countable nondeterminism and random assignment four semantics for a small programming language involving unbounded but countable nondeterminism are provided these comprise an operational semantics two state transformation semantics based on the egli milner and smyth orders respectively and a weakest precondition semantics their equivalence is proved a hoare like proof system for total correctness is also introduced and its soundness and completeness in an appropriate sense are shown finally the recursion theoretic complexity of the notions introduced is studied admission of countable nondeterminism results in a lack of continuity of various semantic functions and this is shown to be necessary for any semantics satisfying appropriate conditions in proofs of total correctness one resorts to the use of countable ordinals and it is shown that all recursive ordinals are needed

transition system specifications with negative premises abstract in this article the general approach to plotkin style operational semantics of groote and vaandrager 1989 is extended to transition system specifications tsss with rules that may contain negative premises two problems arise firstly the rules may be inconsistent and secondly it is not obvious how a tss determines a transition relation we present a general method based on the stratification technique in logic programming to prove consistency of a set of rules and we show how a specific transition relation can be associated with a tss in a natural way then a special format for the rules the ntyft ntyxt format is defined it is shown that for this format three important theorems hold the first theorem says that bisimulation is a congruence if all operators are defined using this format the second theorem states that under certain restrictions a tss in ntyft format can be added conservatively to a tss in pure ntyft ntyxt format finally it is shown that the trace congruence for image finite processes induced by the pure ntyft ntyxt format is precisely bisimulation equivalence

ordered sos process languages for branching and eager bisimulation we present a general and uniform method for defining structural operational semantics sos of process operators by traditional plotkin style transition rules equipped with orderings this new feature allows one to control the order of application of rules when deriving transitions of process terms our method is powerful enough to deal with rules with negative premises and copying we show that rules with orderings called ordered sos rules have the same expressive power as gsos rules we identify several classes of process languages with operators defined by rules with and without orderings in the setting with silent actions and divergence we prove that branching bisimulation and eager bisimulation relations are preserved by all operators in process languages in the relevant classes

structural operational semantics for weak bisimulations in this study we present rule formats for four main notions of bisimulation with silent moves weak bisimulation is a congruence for any process algebra defined by wb cool rules we have similar results for rooted weak bisimulation milner s observational equivalence branching bisimulation and rooted branching bisimulation the theorems stating that say observational equivalence is an appropriate notion of equality for ccs are corollaries of the results of this paper we also give sufficient conditions under which equational axiom systems can be generated from operational rules indeed many equational axiom systems appearing in the literature are instances of this general theory

on guarded recursion abstract we introduce a logical notion of well guardedness for recursive terms on arbitrary signatures defined in plotkin s framework of structural operational specifications restricted by se simone s realizability requirements we then suggest a simpler form for the logical rule that gives the behaviour of a recursively defined expression in terms of the behaviour of its unfoldings for well guarded terms the simplified rule is logically equivalent to the general rule but it does not have the drawback of asking for premises more complex than consequences

bisimulation can t be traced in the concurrent language ccs two programs are considered the same if they are bisimilar several years and many researchers have demonstrated that the theory of bisimulation is mathematically appealing and useful in practice however bisimulation makes too many distinctions between programs we consider the problem of adding operations to ccs to make bisimulation fully abstract we define the class of gsos operations generalizing the style and technical advantages of ccs operations we characterize gsos congruence in as a bisimulation like relation called ready simulation bisimulation is strictly finer than ready simulation and hence not a congruence for any gsos language

tile formats for located and mobile systems abstract standard sos formats are limited in their ability to define the operational semantics of process calculi with concurrency causality and mobility and with bound names and name generation mechanisms in this paper we describe a general approach based on the tile model to the definition of the operational semantics of process calculi by providing tile systems for located ccs and asynchronous calculus we demonstrate that the proposed approach is more suited than sos to provide a uniform treatment of concurrency and mobility within a compositional framework

the patch test as a validation of a new finite element for the solution of convection diffusion equations abstract a first goal of this work is to show how the patch test a well known tool established in the field of continuum mechanics can be fruitfully employed to demonstrate the convergence and robustness of a numerical method for the solution of convection dominated flow problems a new finite element passing the patch test is then proposed for the discrestization of current continuity equations in semiconductors numerical results relative to the study of two dimensional devices are included to validate the effectiveness of the method

preconditioned hermitian and skew hermitian splitting methods for non hermitian positive semidefinite linear systems for the positive semidefinite system of linear equations of a block two by two structure by making use of the hermitian skew hermitian splitting iteration technique we establish a class of preconditioned hermitian skew hermitian splitting iteration methods theoretical analysis shows that the new method converges unconditionally to the unique solution of the linear system moreover the optimal choice of the involved iteration parameter and the corresponding asymptotic convergence rate are computed exactly numerical examples further confirm the correctness of the theory and the effectiveness of the method

a new control volume finite element method for the stable and accurate solution of the drift diffusion equations on general unstructured grids abstract we present a new control volume finite element method with multi dimensional scharfetter gummel upwinding cvfem sg for the drift diffusion equations the method combines a conservative formulation of the carrier density continuity equations with an edge element lifting of the one dimensional scharfetter gummel edge currents into curl conforming elemental currents these elemental currents combine the upwind effect from all element edges and enable accurate computation of the flux on arbitrary surfaces inside the elements in so doing we obtain a formulation that is stable and accurate on general unstructured finite element grids this approach sets our formulation apart from other methods which require the control volumes to be topologically dual to the primal grid numerical studies of the cvfem sg for a suite of scalar advection diffusion test problems confirm the accuracy and the robustness of the new formulation simulations of a pn diode and an n channel mosfet device demonstrate the performance of the method for the fully coupled drift diffusion system

discrete hodge operators many linear boundary value problems arising in computational physics can be formulated in the calculus of differential forms discrete differential forms provide a natural and canonical approach to their discretization however much freedom remains concerning the choice of discrete hodge operators that is discrete analogues of constitutive laws a generic discrete hodge operator is introduced and it turns out that most finite element and finite volume schemes emerge as its specializations we reap the possibility of a unified convergence analysis in the framework of discrete exterior calculus

exponentially fitted shape functions for advection dominated flow problems in two dimensions we sketch out the basic properties of three novel exponentially fitted shape functions that generalize to two dimensional triangular elements the one dimensional functions used in the well known scharfetter gummel method this scheme is widely employed in the finite element approximation of the drift diffusion equations arising in semiconductor device modelling

gsos and finite labelled transition systems recently there has been considerable interest in studying formats of plotkin style inference rules which ensure that the induced labelled transition system semantics have certain properties in this note i shall give a contribution to this line of research by giving a restricted version of bloom istrail and meyer s gsos format bloom et al 1988 bloom 1989 which induces finite labelled transition systems

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

on parameterized inexact uzawa methods for generalized saddle point problems abstract for the large sparse saddle point problems bai et al recently studied a class of parameterized inexact uzawa piu methods z z bai b n parlett z q wang on generalized successive overrelaxation methods for augmented linear systems numer math 102 2005 1 38 for a special case that the 1 1 block is solved exactly they determined the convergence domain and computed the optimal iteration parameters and the corresponding optimal convergence factor for the induced method in this paper we develop these methods to the large sparse generalized saddle point problems for the obtained parameterized inexact uzawa method we prove its convergence under suitable restrictions on the iteration parameters in particular we determine its quasi optimal iteration parameters and the corresponding quasi optimal convergence factor for the saddle point problems furthermore this piu method is generalized to obtain a framework of accelerated variants of the parameterized inexact uzawa methods for solving both symmetric and nonsymmetric generalized saddle point problems by using the techniques of vector extrapolation matrix relaxation and inexact iteration

a theory of communicating processes with value passing a semantic theory of process algebras which allows processes to communicate values is described a behavioural theory of testing is given for such processes and is modelled by an extension of acceptance trees a proof system is also given for this model and is shown to be both sound and complete finally the model is shown to be fully abstract with respect to the behavioural theory

cpo models for compact gsos languages in this paper we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the gsos format of bloom istrail and meyer the canonical model used for this purpose will be abramsky s domain of synchronization trees and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract with respect to the finitely observable part of the bisimulation preorder in the process of establishing the full abstraction result we also obtain several general results on the bisimulation preorder including a complete axiomatization for it and give a novel operational interpretation of gsos languages

modal logics for communicating systems abstract simple modal logics for milner s sccs and ccs are presented we offer sound and complete axiomatizations of validity relative to these calculi as models also we present compositional proof systems for when a program satisfies a formula these involve proof rules which are like gentzen introduction rules except that there are also introduction rules for the program combinators of sccs and ccs the compositional rules for restriction or hiding and parallel combinators arise out of a simple semantic strategy

bisimulation and divergence abstract behavioural preorders based on the idea of bisimulation but refining the notion of bisimulation equivalence and providing explicit treatments of the phenomenon of divergence in communicating systems are investigated particular study is made of these preorders in the context of milner s calculus of communicating systems the precongruence relations generated by the preorders are characterized and axiomatized on the classes of finite closed terms and sequential terms a verification technique based on the theory of the preorders is introduced and illustrated

analysis of the inexact uzawa algorithm for saddle point problems in this paper we consider the so called inexact uzawa algorithm for iteratively solving linear block saddle point problems such saddle point problems arise for example in finite element and finite difference discretizations of stokes equations the equations of elasticity and mixed finite element discretization of second order problems we consider both the linear and nonlinear variants of the inexact uzawa iteration we show that the linear method always converges as long as the preconditioners defining the algorithm are properly scaled bounds for the rate of convergence are provided in terms of the rate of convergence for the preconditioned uzawa algorithm and the reduction factor corresponding to the preconditioner for the upper left hand block in the case of nonlinear iteration the inexact uzawa algorithm is shown to converge provided that the nonlinear process approximating the inverse of the upper left hand block is of sufficient accuracy bounds for the nonlinear iteration are given in terms of this accuracy parameter and the rate of convergence of the preconditioned linear uzawa algorithm applications to the stokes equations and mixed finite element discretization of second order elliptic problems are discussed and finally the results of numerical experiments involving the algorithms are presented

new preconditioners for saddle point problems we present new preconditioners based on matrix splittings for the saddle point problems the spectral property of one of the preconditioned matrix is studied in detail numerical examples are used to illustrate the efficiency of the new preconditioners

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

calculi for synchrony and asynchrony abstract a calculus for distributed computation is studied based upon four combinators a central idea is an abelian group of actions which models the interfaces between components of a distributed computing agent using a notion of bisimulation congruence relations are defined over computing agents and thence an algebraic theory is derived the calculus models both synchronous and asynchronous computation in particular it is shown that the author s calculus of communicating systems 1980 which is an asynchronous model is derivable from the calculus presented here

turning sos rules into equations abstract many process algebras are defined by structural operational semantics sos indeed most such definitions are nicely structured and fit the gsos format of bloom et al j assoc comput mach to appear we give a procedure for converting any gsos language definition to a finite complete equational axiom system possibly with one infinitary induction principle which precisely characterizes strong bisimulation of processes

a format for semantic equivalence comparison this paper presents a new format for process algebras the extended tyft tyxt format which generalises the tyft tyxt format of groote and vaandrager the format differs from most previous formats in that the labels on transitions are treated as many sorted terms bisimulation is a congruence for all operators defined by extended transition system specifications in this format when one extended transition system specification is summed with another the resulting bisimulation can either identify more terms an abstracting extension up to bisimulation or fewer terms a refining extension up to bisimulation than the original bisimulation on the individual system the notions of abstracting extension and refining extension are defined and two theorems are presented giving conditions required for achieving each type of extension these results provide a way to compare different semantic equivalences defined for different process algebras finally an application of this theory to semantic equivalence comparison is given for a new result relating castellani s pomset equivalence and krishan s multiprocessor equivalence

two dimensional exponential fitting and applications to drift diffusion models a class of methods is introduced that generalizes the so called exponential fitting method to two dimensional problems and more specifically to equations of the type operatorname div underset raise0 3em hbox smash scriptscriptstyle nabla u u underset raise0 3em hbox smash scriptscriptstyle nabla psi f with psi given and underset raise0 3em hbox smash scriptscriptstyle nabla psi big in a part of the domain the basic idea is the following i write the equation as operatorname div e psi underset raise0 3em hbox smash scriptscriptstyle nabla rho f through the change of variables u rho e psi ii discretize the symmetric equation by means of a method that uses some kind of harmonic average for the coefficient e psi mixed hybrid etc iii write the discrete scheme in terms of the nodal values of u e psi rho this produces an m matrix

a generalization of the inexact parameterized uzawa methods for saddle point problems abstract for large sparse saddle point problems bai and wang recently studied a class of parameterized inexact uzawa methods see z z bai z q wang on paramaterized inexact uzawa methods for generalized saddle point problems linear algebra appl 428 2008 2900 2932 in this paper we generalize these methods and propose a class of generalized inexact parameterized iterative schemes for solving the saddle point problems we derive conditions for guaranteeing the convergence of these iterative methods with different choices of the parameter matrices the generalized iterative methods lead to a series of existing and new iterative methods including the classical uzawa method the inexact uzawa method the gsor method and the giaor method

termination deadlock and divergence in this paper a process algebra that incorporates explicit representations of successful termination deadlock and divergence is introduced and its semantic theory is analyzed both an operational and a denotational semantics for the language is given and it is shown that they agree the operational theory is based upon a suitable adaptation of the notion of bisimulation preorder the denotational semantics for the language is given in terms of the initial continuous algebra that satisfies a set of equations e ci e it is shown that ci e is fully abstract with respect to our choice of behavioral preorder several results of independent interest are obtained namely the finite approximability of the behavioral preorder and a partial completeness result for the set of equations e with respect to the preorder