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The cryptographic security of the Merkle-Hellman cryptosystem has been a major open problem since 1976. In this paper we show that the basic variant of this cryptosystem, in which the elements of the public key are modular multiples of a superincreasing sequence, is breakable in polynomial time.
In this paper, we propose a notion of fairness for transition systems and a logic for proving properties under the fairness assumption corresponding to this notion. We consider that the concept of fairness which is useful is "fair reachability" of a given set of states P in a system, i.e. reachability of states of P when considering only the computations such that if, during their execution,...
We consider the notion of a (data) format where each format defines a family of data structures. These formats arose from the theory of databases. Previous works have investigated the notion of generic transformations of data structures between formats. We give a novel grouptheoretic view of genericity which unifies the original approaches of Hull-Yap and Aho-Ullman. Among the results are: A necessary...
A central issue in relational database theory is that of decomposition. It has been agreed that decompositions should be injective, so as not to lose information, and surjective, so they decompose a relation into independent components. Injectiveness and surjectiveness are in general second-order notions. We show here how to express these notions in a first-order manner, assuming that we are dealing...
Process Logic (PL) is a language for reasoning about the behavior of a program during a computation, while Propositional Dynamic Logic (PDL) can only reason about the input-output states of a program. Nevertheless, we show that to each PL model M there corresponds in a natural way a PDL, model Mt such that every path in M is represented by a state in Mt. Moreover, to every PL formula p there corresponds...
Polynomial algorithms are described that solve the MIN CUT LINEAR ARRANGEMENT problem on degree restricted trees. For example, the cutwidth or folding number of an arbitrary degree d tree can be found in O(n(logn)d-2) steps. This also yields an algorithm for determining the black/white pebble demand of degree three trees. A forbidden subgraph characterization is given for degree three trees having...
This paper describes and analyzes several algorithms for constructing systolic array networks from cells on a silicon wafer. Some of the cells may be defective, and thus the networks must be configured to avoid them. We adopt a probabilistic model of cell failure, and attempt to construct networks whose maximum wire length is minimal Although the algorithms presented are designed principally for application...
In this paper we show that any channel routing problem of density d involving two-terminal nets can always be solved in the knock-knee mode in a channel of width equal the density d with three conducting layers. An algorithm is described which produces a layout of n nets with the following properties: (i) it has minimal width d; (ii) it can be realized with three layers; (iii) it has at most 3n vias;...
A modification of the ellipsoid algorithm is shown to be capable of testing for satisfiability a system of linear equations and inequalities with integer coefficients of the form Ax = b, x ≥ 0. All the rational arithmetic is performed exactly, without losing polynomiality of the computing time. In case of satisfiability, the approach always provides a rational feasible point. The bulk of the computations...
We present parallel algorithms to compute the determinant and characteristic polynomial of n×n-matrices and the gcd of polynomials of degree ≤n. The algorithms use parallel time O(log2n) and a polynomial number of processors. We also give a fast parallel Las Vegas algorithm for the rank of matrices. All algorithms work over arbitrary fields.
We prove a natural encoding scheme intractable (by showing it UR-complete, a technique which may be used when a problem does not yield to a proof of NP-completeness). This is the first non number-theoretic problem that is UR-complete but not known to be NP-complete. We also redefine UR-completeness (henceforth refered to as PR-completeness) in probabilistic terms thus making the notion conceptually...
A high-resolution raster-graphics display is usually combined with processing power and a memory organization that facilitates basic graphics operations. For many applications, including interactive text processing, the ability to quickly move or copy small rectangles of pixels is essential. This paper proposes a novel organization of raster-graphics memory that permits all small rectangles to be...
Simultaneous Diophantine approximation in d dimensions deals with the approximation of a vector α = (α1, ..., αd) of d real numbers by vectors of rational numbers all having the same denominator. This paper considers the computational complexity of algorithms to find good simultaneous approximations to a given vector α of d rational numbers. We measure the goodness of an approximation using the sup...
We address the question of program size of of perfect and universal hash functions. We prove matching upper and lower bounds (up to constant factors) on program size. Furthermore, we show that minimum or nearly minimum size programs can be found efficiently. In addition, these (near) minimum size programs have time complexity at most O(log* N) where N is the size of the universe in the case of perfect...
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