5,213 research outputs found
Analysis of Affinely Equivalent Boolean Functions
By walsh
transform, autocorrelation function, decomposition, derivation and
modification of truth table, some new invariants are obtained.
Based on invariant theory, we get two results: first a general
algorithm which can be used to judge if two boolean functions are
affinely equivalent and to obtain the affine equivalence
relationship if they are equivalent. For example, all 8-variable
homogenous bent functions of degree 3 are classified into 2
classes; second, the classification of the Reed-Muller code
which can be used to almost
enumeration of 8-variable bent functions
A STUDY OF BINARY DECISION DIAGRAM CHARACTERISTICS OF BENT BOOLEAN FUNCTIONS
Bent Boolean functions exist only for an even number of variables, moreover, they are unbalanced. Therefore, they are used in coding theory and in many areas of computer science. General form of bent functions is still unknown. One way of representing Boolean functions is with a reduced ordered binary decision diagram (ROBDD). The strength of ROBDDs is that they can represent Boolean functions data with a high level of redundancy in a compact form, as long as the data is encoded in such a way that the redundancy is exposed. This paper investigates characteristics of bent functions with focus on their ROBDD parameters. Decision diagram experimental framework has been used for implementation of a program for calculation of the ROBDD parameters. The results presented in this paper are intended to be used to create methods for the construction of bent functions using a ROBDD as a data structure from which the bent functions can be discovered
Boolean Functions and Permanents of Sylvester Hadamard Matrices
One of the fastest known general techniques for computing permanents is Ryser’s formula. On this note, we show that this formula over Sylvester Hadamard matrices of order 2m, Hm, can be carried out by enumerating m-variable Boolean functions with an arbitrary Walsh spectrum. As a consequence, the quotient per(Hm)/22m might be a measure of the “density” of m-variable Boolean functions with high nonlinearity
A Construction of Bent Functions of n + 2 Variables from a Bent Function of n Variables and Its Cyclic Shifts
We present a method to iteratively construct new bent functions of n + 2 variables from a bent function of n variables and its cyclic shift permutations using minterms of n variables and minterms of 2 variables. In addition, we provide the number of bent functions of n + 2 variables that we can obtain by applying the method here presented, and finally we compare this method with a previous one introduced by us in 2008 and with the Rothaus and Maiorana-McFarland constructions.The work of the first author was partially supported by Spanish Grant MTM2011-24858 of the Ministerio de Economía y Competitividad of the Gobierno de España
Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data
Constraint Programming (CP) has proved an effective paradigm to model and
solve difficult combinatorial satisfaction and optimisation problems from
disparate domains. Many such problems arising from the commercial world are
permeated by data uncertainty. Existing CP approaches that accommodate
uncertainty are less suited to uncertainty arising due to incomplete and
erroneous data, because they do not build reliable models and solutions
guaranteed to address the user's genuine problem as she perceives it. Other
fields such as reliable computation offer combinations of models and associated
methods to handle these types of uncertain data, but lack an expressive
framework characterising the resolution methodology independently of the model.
We present a unifying framework that extends the CP formalism in both model
and solutions, to tackle ill-defined combinatorial problems with incomplete or
erroneous data. The certainty closure framework brings together modelling and
solving methodologies from different fields into the CP paradigm to provide
reliable and efficient approches for uncertain constraint problems. We
demonstrate the applicability of the framework on a case study in network
diagnosis. We define resolution forms that give generic templates, and their
associated operational semantics, to derive practical solution methods for
reliable solutions.Comment: Revised versio
A generalized theory of semiflexible polymers
DNA bending on length scales shorter than a persistence length plays an
integral role in the translation of genetic information from DNA to cellular
function. Quantitative experimental studies of these biological systems have
led to a renewed interest in the polymer mechanics relevant for describing the
conformational free energy of DNA bending induced by protein-DNA complexes.
Recent experimental results from DNA cyclization studies have cast doubt on the
applicability of the canonical semiflexible polymer theory, the wormlike chain
(WLC) model, to DNA bending on biological length scales. This paper develops a
theory of the chain statistics of a class of generalized semiflexible polymer
models. Our focus is on the theoretical development of these models and the
calculation of experimental observables. To illustrate our methods, we focus on
a specific toy model of DNA bending. We show that the WLC model generically
describes the long-length-scale chain statistics of semiflexible polymers, as
predicted by the Renormalization Group. In particular, we show that either the
WLC or our new model adequate describes force-extension, solution scattering,
and long-contour-length cyclization experiments, regardless of the details of
DNA bend elasticity. In contrast, experiments sensitive to short-length-scale
chain behavior can in principle reveal dramatic departures from the linear
elastic behavior assumed in the WLC model. We demonstrate this explicitly by
showing that our toy model can reproduce the anomalously large
short-contour-length cyclization J factors observed by Cloutier and Widom.
Finally, we discuss the applicability of these models to DNA chain statistics
in the context of future experiments
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