event structures and trace monoids event structures are a poset based model for describing the behaviour of distributed systems they give rise to a well understood class of scott domains event structures are also related to petri nets in a fundamental way trace monoids are a string based formalism for describing the behaviour of distributed systems they have an independent theory rooted in the theory of formal languages here we obtain a representation of trace monoids in terms of a subclass of labelled event structures

the poset of infinitary traces gastin p and b rozoy the poset of infinitary traces theoretical computer science 120 1993 101 121 partially commutative monoids also called trace monoids are among the most studied formalisms to describe the behaviour of distributed systems in order to model systems which never stop we have to consider an extension of traces namely infinite traces finite trace monoids are strongly related to partial order sets posets domains and went structures which are other models to describe the behaviour of distributed systems the aim of this paper is to establish similar connexions between infinite trace monoids posets and event structures we prove that the set of finite and infinite traces with the prefix order is a scott domain and a coherently complete prime algebraic poset moreover we establish a representation theorem between the class of jirtite and infinite trace posets and a subclass of labelled prime event structures

musings around the geometry of interaction and coherence we introduce the danos regnier category dr m of a linear inverse monoid m as a categorical description of geometries of interaction goi inspired from the weight algebra the natural setting for goi is that of a so called weakly cantorian linear inverse monoid in which case dr m is a kind of symmetrized version of the classical abramsky haghverdi scott construction of a weak linear category from a goi situation it is well known that goi is perfectly suited to describe the multiplicative fragment of linear logic and indeed dr m will be a autonomous category in this case it is also well known that the categorical interpretation of the other linear connectives conflicts with goi interpretations we make this precise and show that dr m has no terminal object no cartesian product of any two objects and no exponential whatever m is unless m is trivial however a form of coherence completion of dr m a la hu joyal which for additives resembles a layered approach a la hughes van glabbeek provides a model of full classical linear logic as soon as m is weakly cantorian one finally notes that girard s notion of coherence is pervasive and instrumental in every aspect of this work

coupled mode equations and gap solitons in higher dimensions abstract we study wave packets in nonlinear periodic media in arbitrary d spatial dimension modeled by the cubic gross pitaevskii equation in the asymptotic setting of small and broad wave packets with n n carrier bloch waves the effective equations for the envelopes are first order coupled mode equations cmes we provide a rigorous justification of the effective equations the estimate of the asymptotic error is carried out in an l 1 norm in the bloch variables this translates to a supremum norm estimate in the physical variables in order to investigate the existence of gap solitons of the d dimensional cmes we discuss spectral gaps of the cmes for n 4 and d 2 a family of time harmonic gap solitons is constructed formally asymptotically and numerically moving gap solitons have not been found for d 1 and for the considered values of n due to the absence of a spectral gap in the standard moving frame variables

well behaved flow event structures for parallel composition and action refinement flow event structures were introduced as a model for giving semantics to process algebras however it turned out that certain restrictions have to be made to make them suitable for this purpose in this paper we investigate subclasses of flow event structures which are both suited for the process algebraic composition operators and for action refinement as a means of regarding processes on different levels of abstraction first suitable subclasses are characterised then two specific subclasses are proposed the larger class generalises the one from castellani and zhang theoret comput sci 179 1997 203 215 which is not suitable for action refinement the smaller one is still sufficiently expressive for dealing with all standard process algebras and action refinement

the non sequential behaviour of petri nets the idea of representing non sequential processes as partially ordered sets occurrence nets is applied to place transition nets petri nets based on the well known notion of process for condition event systems for occurrence nets some theorems relating k density cut finiteness and discreteness are proved with these theorems the result that a place transition net is bounded if and only if its processes are k dense is obtained

series parallel languages and the bounded width property abstract in order to model concurrency we extend automata theory from the usual languages of words to sets of labelled series parallel posets or sp languages we use the algebraic properties of the set of series parallel posets to investigate the notion of recognizability based on finite index congruences and a notion of regularity based on a new class of branching automata the main results of the paper concern the sp languages having bounded width we show that such languages are recognizable if and only if they are regular in addition the regular bounded width sp languages are exactly those which can be described by series rational expressions that is expressions using the letters the operations of sequential and parallel product and sequential iterations we also give a strictly algebraic characterization of the bounded width property in terms of depth nilpotent series parallel algebras

a partial ordering semantics for ccs a new operational semantics for pure ccs is proposed that considers the parallel operator as a first class one and permits a description of the calculus in terms of partial orderings the new semantics also for unguarded agents is given in the sos style via the partial ordering derivation relation ccs agents are decomposed into sets of sequential subagents the new derivations relate sets of subagents and describe their actions and the casual dependencies among them the computations obtained by composing partial ordering derivations are observed either as interleaving or partial orderings of events interleavings coincide with milner s many step derivations and linearizations of partial orderings are all and only interleavings abstract semantics are obtained by introducing two relations of observational equivalence and congruence that preserve concurrency these relations are finer than milner s in that they distinguish interleaving of sequential nondeterministic agents from their concurrent execution

quasi prime algebraic domains abstract the purpose of this paper is to introduce a new class of domains called quasi prime algebraic domains we show that this class is a good candidate for the purpose of denotational semantics of programming languages this is achieved by exhibiting many constructions usually needed for denotational semantics on quasi prime algebraic domains in the first part we motivate the notion of quasi primes and quasi prime algebraic domains by studying the effect of linear functions on domains that are not prime algebraic in the second part we study categories of quasi prime algebraic domains by representing them as irreducible information systems we introduce a symmetric monoidal closed category of quasi prime algebraic domains with quasi linear functions we show further that with the usual scott continuous functions as morphisms quasi prime algebraic domains are cartesian closed in the third part we show the existence of a saturated quasi prime algebraic domain and introduce a framework for solving domain equations in quasi prime algebraic domains it is then possible to give for example a model for the un typed lambda calculus with a reflexive quasi prime algebraic domain

intrinsic ultracontractivity and the dirichlet laplacian we show that if d x y 0 x 1 f x y 1 where f is negative upper semicontinuous and bounded below then the semigroup associated with the dirichlet laplacian on d is intrinsically ultracontractive analogs in higher dimensions are proved we construct domains of infinite area with this property

transition systems event structures and unfoldings a subclass of transition systems called elementary transition systems can be identified with the help of axioms based on a structural notion called regions elementary transition systems have been shown to be the transition system model of a basic system model of net theory called elementary net systems here we show that by smoothly strengthening the regional axioms for elementary transition systems one obtains a subclass called occurrence transition system we then prove that occurrence transition systems are the transition system model of yet another basic model of concurrency namely prime event structures we then propose an operation of unfolding elementary transition systems into occurrence transition systems we prove that it is correct in a strong categorical sense

determinism event structure isomorphism step sequence equivalence abstract a concurrent system s is called determinism if for all states s of s we have that whenever s can evolve from state s into states s and s by doing an action a it must be the case that s equals s it is well known that for deterministic concurrent systems most of the interleaved equivalences bisimulation failure trace equivalence coincide in this paper we prove in the setting of event structures that also most of the non interleaved equivalences coincide with each other on this domain in the last section of the paper we show that as a consequence of our result the causal structure of a deterministic concurrent system can be unravelled by observers who are capable of observing the beginning and termination of events

an approach to innocent strategies as graphs this paper proposes an approach for extending to graphs the close relation between proofs and innocent strategies we work in the setting of l nets introduced by faggian and maurel as a game model of concurrent interaction we show how l nets satisfying an additional condition which we call l s nets can be sequentialized into traditional tree like strategies conversely sequential strategies can be relaxed into more asynchronous ones we develop an algebra of constructors and destructors that serve to build and decompose graph strategies and to describe a class of minimally sequential graph strategies which can be seen as an abstract kind of multiplicative additive proof nets

ultracontractivity and the heat kernel for schrodinger operators and dirichlet laplacians abstract abstract connections between integral kernels of positivity preserving semigroups and suitable lp contractivity properties are established then these questions are studied for the semigroups generated by v and h the dirichlet laplacian for an open connected region as an application under a suitable hypothesis sobolev estimates are proved valid up to of the form x c 0 x h k 2 where 0 is the unique positive l2 eigenfunction of h

reversibility in the higher order π calculus the notion of reversible computation is attracting increasing interest because of its applications in diverse fields in particular the study of programming abstractions for reliable systems in this paper we continue the study undertaken by danos and krivine on reversible ccs by defining a reversible higher order calculus called rho we prove that reversibility in our calculus is causally consistent and that the causal information used to support reversibility in rho is consistent with the one used in the causal semantics of the calculus developed by boreale and sangiorgi finally we show that one can faithfully encode rho into a variant of higher order substantially improving on the result we obtained in the conference version of this paper

configuration structures event structures and petri nets in this paper the correspondence between safe petri nets and event structures due to nielsen plotkin and winskel is extended to arbitrary nets without self loops under the collective token interpretation to this end we propose a more general form of event structure matching the expressive power of such nets these new event structures and nets are connected by relating both notions with configuration structures which can be regarded as representations of either event structures or nets that capture their behaviour in terms of action occurrences and the causal relationships between them but abstract from any auxiliary structure a configuration structure can also be considered logically as a class of propositional models or equivalently as a propositional theory in disjunctive normal from converting this theory to conjunctive normal form is the key idea in the translation of such a structure into a net for a variety of classes of event structures we characterise the associated classes of configuration structures in terms of their closure properties as well as in terms of the axiomatisability of the associated propositional theories by formulae of simple prescribed forms and in terms of structural properties of the associated petri nets

context free event domains are recognizable the possibly non distributive event domains which arise from winskel s event structures with binary conflict are known to coincide with the domains of configurations of stark s trace automata we prove that whenever the transitive reduction of the order on finite elements in an event domain is a context free graph in the sense of muller and schupp the event domain may also be generated from a finite trace automaton where both the set of states and the concurrent alphabet are finite we show that the set of graph grammars which generate event domains is a recursive set we obtain altogether an effective procedure which decides from an unlabeled graph grammar whether it generates an event domain and which constructs in that case a finite trace automaton recognizing that event domain

split step methods for the solution of the nonlinear schro dinger equation a split step method is used to discretize the time variable for the numerical solution of the nonlinear schrodinger equation the space variable is discretized by means of a finite difference and a fourier method these methods are analyzed with respect to various physical properties represented in the nls in particular it is shown how a conservation law dispersion and instability are reflected in the numerical schemes analytical and numerical instabilities of wave train solutions are identified and conditions which avoid the latter are derived these results are demonstrated by numerical examples

using information systems to solve recursive domain equations abstract this paper aims to make the following main contribution to show how to use the concrete nature of scott s information systems to advantage in solving recursive domain equations the method is based on the substructure relation between information systems this essentially makes a complete partial order cpo of information systems standard domain constructions like function space can be made continous on this cpo so the solution of recursive domain equations reduces to the more familiar construction of forming the least fixed point of a continuous function

justification of the coupled mode asymptotics for localized wavepackets in the periodic nonlinear schrodinger equation abstract we consider wavepackets composed of two modulated carrier bloch waves with opposite group velocities in the one dimensional periodic nonlinear schrodinger gross pitaevskii equation these can be approximated by first order coupled mode equations cmes for the two slowly varying envelopes under a suitably selected periodic perturbation of the periodic structure the cmes possess a spectral gap of the corresponding spatial operator and allow families of exponentially localized solitary waves parametrized by velocity this leads to a family of approximate solitary waves in the periodic nonlinear schrodinger equation besides a formal derivation of the cmes a rigorous justification of the approximation and an error estimate in the supremum norm are provided several numerical tests corroborate the analysis

a decomposition theorem for domains a domain constructor that generalizes the product is defined it is shown that with this constructor exactly the prime algebraic coherent scott domains can be generated from two chains and boolean flat domains

perfectly matched layers in photonics computations 1d and 2d nonlinear coupled mode equations extending the general approach for first order hyperbolic systems developed in d appelo t hagstrom g kreiss perfectly matched layers for hyperbolic systems general formulation well posedness and stability siam j appl math 2006 to appear we construct pml equations for the mixed type system governing propagation of optical wave packets in both 1d and 2d bragg resonant photonic waveguides with a cubic nonlinearity i e the coupled mode equations we prove that in the linear case the layer equations are absorbing and perfectly matched we also prove they are stable for constant parameters a number of numerical experiments are performed to assess the layer s performance in both the linear and nonlinear regimes

unfolding semantics of graph transformation several attempts have been made of extending to graph grammars the unfolding semantics originally developed by winskel for safe petri nets but only partial results were obtained in this paper we fully extend winskel s approach to single pushout grammars providing them with a categorical concurrent semantics expressed as a coreflection between the category of semi weighted graph grammars and the category of prime algebraic domains which factorises through the category of occurrence grammars and the category of asymmetric event structures for general possibly nonsemi weighted single pushout grammars we define an analogous functorial concurrent semantics which however is not characterised as an adjunction similar results can be obtained for double pushout graph grammars under the assumptions that nodes are never deleted

non interleaving semantics for mobile processes abstract this paper studies causality in the calculus our notion of causality combines the dependencies given by the syntactic structure of processes with those originated by passing names our studies show that two transitions not causally related may however occur in a fixed ordering in any computation i e the calculus may implicitly express a precedence between actions the same partial order of transitions is associated with all the computations that are obtained by shuffling transitions that are concurrent i e related neither by causality nor by precedence other non interleaving semantics are investigated and compared the presentation takes advantage of a parametric definition of process behaviour given in sos style that permits us to take almost for free the interleaving theory and tools finally we extend our approach to higher order calculus enriched with a spawn operation

event structures and domains abstract in the theory of denotational semantics we study event structures which generalize kahn and plotkin s concrete data structures and which model computational processes with each event structure we associate canonically an event domain a particular algebraic complete partial order and conversely we derive a representation result for event domains for a particular class of event structures the canonical event structures we obtain that any two canonical event structures are isomorphic iff they have order isomorphic canonical domains

typed event structures and the linear π calculus we propose a typing system for the true concurrent model of event structures that guarantees the interesting behavioural properties known as conflict freeness and confusion freeness conflict freeness is the true concurrent version of the notion of confluence a system is confusion free if nondeterministic choices are localised and do not depend on the scheduling of independent components ours is the first typing system to control behaviour in a true concurrent model to demonstrate its applicability we show that typed event structures give a semantics of linearly typed version of the p calculi with internal mobility the semantics we provide is the first event structure semantics of the p calculus and generalises winskel s original event structure semantics of ccs

recursive domain equations for concrete data structures abstract in the theory of denotational semantics of programming languages we study event structures which combine features of scott s information systems and kahn and plotkin s concrete data structures and model computational processes we show that a simple approximation concept for event structures allows us to obtain straightforward solutions of recursive domain equations for event domains from this we derive a generalization of corresponding theorems of kahn and plotkin respectively berry and curien for concrete data structures and concrete domains

sharp constants related to the triangle inequality in lorentz spaces we study the lorentz spaces lp s r in the range 1 p s for which the standard functional f p s 0 t1 pf t s dt t 1 s is only a quasi norm we find the optimal constant in the triangle inequality for this quasi norm which leads us to consider the following decomposition norm f p s inf

petri nets event structures and domains part i abstract the general aim of this paper is to find a theory of concurrency combining the approaches of petri and scott and others in part i we introduce our formalisms to connect the abstract ideas of events and domains of information we show how casual nets induce certain kinds of domains where the information points are certain sets of events this allows translations between the languages of net theory and domain theory following the idea that events of causal nets are occurrences we generalise causal nets to occurrence nets by adding forwards conflict just as infinite flow charts unfold finite ones so transition nets can be unfolded into occurrence nets next we extend the above connections between nets and domains to these new nets event structures which are intermediate between nets and domains play an important part in all our work finally as an example of how concepts translate from one formalism to the other we show how petri s notion of confusion ties up with kahn and plotkin s concrete domains in part ii we shall continue the job of connecting up notions within net theory and the theory of domains in particular we shall examine the idea of states of computations

on the expressiveness of higher dimensional automata in this paper i compare the expressive power of several models of concurrency based on their ability to represent causal dependence to this end i translate these models in behaviour preserving ways into the model of higher dimensional automata hda which is the most expressive model under investigation in particular i propose four different translations of petri nets corresponding to the four different computational interpretations of nets found in the literature i also extend various equivalence relations for concurrent systems to hda these include the history preserving bisimulation which is the coarsest equivalence that fully respects branching time causality and their interplay as well as the st bisimulation a branching time respecting equivalence that takes causality into account to the extent that it is expressible by actions overlapping in time through their embeddings in hda it is now well defined whether members of different models of concurrency are equivalent

traveling solitary waves in the periodic nonlinear schrodinger equation with finite band potentials this paper studies asymptotics of moving gap solitons in nonlinear periodic structures of finite contrast deep grating within the one dimensional periodic nonlinear schrodinger equation pnls periodic structures described by a finite band potential feature transversal crossings of band functions in the linear band structure and a periodic perturbation of the potential yields new small gaps novel gap solitons with o 1 velocity despite the deep grating are presented in these gaps an approximation of gap solitons is given by slowly varying envelopes which satisfy a system of generalized coupled mode equations gcme and by bloch waves at the crossing point the eigenspace at the crossing point is two dimensional and it is necessary to select bloch waves belonging to the two band functions this is achieved by an optimization algorithm traveling solitary wave solutions of the gcme then result in nearly solitary wave solutions of the pnls moving at an o 1 velocity across the periodic structure

coupled mode equations and gap solitons for the 2d gross pitaevskii equation with a non separable periodic potential abstract gap solitons near a band edge of a spatially periodic nonlinear pde can be formally approximated by solutions of coupled mode equations cmes here we study this approximation for the case of the 2d periodic nonlinear schrodinger gross pitaevskii equation with a non separable potential of finite contrast we show that unlike in the case of separable potentials t dohnal d pelinovsky g schneider coupled mode equations and gap solitons in a two dimensional nonlinear elliptic problem with a separable periodic potential j nonlinear sci 19 2009 95 131 the cme derivation has to be carried out in bloch rather than physical coordinates using the lyapunov schmidt reduction we then give a rigorous justification of the cmes as an asymptotic model for reversible non degenerate gap solitons and provide h s estimates for this approximation the results are confirmed by numerical examples including some new families of cmes and gap solitons absent for separable potentials

an event structure semantics for general petri nets abstract in this paper we address the following question what type of event structures are suitable for representing the behaviour of general petri nets as a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called ul event structures we propose that ul event structures are appropriate for capturing the behaviour of general petri nets our answer is a partial one in that in the proposed event structure semantics auto concurrency is filtered out from the behaviour of petri nets it turns out that this limited event structure semantics for petri nets is nevertheless a non trivial and conservative extension of the prime event structure semantics of 1 safe petri nets provided in nielsen et al 1981 we also show that the strong relationship between prime event structures and 1 safe petri nets established in a categorical framework in winskel 1987 can be extended to the present setting provided we restrict our attention to the subclass of petri nets whose behaviours do not exhibit any auto concurrency finally we show that winskel s general and stable event structures can be smoothly related to local event structures and that similarly prime event structures can be related to ul event structures

p calculus internal mobility and agent passing calculi abstract the calculus is a process algebra which originates from ccs and permits a natural modelling of mobility i e dynamic reconfigurations of the process linkage using communication of names previous research has shown that the calculus has a much greater expressiveness than ccs but it also has a much more complex mathematical theory the primary goal of this work is to understand the reasons for this gap another goal is to compare the expressiveness of name passing calculi i e calculi like calculus where mobility is achieved via exchange of names and that of agent passing calculi i e calculi where mobility is achieved via exchange of agents we divide the mobility mechanisms of the calculus into internal and external mobility mechanisms the study of the subcalculus which only uses internal mobility called i suggests that internal mobility is responsible for much of the expressiveness of the calculus whereas external mobility is responsible for many of the semantic complications a pleasant property of i is the full symmetry between input and output constructs internal mobility is strongly related to agent passing mobility by imposing bounds on the order of the types of i and of the higher order calculus sangiorgi 1992 we define a hierarchy of name passing calculi based on internal mobility and one of agent passing calculi we show that there is an exact correspondence in terms of expressiveness between the two hierarchies

the dirichlet heat kernel in inner uniform domains local results compact domains and non symmetric forms abstract this paper provides sharp dirichlet heat kernel estimates in inner uniform domains including bounded inner uniform domains in the context of certain possibly non symmetric bilinear forms resembling dirichlet forms for instance the results apply to the dirichlet heat kernel associated with a uniformly elliptic divergence form operator with symmetric second order part and bounded measurable real coefficients in inner uniform domains in r n the results are applicable to any convex domain to the complement of any convex domain and to more exotic examples such as the interior and exterior of the snowflake

an exact correspondence between a typed pi calculus and polarised proof nets this paper presents an exact correspondence in typing and dynamics between polarised linear logic and a typed p calculus based on io typing the respective incremental constraints one on geometric structures of proof nets and one based on types precisely correspond to each other leading to the exact correspondence of the respective formalisms as they appear in olivier laurent 2003 27 for proof nets and kohei honda et al 2004 24 for the p calculus

global integrability of supertemperatures let d be a lipschitz domain or a john domain in mathbb r n with n ge 2 we study the global integrability of nonnegative supertemperatures on the cylinder d times 0 t we show that the integrability depends on the lower estimate of the green function for the dirichlet laplacian on d in particular if d is a c 1 domain then every nonnegative supertemperature on d times 0 t is l p integrable over d times 0 t prime for any 0 t prime t provided 0 p n 2 n 1 the bound n 2 n 1 is sharp

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

denotational semantics in the cpo and metric approach abstract we investigate the implications of choosing a cpo framework resp a complete metric space framework for defining denotational semantics of languages that allow for recursion iteration communication and concurrency we first establish a general framework for the cpo and the metric approach the existence and uniqueness of meaning functions is studied in the metric case the existence and uniqueness of a meaning function can be established under some reasonable assumptions in the cpo case we obtain the existence of a least meaning function from these theorems consistency results can be concluded in the second part we study the impact of the choice between cpo and metric for semantics based on event structures and for semantics based on pomset classes

metric semantics for true concurrent real time this paper investigates the use of a complete metric space framework for providing denotational semantics to a real time process algebra the study is carried out in a non interleaving setting and is based on a timed extension of langerak s bundle event structures a variant of winskel s event structures the distance function is based on the amount of time to which event structures do agree we show that this intuitive notion of distance is a pseudo metric but not a metric on the set of timed event structures a generalisation to equivalence classes of timed event structures in which we abstract from event names and non executable events events that can never appear is shown to be a complete ultra metric space we show that the resulting metric semantics is an abstraction of an existing cpo based denotational and a related operational semantics for the considered language

strong normalisation in the π calculus we introduce a typed calculus where strong normalisation is ensured by typability strong normalisation is a useful property in many computational contexts including distributed systems in spite of its simplicity our type discipline captures a wide class of converging name passing interactive behaviour the proof of strong normalisability combines methods from typed calculi and linear logic with process theoretic reasoning it is adaptable to systems involving state non determinism polymorphism control and other extensions strong normalisation is shown to have significant consequences including finite axiomatisation of weak bisimilarity a fully abstract embedding of the simply typed calculus with products and sums and basic liveness in interaction strong normalisability has been extensively studied as a fundamental property in functional calculi term rewriting and logical systems this work is one of the first steps to extend theories and proof methods for strong normalisability to the context of name passing processes

true concurrency probabilistic models branching cells and distributed probabilities for event structures this paper is devoted to probabilistic models for concurrent systems under their true concurrency semantics here we address probabilistic event structures we consider a new class of event structures called locally finite that extend confusion free event structure in locally finite event structures maximal configurations can be tiled with branching cells branching cells are minimal and finite sub structures capturing the choices performed while scanning a maximal configuration the probabilistic event structures that we introduce have the property that concurrent processes are independent in the probabilistic sense

bisimulation and action refinement abstract for event structures with silent moves we consider several types of bisimulation that incorporate true concurrency to a varying degree and show how each can be lifted in a uniform way to a congruence with respect to action refinement we prove that we have constructed the coarsest congruences that respect interleaving pomset and history preserving bisimulation