open bisimulation revisited in the context of the p calculus open bisimulation is prominent and popular due to its congruence properties and its easy implementability motivated by the attempt to generalise it to the spi calculus we offer a new more refined definition and show how far it coincides with the original one

discontinuous spectral element methods for time and space fractional advection equations we develop spectral element methods for a time and space fractional advection equation of the form prescript 0 mathcal d tau t u x t theta prescript 0 mathcal d nu x u x t f x t of order tau in 0 1 nu in 0 1 subject to dirichlet initial boundary conditions we present two spectrally accurate and efficient methods for global discretization of both temporal and spatial terms instead of employing traditional low order time integration methods to this end we first develop a petrov galerkin in time and discontinuous galerkin in space pg dg method where we carry out the time integration using a single time domain spectral method sm and we perform the spatial discretization using the discontinuous spectral hp element method dsem this scheme also leads to a more efficient time integration when the time derivative is integer order i e tau 1 we develop the sm dsem scheme based on a new spectral theory for fractional sturm liouville problems

control and synchronize a novel hyperchaotic system the control and hybrid projective synchronization hps strategies for a novel hyperchaotic system are investigated firstly the novel hyperchaotic system is controlled to the unsteady equilibrium point or limit cycle via only one scalar controller which includes two state variables secondly based on lyapunov s direct method hps between two novel hyperchaotic systems is studied a new nonlinear feedback vector controller is designed to guarantee hps which can be simplified ulteriorly into a single scalar controller to achieve complete synchronization between two novel hyperchaotic systems finally numerical simulations are given to verify the effectiveness of these strategies the proposed methods have certain significances for reducing the cost and complexity for controller implementation

convergence analysis of the chebyshev legendre spectral method for a class of fredholm fractional integro differential equations abstract in this paper we propose and analyze a spectral chebyshev legendre approximation for fractional order integro differential equations of fredholm type the fractional derivative is described in the caputo sense our proposed method is illustrated by considering some examples whose exact solutions are available we prove that the error of the approximate solution decays exponentially in l 2 norm

synchronization of a chaotic finance system synchronization strategies of a three dimensional chaotic finance system are investigated in this paper based on lyapunov stability theory and routh hurwitz criteria some effective controllers are designed for the global asymptotic synchronization on different conditions when the system parameters are known the hybrid feedback control and a method based on special matrix structure are adopted respectively to realize the synchronization of the chaotic finance system when the parameters are unknown the active control is extended and introduced to realize the synchronization numerical simulations show the validity and feasibility of the synchronization schemes

a framework for analyzing probabilistic protocols and its application to the partial secrets exchange we propose a probabilistic variant of the pi calculus as a framework to specify randomized security protocols and their intended properties in order to express and verify the correctness of the protocols we develop a probabilistic version of the testing semantics we then illustrate these concepts on an extended example the partial secret exchange a protocol which uses a randomized primitive the oblivious transfer to achieve fairness of information exchange between two parties

weakening the perfect encryption assumption in dolev yao adversaries we consider secrecy and authentication in a simple process calculus with cryptographic primitives the standard dolev yao adversary is enhanced so that it can guess the key required to decrypt an intercepted message we borrow from the computational complexity approach the assumptions that guessing succeeds with a given negligible probability and that the resources available to adversaries are polynomially bounded under these hypotheses we prove that the standard dolev yao adversary is as powerful as the enhanced one

a unified petrov galerkin spectral method for fractional pdes existing numerical methods for fractional pdes suffer from low accuracy and inefficiency in dealing with three dimensional problems or with long time integrations we develop a unified and spectrally accurate petrov galerkin pg spectral method for a weak formulation of the general linear fractional partial differential equations fpdes of the form 0dt2 u j 1dcj ajdxj2 ju u f where 2 2 j 0 1 j 0 1 in a 1 d1 d dimensional space time domain subject to dirichlet initial and boundary conditions we perform the stability analysis in 1 d and the corresponding convergence study of the scheme in multi d the unified pg spectral method applies to the entire family of linear hyperbolichyperbolic parabolicparabolic and ellipticelliptic like equations we develop the pg method based on a new spectral theory for fractional sturm liouville problems fslps recently introduced in zayernouri and karniadakis 2013 specifically we employ the eigenfunctions of the fslp of first kind fslp i called jacobi poly fractonomials as temporal spatial bases next we construct a different space for test functions from poly fractonomial eigenfunctions of the fslp of second kind fslp ii besides the high order spatial accuracy of the pg method we demonstrate its efficiency and spectral accuracy in time integration schemes for solving time dependent fpdes as well rather than employing algebraically accurate traditional methods especially when 2 12 1 finally we formulate a general fast linear solver based on the eigenpairs of the corresponding temporal and spatial mass matrices with respect to the stiffness matrices which reduces the computational cost drastically we demonstrate that this framework can reduce to hyperbolic fpdes such as time and space fractional advection tsfa parabolic fpdes such as time and space fractional diffusion tsfd model and elliptic fpdes such as fractional helmholtz poisson equations with the same ease and cost several numerical tests confirm the efficiency and spectral convergence of the unified pg spectral method for the aforementioned families of fpdes moreover we demonstrate the computational efficiency of the new approach in higher dimensions e g 1 3 1 5 and 1 9 dimensional problems

on the convergence of spline collocation methods for solving fractional differential equations in the first part of this paper we study the regularity properties of solutions of initial value problems of linear multi term fractional differential equations we then use these results in the convergence analysis of a polynomial spline collocation method for solving such problems numerically using an integral equation reformulation and special non uniform grids global convergence estimates are derived from these estimates it follows that the method has a rapid convergence if we use suitable nonuniform grids and the nodes of the composite gaussian quadrature formulas as collocation points theoretical results are verified by some numerical examples

a new operational matrix for solving fractional order differential equations abstract fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations for that reason we need a reliable and efficient technique for the solution of fractional differential equations this paper deals with the numerical solution of a class of fractional differential equations the fractional derivatives are described in the caputo sense our main aim is to generalize the legendre operational matrix to the fractional calculus in this approach a truncated legendre series together with the legendre operational matrix of fractional derivatives are used for numerical integration of fractional differential equations the main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus greatly simplifying the problem the method is applied to solve two types of fractional differential equations linear and nonlinear illustrative examples are included to demonstrate the validity and applicability of the presented technique

numerical solution of semidifferential equations by collocation method we study the numerical solution of semidifferential equation of order 4 by collocation spline method we derive a system of equations that characterizing the numerical solution some numerical examples are also presented to illustrate our results

static analysis for the π calculus with applications to security abstract control flow analysis is a static technique for predicting safe and computable approximations to the set of values that the objects of a program may assume during its execution we present an analysis for the calculus that shows how names will be bound to actual channels at run time the result of our analysis establishes a super set of the set of channels to which a given name may be bound and of the set of channels that may be sent along a given channel besides a set of rules that permits one to validate a given solution we also offer a constructive procedure that builds solutions in low polynomial time applications of our analysis include establishing two simple security properties of processes one example is that p has no leaks p offers communication to the external environment through public channels only and confines its secret channels within itself the other example is connected to the no read up no write down property of bell and lapadula once processes are given levels of security clearance we check that a process at a high level never sends channels to processes at a lower level

stability and bifurcation of pan chaotic system by using routh hurwitz and gardan methods abstract in this paper a new three dimensional pan chaotic system is reported dynamical behaviors of the new system are analyzed both theoretically and numerically including some basic dynamical properties stability and hopf bifurcation the stability and hopf bifurcation are investigated by routh hurwitz method and cardan method stability analysis shows that both methods justified the same results finally an illustrative example is given

testing equivalences for processes abstract given a set of processes and a set of tests on these processes we show how to define in a natural way three different equivalences on processes these equivalences are applied to a particular language ccs we give associated complete proof systems and fully abstract models these models have a simple representation in terms of trees

testing equivalence for mobile processes the impact of applying the testing approach to a calculus of processes with dynamic communication topology is investigated a proof system is introduced that consists of two groups of laws those for strong observational equivalence and those needed to deal with invisible actions soundness and completeness of this proof system w r t a testing preorder are shown a fully abstract denotational model for the language is presented that takes advantage of reductions of processes to normal forms

collocation method with convergence for generalized fractional integro differential equations abstract in this paper we study a numerical approach for some class of generalized fractional integro differential equations gfides defined in terms of the b operators presented recently we develop collocation method for linear and nonlinear forms of gfides the numerical approach uses the idea of collocation methods for solving integral equations legendre polynomials are used to approximate the solution in finite dimensional space with convergence analysis the obtained approximate solution recovers the solution of the fractional integro differential equation fide defined using caputo derivatives in a special case fides containing convolution type kernels appear in diverse area of science and engineering applications therefore some test examples varying the kernel in the b operator are considered to perform the numerical investigations the numerical results validate the presented scheme and provide good accuracy using few legendre basis functions

comparative study of three numerical schemes for fractional integro differential equations this paper presents a comparative study of three numerical schemes such as linear quadratic and quadratic linear scheme for the fractional integro differential equations defined in terms of the caputo fractional derivatives the error estimates of the respective approximations are also established numerical tests of the discussed schemes show that all schemes work well and when the number of terms approximating the solution is increased the desired solution is achieved the accuracy of the numerical schemes with respect to the step size h is analysed and illustrated through various tables finally comparative performances of the schemes are discussed comparative study of three schemes such as linear quadratic and quadratic linear schemes is presented for the fractional integro differential equations the convergences of the schemes are also established the performances of the schemes are compared through the test examples

application of the collocation method for solving nonlinear fractional integro differential equations in this paper using the collocation method we solve the nonlinear fractional integro differential equations nfide of the form f t y t a cd t a 0y t a cd t a ry t email protected t y t a tk t s f s y s ds y k a d k k 0 1 m 0 1 we study the convergence and the stability analysis of this method for f t y t a cd t a 0y t a cd t a ry t y t email protected j 0 rb j a cd t a jy t g t some numerical examples are given to show the efficiency of the presented method

numerical algorithm to solve system of nonlinear fractional differential equations based on wavelets method and the error analysis in this paper a system of nonlinear fractional differential equations fdes are considered they have been solved by legendre wavelets method combining with its operational matrix however there are no articles about solving this system using wavelets method the main purpose of this technique is to transform the initial equations into a nonlinear system of algebraic equations which can be solved easily the convergence and error analysis are presented to show the correctness and feasibility of method proposed for solving the above mentioned problem finally the applicability and efficiency of the mentioned approach are demonstrated by three numerical examples

the function cascade synchronization approach with uncertain parameters or not for hyperchaotic systems the function cascade synchronization scheme for the hyperchaotic systems is proposed to make the states of two identical the hyperchaotic systems both with and without uncertain parameters asymptotically synchronized based on lyapunov stability theory and the proposed scheme the lu system and chen hyperchaotic system with and without uncertain parameters are chosen to achieve the function cascade synchronization simultaneously numerical simulations are used to verify the effectiveness and feasibility of the presented control scheme

typing correspondence assertions for communication protocols woo and lam propose correspondence assertions for specifying authenticity properties of security protocols prior work on checking correspondence assertions depends on model checking and is limited to finite state systems we propose a dependent type and effect system for checking correspondence assertions since it is based on type checking our method is not limited to finite state systems this paper presents our system in the simple and general setting of the calculus we show how to type check correctness properties of example communication protocols based on secure channels in a related paper we extend our system to the more complex and specific setting of checking cryptographic protocols based on encrypted messages sent over insecure channels

controlling hyperchaos in hyperchaotic lorenz system using feedback controllers abstract in this paper the control strategies for hyperchaotic lorenz system is investigated the ordinary dislocated enhancing and speed feedback controls are used to suppress hyperchaos to unstable equilibrium the routh hurwitz criterion is used to derive the conditions of stability of the controlled hyperchaotic systems it is found that the coefficients of enhancing feedback control and dislocated feedback control may be smaller than those of ordinary feedback control so the complexity and cost of the system control are reduced numerical simulations are given to illustrate the effectiveness of the proposed controllers

deciding knowledge in security protocols under equational theories the analysis of security protocols requires precise formulations of the knowledge of protocol participants and attackers in formal approaches this knowledge is often treated in terms of message deducibility and indistinguishability relations in this paper we study the decidability of these two relations the messages in question may employ functions encryption decryption etc axiomatized in an equational theory one of our main positive results says that deducibility and indistinguishability are both decidable in polynomial time for a large class of equational theories this class of equational theories is defined syntactically and includes for example theories for encryption decryption and digital signatures we also establish general decidability theorems for an even larger class of theories these theorems require only loose abstract conditions and apply to many other useful theories for example with blind digital signatures homomorphic encryption xor and other associative commutative functions

a calculus for cryptographic protocols we introduce the spi calculus an extension of the pi calculus designed for describing and analyzing cryptographic protocols we show how to use the spi calculus particularly for studying authentication protocols the pi calculus without extension suffices for some abstract protocols the spi calculus enables us to consider cryptographic issues in more detail we represent protocols as processes in the spi calculus and state their security properties in terms of coarse grained notions of protocol equivalence

a bisimulation for dynamic sealing we define l s e a l an untyped call by value l calculus with primitives for protecting abstract data by sealing and develop a bisimulation proof method that is sound and complete with respect to contextual equivalence this provides a formal basis for reasoning about data abstraction in open dynamic settings where static techniques such as type abstraction and logical relations are not applicable

reconstruction of exponentially rate of convergence to legendre collocation solution of a class of fractional integro differential equations in this paper legendre collocation method an easy to use variant of the spectral methods for the numerical solution of a class of fractional integro differential equations fide s is researched in order to obtain high order accuracy for the approximation the integral term in the resulting equation is approximated by using legendre gauss quadrature formula an efficient convergence analysis of the proposed method is given and rate of convergence is established in the l 2 norm due to the fact that the solutions of fide s usually have a weak singularity at origin we use a variable transformation to change the original equation into a new equation with a smooth solution we prove that after this regularization technique numerical solution of the new equation by adopting the legendre collocation method has exponentially rate of convergence numerical results are presented which clarify the high accuracy of the proposed method

application of the fractional differential transform method to fractional order integro differential equations with nonlocal boundary conditions in this paper the fractional differential transform method is developed to solve fractional integro differential equations with nonlocal boundary conditions the method is described and illustrated with numerical examples the results reveal that the method is accurate and easy to apply

exponentially accurate spectral and spectral element methods for fractional odes current discretizations of fractional differential equations lead to numerical solutions of low order of accuracy here we present different methods for fractional odes that lead to exponentially fast decay of the error first we develop a petrov galerkin pg spectral method for fractional initial value problems fivps of the form d t 0 u t f t and fractional final value problems ffvps d t t u t g t where 0 1 subject to dirichlet initial final conditions these schemes are developed based on a new spectral theory for fractional sturm liouville problems fslps which has been recently developed in 1 specifically we obtain solutions to fivps and ffvps in terms of the new fractional non polynomial basis functions called jacobi polyfractonomials which are the eigenfunctions of the fslp of first kind fslp i correspondingly we employ another space of test functions as the span of polyfractonomial eigenfunctions of the fslp of second kind fslp ii subsequently we develop a discontinuous spectral method dsm of petrov galerkin sense for the aforementioned fivps and ffvps where the basis functions do not satisfy the initial final conditions finally we extend the dsm scheme to a discontinuous spectral element method dsem for efficient longer time integration and adaptive refinement in these discontinuous schemes we employ the asymptotic eigensolutions to fslp i ii which are of jacobi polynomial forms as basis and test functions our numerical tests confirm the exponential algebraic convergence respectively in p and h refinements for various test cases with integer and fractional order solutions

probabilistic and nondeterministic aspects of anonymity the concept of anonymity comes into play in a wide range of situations varying from voting and anonymous donations to postings on bulletin boards and sending emails the protocols for ensuring anonymity often use random mechanisms which can be described probabilistically while the agents behavior may be totally unpredictable irregular and hence expressible only nondeterministically formal definitions of the concept of anonymity have been investigated in the past either in a totally nondeterministic framework or in a purely probabilistic one in this paper we investigate a notion of anonymity which combines both probability and nondeterminism and which is suitable for describing the most general situation in which the protocol and the users can have both probabilistic and nondeterministic behavior we also investigate the properties of the definition for the particular cases of purely nondeterministic users and purely probabilistic users we formulate the notions of anonymity in terms of probabilistic automata and we describe protocols and users as processes in the probabilistic p calculus whose semantics is again based on probabilistic automata throughout the paper we illustrate our ideas by using the example of the dining cryptographers

quantifying information leakage in process calculi building on simple information theoretic concepts we study two quantitative models of information leakage in the pi calculus the first model presupposes an attacker with an essentially unlimited computational power the resulting notion of absolute leakage measured in bits is in agreement with secrecy as defined by abadi and gordon a process has an absolute leakage of zero precisely when it satisfies secrecy the second model assumes a restricted observation scenario inspired by the testing equivalence framework where the attacker can only conduct repeated success or failure experiments on processes moreover each experiment has a cost in terms of communication effort the resulting notion of leakage rate measured in bits per action is in agreement with the first model the maximum amount of information that can be extracted by repeated experiments coincides with the absolute leakage a of the process moreover the overall extraction cost is at least a r where r is the rate of the process the compositionality properties of the two models are also investigated

cubic b spline approximation for linear stochastic integro differential equation of fractional order abstract in this paper the cubic b spline collocation method is used for solving the stochastic integro differential equation of fractional order we show that stochastic integro differential equation of fractional order is equivalent to a modified stochastic integral equation then we apply the proposed method to obtain a numerical scheme of the modified stochastic integral equation using this method the problem solving turns into a linear system solution of equations also the convergence analysis of this numerical approach has been discussed in the end examples are given to test the accuracy and the implementation of the method the results are compared with the results obtained by other methods to verify that this method is accurate and efficient

controlling hyperchaos in the new hyperchaotic chen system in this paper we investigate the new hyperchaotic chen system which was present recently by introducing a feedback controller to the chen system the linear speed nonlinear doubly periodic function and nonlinear hyperbolic function feedback controls are used to suppress hyperchaos to unstable equilibrium the routh hurwitz theorem is used to derive the conditions of stability of controlled hyperchaotic chen systems moreover numerical simulations are used to verify the effectiveness of the proposed controllers

a pure labeled transition semantics for the applied pi calculus the applied pi calculus proposed by abadi and fournet is successful in the analysis of security protocols its semantics mainly depends on several structural rules structural rules are convenient for specification but inefficient for implementation in this paper we establish a new semantics for applied pi calculus based upon pure labeled transition system and propose a new formulation of labeled bisimulation we prove that the new labeled bisimularity coincides with observational equivalence a zero knowledge protocol is given as an example to illustrate the effectiveness of this new semantics

numerical solution of fractional integro differential equations by collocation method abstract this paper deals with the numerical solution of fractional integro differential equations of the type d q y t p t y t f t 0 t k t s y s d s t i 0 1 by polynomial spline functions we derive a system of equations that characterizing the numerical solution some numerical examples are also provided to illustrated our results

multiset rewriting for the verification of depth bounded processes with name binding we combine two of the existing approaches to the study of concurrency by means of multiset rewriting multiset rewriting with existential quantification msr and constrained multiset rewriting we obtain n msr where we rewrite multisets of atomic formulae in which terms can only be pure names where some names can be restricted we consider the subclass of depth bounded n msr for which the interdependence of names is bounded we prove that they are strictly well structured transition systems so that coverability termination and boundedness are all decidable for depth bounded n msr this allows us to obtain new verification results for several formalisms with name binding that can be encoded within n msr namely polyadic n pn petri nets with tuples of names as tokens the p calculus msr or mobile ambients

types and full abstraction for polyadic π calculus a type system for terms of the monadic p calculus is introduced and used to obtain a full abstraction result for the translation of the polyadic p calculus into the monadic calculus well sorted terms of the polyadic calculus are barbed congruent iff their translations are typed barbed congruent

structured coalgebras and minimal hd automata for the π calculus the coalgebraic framework developed for the classical process algebras and in particular its advantages concerning minimal realizations does not fully apply to the calculus due to the constraints on the freshly generated names that appear in the bisimulation in this paper we propose to model the transition system of the calculus as a coalgebra on a category of name permutation algebras and to define its abstract semantics as the final coalgebra of such a category we show that permutations are sufficient to represent in an explicit way fresh name generation thus allowing for the definition of minimal realizations we also link the coalgebraic semantics with a slightly improved version of history dependent hd automata a model developed for verification purposes where states have local names and transitions are decorated with names and name relations hd automata associated with agents with a bounded number of threads in their derivatives are finite and can be actually minimized we show that the bisimulation relation in the coalgebraic context corresponds to the minimal hd antomaton

intruder deduction for the equational theory of abelian groups with distributive encryption cryptographic protocols are small programs which involve a high level of concurrency and which are difficult to analyze by hand the most successful methods to verify such protocols are based on rewriting techniques and automated deduction in order to implement or mimic the process calculus describing the execution of a protocol we are interested in the intruder deduction problem that is vulnerability to passive attacks in presence of equational theories which model the protocol specification and properties of the cryptographic operators in the present paper we consider the case where the encryption distributes over the operator of an abelian group or over an exclusive or operator we prove decidability of the intruder deduction problem in both cases we obtain a ptime decision procedure in a restricted case the so called binary case these decision procedures are based on a careful analysis of the proof system modeling the deductive power of the intruder taking into account the algebraic properties of the equational theories under consideration the analysis of the deduction rules interacting with the equational theory relies on the manipulation of z modules in the general case and on results from prefix rewriting in the binary case

a novel method for solving second order fractional eigenvalue problems the paper presents a new numerical method for solving eigenvalue problems for fractional differential equations it combines two techniques the method of external excitation mee and the backward substitution method bsm the first one is a mathematical model of physical measurements when a mechanical electrical or acoustic system is excited by some source and resonant frequencies can be determined by using the growth of the amplitude of oscillations near these frequencies the bsm consists of replacing the original equation by an approximate equation which has an exact analytic solution with a set of free parameters these free parameters are determined by the use of the collocation procedure some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results the numerical results show that the proposed method is of a high accuracy and is efficient for solving of a wide class of eigenvalue problems

numerical solution of fractional integro differential equations by a hybrid collocation method fractional integro differential equations have been recently solved by many methods such as adomian decomposition method differential transform method collocation method and taylor expansion approach in this paper a hybrid collocation method is used which combines a non polynomial collocation used on the first subinterval and graded piecewise polynomial collocation used on the rest of the interval a theoretical analysis for the convergence order of the method is presented some numerical examples are given which confirm the theoretical results

approximate solution of fractional integro differential equations by taylor expansion method in this paper taylor expansion approach is presented for solving approximately a class of linear fractional integro differential equations including those of fredholm and of volterra types by means of the mth order taylor expansion of the unknown function at an arbitrary point the linear fractional integro differential equation can be converted approximately to a system of equations for the unknown function itself and its m derivatives under initial conditions this method gives a simple and closed form solution for a linear fractional integro differential equation in addition illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method