Sharif Digital Repository

Let G be a simple graph of order n. A dominating set of G is a set S of vertices of G so that every vertex of G is either in S or adjacent to a vertex in 5. The domination polynomial of G is the polynomial D(G, x) = Σn i=1 d(G, i) xi, where d(G, i) is the number of dominating sets of G of size i. In this paper we show that cycles are determined by their domination polynomials  

Constraint automaton is a formalism to capture the operational semantics of the channel based coordination language Reo. In general constraint automaton can be used as a formalism for modeling coordination of some components. In this paper we introduce a standard linear temporal logic and two fragments of it for expressing the properties of the systems modeled by constraint automata and show that the equivalence relation defined by Valmari et al. is the minimal compositional equivalence preserving that fragment of linear time temporal logic which has no next-time operator and has an extra operator distinguishing deadlocks and a slight modification of this equivalence is the minimal... 

Considering the space of constant-weight sequences as the reference set for every optical orthogonal code (OOC) design algorithm, we propose a classification method that preserves the correlation properties of sequences. First, we introduce the circulant matrix representation of optical orthogonal codes and, based on the spectrum of circulant matrices, we define the spectral classification of the set Sn,w of all (0, 1)-sequences with length n, weight w, and the first chip 1. Then, as a method for spectrally classifying the set Sn,w, we discuss an algebraic structure called multiplicative group action. Using the above multiplicative group action, we define an equivalence relation on Sn,w in... 

We consider the computational complexity of pure Nash equilibria in graphical games. It is known that the problem is NP-complete in general, but tractable (i.e., in P) for special classes of graphs such as those with bounded treewidth. It is then natural to ask: is it possible to characterize all tractable classes of graphs for this problem? In this work, we provide such a characterization for the case of bounded in-degree graphs, thereby resolving the gap between existing hardness and tractability results. In particular, we analyze the complexity of PURE-GG(C, -), the problem of deciding the existence of pure Nash equilibria in graphical games whose underlying graphs are restricted to class... 

Developing an accurate network equivalent to reduce the computational time of an electromagnetic transient study has been the major task of many researches in the past two decades. However, still no accurate wide band equivalent for an asymmetrical network is addressed in the literature. This paper presents a Hybrid equivalent for the external system, assuming that it contains an asymmetrical transmission system at the terminal of this external system. The proposed method is based on the introduction of an asymmetrical transmission system in the model through application of a real constant transformation matrix in the subsystem and dealing with its asymmetrical effects in the external... 

A group-characterizable (GC) random variable is induced by a finite group, called main group, and a collection of its subgroups. The notion extends directly to secret sharing schemes (SSSs). It is known that linear and abelian SSSs can be equivalently described in terms of GC SSSs. In this paper, we present a necessary and sufficient condition for a SSS to be equivalent to a GC one. Using this result, we show that homomorphic SSSs (HSSSs) are equivalent to GC SSSs whose subgroups are normal in the main group. We also present two applications for this equivalent description of HSSSs. One concerns lower bounding the information ratio of access structures for the class of HSSSs, and the other... 

Constructing all extreme instances of the set of completely positive trace-preserving (CPTP) maps, i.e., quantum channels, is a challenging and valuable open problem in quantum information theory. Here we introduce a systematic approach that, despite the lack of knowledge about the full parametrization of the set of CPTP maps on arbitrary Hilbert-spaced dimension, enables us to construct exactly those extreme channels that are covariant with respect to a finite discrete group or a compact connected Lie group. Innovative labeling of quantum channels by group representations enables us to identify the subset of group-covariant channels whose elements are group-covariant generalized-extreme... 

By increasing the complexity of system on a chip (SoC) formal equivalence checking has become more and more important and a major economical issue to detect design faults at early stages of the design cycle in order to reduce time-to-market as much as possible. However, lower level methods such as BDDs and SAT solvers suffer from memory and computational explosion problems to match sizes of industrial designs in formal equivalence verification. In this paper, we describe a hybrid bit- and word-level canonical representation called Linear Taylor Expansion Diagram (LTED) [1] which can be used to check the equivalence between two descriptions in different levels of abstractions. To prove the...