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In recent years, string solvers have become an essential component in many formal-verification, security-analysis and bug-finding tools. Such solvers typically support a theory of string equations, the length function as well as the regular-expression membership predicate. These enable considerable expressive power, which comes at the cost of slow solving… (More)
We show that a principal G bundle on a smooth projective curve over a finite field is strongly semistable if and only if it is defined by a representation of the fundamental group scheme of the curve into G.
In this paper we present a solver for a many-sorted first-order quantifier-free theory T w,bv of string equations, string length represented as bit-vectors, and bit-vector arithmetic aimed at formal verification, automated testing, and security analysis of C/C++ applications. Our key motivation for building such a solver is the observation that existing… (More)
In this paper we give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks. Given an error parameter ε such that 0 < ε, our algorithm maintains approximate all-pairs shortest paths in an undirected planar graph G with nonnegative edge lengths. The approximate paths are guaranteed to be accurate to within a 1 + ε… (More)
1. Let G be a semisimple algebraic group defined over an algebraically closed field k of characteristic p. In this article, we construct the moduli space of semistable principal G bundles on a smooth projective curve X over k, of genus g ≥ 2. When the characteristic is zero, for example the field of complex numbers, these moduli spaces were first… (More)
In this paper, we introduce the notion of Q-fuzzification of Bipolar left R-subgroups in a near-ring and investigate some related properties. Characterization of Bipolar Q-fuzzy left R-subgroups with respect to(T,S)are given.
In this paper, we introduce the notion of Q-Fuzzification of left N-Subgroups in a near ring and investigate some related properties, characterization of Q-Fuzzy left N-Subgroups with respect to a triangular norm are given. The theory of Fuzzy sets which was introduced by Zedah  is applied to many mathematical branches. Abou-Zoid  , introduced the… (More)
Let X be an irreducible smooth projective curve over an algebraically closed field k of characteristic p, with p > 5. Let G be a connected reductive algebraic group over k. Let H be a Levi factor of some parabolic subgroup of G and χ a character of H. Given a reduction E H of the structure group of a G-bundle E G to H, let E χ be the line bundle over X… (More)