Exact Boolean Abstraction of Linear Equation Systems

Parameterised boolean equation systems

Boolean equation system are a useful tool for verifying formulas from modal mu-calculus on transition systems (see [18] for an excellent treatment). We are interested in an extension of boolean equation systems with data. This allows to formulate and prove a substantially wider range of properties on much larger and even infinite state systems. In previous works [11, 15] it has been outlined ho...

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Eecient Diagnostic Generation for Boolean Equation Systems Eecient Diagnostic Generation for Boolean Equation Systems

Boolean Equation Systems (Bess) provide a useful framework for the veriica-tion of concurrent nite-state systems. In practice, it is desirable that a Bes resolution also yields diagnostic information explaining, preferably in a concise way, the truth value computed for a given variable of the Bes. Using a representation of Bess as extended boolean graphs (Ebgs), we propose a characterization of...

Exact soultion of full interval linear equation AX=B based on Kaucher arithmetic

Exact solutions of a linear fractional partial differential equation via characteristics method

‎In recent years‎, ‎many methods have been studied for solving differential equations of fractional order‎, ‎such as Lie group method, ‎invariant subspace method and numerical methods‎, ‎cite{6,5,7,8}‎. Among this‎, ‎the method of characteristics is an efficient and practical method for solving linear fractional differential equations (FDEs) of multi-order‎. In this paper we apply this method f...