A Hierarchy of Resolution Systems with Restricted Substitution Rules

The proof system, based on resolution method, has become quite popular in automatic theorem proving, because this method is simple to implement. At present many kinds of extensions for resolution method are known： Resolution with restricted number of variables in disjuncts, resolution over Linear Equations, Cutting planes, etc. For Classical, Intuitionistic and Minimal （Johansson＇s） propositional logics, the authors introduce the family of resolution systems with full substitution rule （SRC, SRI and SRM） and with e-restricted substitution rule （SeRC, SeRf and SeRM）, where the number of substituted formula connectives is bounded by . The authors show that for each of mentioned logic the SR-type system （in tree form） is polynomially equivalent to Frege systems by size, but for every ~＇ 〉 0, Se＋lR-type has exponential speed-up over the SeR-type （in tree form）.

Substitutions of vertex configuration of Ammann–Beenker tiling in framework of Ammann lines

The Ammann–Beenker tiling is a typical model for two-dimensional octagonal quasicrystals. The geometric properties of local configurations are the key to understanding its formation mechanism. We study the configuration correlations in the framework of Ammann lines, giving an in-depth inspection of this eightfold symmetric structure. When both the vertex type and the orientation are taken into account, strict confinements of neighboring vertices are found. These correlations reveal the structural properties of the quasilattice and also provide substitution rules of vertex along an Ammann line.

Graphical password： prevent shoulder-surfing attack using digraph substitution rules

In this paper, a new scheme that uses digraph substitution rules to conceal the mechanism or activity re- quired to derive password-images is proposed. In the pro- posed method, a user is only required to click on one of the pass-image instead of both pass-images shown in each chal- lenge set for three consecutive sets. While this activity is sim- ple enough to reduce login time, the images clicked appear to be random and can only be obtained with complete knowl- edge of the registered password along with the activity rules. Thus, it becomes impossible for shoulder-surfing attackers to obtain the information about which password images and pass-images are used by the user. Although the attackers may know about the digraph substitution rules used in the pro- posed method, the scenario information used in each chal- lenge set remains. User study results reveal an average login process of less than half a minute. In addition, the proposed method is resistant to shoulder-surfing attacks.

Applications of Markov spectra for the weighted partition network by the substitution rule

The weighted self-similar network is introduced in an iterative way.In order to understand the topological properties of the self-similar network,we have done a lot of research in this field.Firstly,according to the symmetry feature of the self-similar network,we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted matrix.Then,we obtain eigenvalues of the Laplacian matrix from these two successive generations.Finally,we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix.