2m). To tackle the problem of errors in computation, we propose error detection and correction using multiple parity prediction technique based on low density parity check (LDPC) code. For error detection and correction, we need additional garbage...
An algorithm is presented to compute a canonical form of regular graphs. There is a constant c such that for each constant d the average running time of the algorithm over all d-regular graphs with N vertices is not greater than cNd, provided N is sufficiently large.
We demonstrate that the class of languages accepted by deterministic one-counter machines, or DOCAs (a natural subset of the context-free languages), is learnable in polynomial time. Our learning protocol is based upon Angluin's concept of a "minimally adequate teacher" who can answer membership queries about a concept and provide counterexamples to incorrect hypothesized concepts. We also...
We present a new procedure for inferring the structure of a finitestate automaton (FSA) from its input/output behavior, using access to the automaton to perform experiments. Our procedure uses a new representation for FSA's, based on the notion of equivalence between testa. We call the number of such equivalence classes the diversity of the automaton; the diversity may be as small as the logarithm...
This paper discusses some new integer factoring methods involving cyclotomic polynomials. There are several polynomials f(X) known to have the following property: given a multiple of f(p), we can quickly split any composite number that has p as a prime divisor. For example -- taking f(X) to be X- 1 -- a multiple of p - 1 will suffice to easily factor any multiple of p, using an algorithm of Pollard...
The main results of this paper are an O(n3) probabilistic algorithm and an O(n3 log n) deterministic algorithm that test whether two given trivalent graphs are isomorphic. In fact, the algorithms construct the set of all isomorphisms of the two graphs. Variants of these algorithms construct the set of all automorphisms of a trivalent graph. The algorithms make use of some new improved permutation...
An algorithm is presented which reduces the problem of finding the irreducible factors of a bivariate polynomial with integer coefficients in polynomial time in the total degree and the coefficient lengths to factoring a univariate integer polynomial. Together with A. Lenstra's, H. Lenstra's and L. Lovasz' polynomial-time factorization algorithm for univariate integer polynomials and the author's...
Deterministic exponential lower time bounds are obtained for analyzing monadic recursion schemes, multi-variable recursion schemes, and recursive programs. The lower bound for multivariable recursion schemes holds for any domain of interpretation with at least two elements. The lower bound for recursive programs holds for any recursive programming language with a nontrivial predicate test (i.e. a...
We show that there can be no computationally tractable description by linear inequalities of the polyhedron associated with any NP-complete combinatorial optimization problem unless NP = co-NP -- a very unlikely event. We also apply the ellipsoid method for linear programming to show that a combinatorial optimization problem is solvable in polynomial time if and only if it admits a small generator...
From the users' point of view, resource management schemes may be considered as an abstract data type. An abstract specification of such schemes using axioms holding in partial algebras and relatively distributed implementations (expressed as CSP programs) are given and analyzed. Then the idea of probabilistic implementation of guard scheduling is suggested, which allows completely distributed symmetric...
In this paper we exhibit several new classes of hash functions with certain desirable properties, and introduce two novel applications for hashing which make use of these functions. One class of functions is small, yet is almost universal2. If the functions hash n-bit long names into m-bit indices, then specifying a member of the class requires only O((m + log2log2(n)) log2(n)) bits as compared to...
Straight line programs in which array elements can be referenced and set are considered. Two programs are equivalent if they compute the same expression as a function of the inputs. Testing the equivalence of programs with arrays is shown to be NP-complete, while programs without arrays can be tested for equivalence in linear time. Equivalence testing takes polynomial time when programs have either...
Trie structures are a convenient way of indexing files in which keys are specified by values of attributes. Records correspond to leaves in the trie. Retrieval proceeds by following a path from the root to a leaf, the choice of edges being determined by attribute values. The size of a trie for a file depends on the order in which attributes are tested. We show that determining minimal size tries is...
In this note we show that the tape bounded complexity classes of languages over single letter alphabets are closed under complementation. We then use this result to show that there exists an infinite hierarchy of tape bounded complexity classes of sla languages between log n and log log n tape bounds. We also show that every infinite sla language recognizable on less than log n tape has infinitely...
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