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 topology on the primitive ideal space of transformation group c algebras and c c r transformation group c algebras if g 8 is a second countable transformation group and the stability groups are amenable then c g 8 is c c r if and only if the orbits are closed and the stability groups are c c r in addition partial results relating closed orbits to c c r algebras are obtained in the nonseparable case in several cases the topology of the primitive ideal space is calculated explicitly in particular if the stability groups are all contained in a fixed abelian subgroup h then the topology is computed in terms of h and the orbit structure provided c g 8 and c h 8 are eh regular these conditions are automatically met if g is abelian and g 8 is second countable

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

di domains as prime information systems abstract this paper introduces prime information systems prime information systems determine di domains and stable approximable mappings give stable functions and vice versa the notion of rigid embedding is captured by a subsystem relation under this relation prime information systems form a complete partial order cpo constructions like lifting sum product and function space are proposed which induce continuous functions on the cpo in this way recursive prime information systems can be defined using fixed point theory

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

on transformation group algebras with continuous trace in this paper we answer some questions posed by dana williams in 19 concerning the problem under which conditions the transformation group c algebra c g q of a locally compact transformation group g li has continuous trace one consequence will be for compact g that c g q2 has continuous trace if and only if the stabilizer map is continuous we also give a complete solution to the problem if g is discrete

pull backs of algebras and crossed products by certain diagonal actions let g be a locally compact group and p q t a principal g bundle if a is a c algebra with primitive ideal space t the pull back p a of a along p is the balanced tensor product co q c t a if 3 g aut a consists of c t module automorphisms and y g aut co q is the natural action then the automorphism group y 0x 3 of co q 0 a respects the balancing and induces the diagonal action p 3 of g on p a we discuss some examples of such actions and study the crossed product p a x p g we suggest a substitute d for the fixed point algebra prove p a x g is strongly morita equivalent to d and investigate the structure of d in various cases in particular we ask when d is strongly morita equivalent to a sometimes but by no means always and investigate the case where a has continuous trace let b be a c algebra and g a locally compact group acting on b as a strongly continuous automorphism group a our goal here is to study the crossed product c algebra b x g for two classes of diagonal actions for which the induced action of g on b is free the first class includes actions of the form y 0x3 on b co q 0 a where p q t is a principal g bundle y is the dual action of g on co q and 3 g aut a is an action of g on another c algebra a we also consider diagonal actions on algebras which are the pull backs of another algebra a along a principal bundle p q t if a is a c algebra with primitive ideal space t then the pull back p a is the balanced tensor product co q cb t a when 3 g aut a consists of c t module automorphisms the product action ty 0 3 preserves the balancing and the diagonal action p 3 is by definition the induced action on p a in general if f x y and q prima y are continuous then cb y acts on co x by composition with f and on a by composition with q and the daunshofmann theorem we can therefore define the pull back f a of a along f as the c algebraic tensor product co x cb y a the reason for the name is that when a is the algebra of sections of some c bundle e over y there is a natural isomorphism of f a onto the algebra of sections of the pull back f e in 1 we discuss this and other basic properties of pull backs and give some evidence to show they are likely to be of interest in particular we show that if g is abelian and a g aut a is locally unitary in the sense of 18 then the crossed product received by the editors october 20 1983 and in revised form february 15 1984 1980 mathematics subject classification primary 46l40 46l55

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

a new look at the fractional poisson problem via the logarithmic laplacian abstract we analyze the s dependence of solutions u s to the family of fractional poisson problems s u f in u 0 on r n in an open bounded set r n s 0 1 in the case where is of class c 2 and f c for some 0 we show that the map 0 1 l s u s is of class c 1 and we characterize the derivative s u s in terms of the logarithmic laplacian of f as a corollary we derive pointwise monotonicity properties of the solution map s u s under suitable assumptions on f and moreover we derive explicit bounds for the corresponding green operator on arbitrary bounded domains which are new even for the case s 1 i e for the local dirichlet problem u f in u 0 on

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

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

green function and martin kernel for higher order fractional laplacians in balls abstract we give the explicit formulas for the green function and the martin kernel for all integer and fractional powers of the laplacian s 1 in balls as consequences we deduce interior and boundary regularity estimates for solutions to linear problems and positivity preserving properties our proofs rely on a characterization of suitable s harmonic functions and on a differential recurrence equation

domain theory for concurrency a simple domain theory for concurrency is presented based on a categorical model of linear logic and associated comonads it highlights the role of linearity in concurrent computation two choices of comonad yield two expressive metalanguages for higher order processes both arising from canonical constructions in the model their denotational semantics are fully abstract with respect to contextual equivalence one language derives from an exponential of linear logic it supports a straightforward operational semantics with simple proofs of soundness and adequacy the other choice of comonad yields a model of affine linear logic and a process language with a tensor operation to be understood as a parallel composition of independent processes the domain theory can be generalised to presheaf models providing a more refined treatment of nondeterministic branching the article concludes with a discussion of a broader programme of research towards a fully fledged domain theory for concurrency

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

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

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

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

a model for distributed systems based on graph rewriting in our model a graph describes a net of processes communicating through ports and at the same time its computation history consisting of a partial ordering of events stand alone evolution of processes is specified by context free productions from productions and a basic synchronization mechanism a set of context sensitive rewriting rules that models the evolution of processes connected to the same ports can be derived a computation is a sequence of graphs obtained by successive rewritings the result of a finite computation is its last graph whereas the result of an infinite computation is the limit infinite graph defined through a completion technique based on metric spaces a result characterizes a concurrent computation since it abstracts from any particular interleaving of concurrent events while in the meantime providing information about termination partial or complete deadlocks and fairness not every result is acceptable however but only the computations that produce a result no longer rewritable are successful infinite successful computations are shown to coincide with weakly fair computations and a scheduler yielding all and only such computations is defined

projective topology on bifinite domains and applications we revisit extension results from continuous valuations to radon measures for bifinite domains in the framework of bifinite domains the prokhorov theorem existence of projective limits of radon measures appears as a natural tool and helps building a bridge between measure theory and domain theory the study we present also fills a gap in the literature concerning the coincidence between projective and lawson topology for bifinite domains motivated by probabilistic considerations we study the extension of measures in order to define borel measures on the space of maximal elements of a bifinite domain

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

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

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

a global compactness type result for palais smale sequences in fractional sobolev spaces abstract we extend the global compactness result by struwe 1984 to any fractional sobolev spaces h s for 0 s n 2 and r n a bounded domain with smooth boundary the proof is a simple direct consequence of the so called profile decomposition of gerard 1998

crossed products by actions which are locally unitary on the stabilisers let a g be a c dynamical system with g abelian and hausdorff we investigate the ideal structure of the crossed product a g under the hypothesis that the stabiliser subgroups for the action of g on vary continuously we discuss a new notion of locally trivial g space for such actions and dually actions which are locally unitarily implemented on the stabiliser groups our main result asserts that when is locally unitary in this sense and is a locally trivial g space a g is a locally trivial space

prime algebraicity a prime algebraic lattice can be characterised as isomorphic to the downwards closed subsets ordered by inclusion of its complete primes it is easily seen that the downwards closed subsets of a partial order form a completely distributive algebraic lattice when ordered by inclusion the converse also holds any completely distributive algebraic lattice is isomorphic to such a set of downwards closed subsets of a partial order the partial order can be recovered from the lattice as the order of the lattice restricted to its complete primes consequently prime algebraic lattices are precisely the completely distributive algebraic lattices the result extends to scott domains several consequences are explored briefly the representation of berry s di domains by event structures a simplified form of information systems for completely distributive scott domains and a simple domain theory for concurrency

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

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

an elementary proof that the biharmonic green function of an eccentric ellipse changes sign p r garabedian showed in 1951 that the green function for the biharmonic boundary value problem with vanishing dirichlet data changes sign in case the domain is a sufficiently eccentric ellipse this refuted a conjecture made by j hadamard in 1908 the proof of garabedian was based on kernel functions the present note gives an elementary proof

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

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

partially inner c dynamical systems a c dynamical system a g is called h inner if there is a strictly continuous unitary representation v from the closed subgroup h of g into the invariant multipliers of a such that t ad vt for every t in h assuming that g is a locally compact abelian group we show that in this case the crossed product g a is isomorphic to indh g g ha here g h a is the restricted or twisted crossed product studied by n dang ngoc and p green which naturally carries a dual action of the subgroup h of g and indh g refers to the induced c algebra obtained from this action

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

synthesis and equivalence of concurrent systems a framework for synthesis of synchronous concurrent systems with local memory is developed given an output specification of the system a cell action structure can be derived this structure can be mapped into a communication structure a model of the events in the target hardware with constraints on the communication possible between events giving a schedule for the cell actions communication structures are interesting in their own right and transformations defined on such can be used for showing equivalence between different computational networks as an example the equivalence between two specific communication structures is proved and it is shown that a fft algorithm can be implemented on them

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

rabin s theorem in the concurrency setting a conjecture rabin s theorem says that the monadic second order theory of the infinite binary tree is decidable this result has had a far reaching influence in the theory of branching time temporal logics a simple consequence of rabin s theorem is that for every finite state transition system the monadic second order theory of its computation tree is decidable concurrency theory strongly suggests that finite 1 safe petri nets or simply net systems are a natural generalization of the notion of a finite state transition system while labelled event structures arising as the unfoldings of net systems are the proper counterparts to the computation trees obtained by unwinding finite sequential transition systems it is easy to define the monadic second order theory of such event structures it turns out that unlike the sequential case not every net system i e its event structure unfolding has a decidable monadic second order theory this gives rise to the question which net systems admit a decidable monadic second order theory here we present a conjecture based on a property called grid freeness our conjecture is that a net system has a decidable monadic second order theory iff its event structure unfolding is grid free we show that it is decidable whether a net system has this property we also prove that the monadic second order theory of a net system is undecidable if its event structure unfolding is not grid free in addition we show that our conjecture can be effectively reduced to the sub class of free choice net systems finally we point out how the positive resolution of our conjecture will settle the decidability of a range of distributed controller synthesis problems

concurrent systems and inevitability abstract concurrent systems viewed as partially ordered sets of states are considered a property of system states is called inevitable if the system will eventually reach a state with this property this notion is discussed within the partial order framework

spectral results for mixed problems and fractional elliptic operators abstract one purpose of the paper is to show weyl type spectral asymptotic formulas for pseudodifferential operators p a of order 2a with type and factorization index a r when restricted to a compact set with smooth boundary the p a include fractional powers of the laplace operator and of variable coefficient strongly elliptic differential operators also the regularity of eigenfunctions is described the other purpose is to improve the knowledge of realizations a in l 2 of mixed problems for second order strongly elliptic symmetric differential operators a on a bounded smooth set r n here the boundary is partitioned smoothly into the dirichlet condition 0 u 0 is imposed on and a neumann or robin condition u 0 is imposed on it is shown that the dirichlet to neumann operator p is principally of type 1 2 with factorization index 1 2 relative to the above theory allows a detailed description of d a with singular elements outside of h 3 2 and leads to a spectral asymptotic formula for the krein resolvent difference a 1 a 1

crossed products byc0 x actions abstract suppose thatghas a representation grouph thatgab g g g is compactly generated and thatais ac algebra for which the complete regularization of prim a is a locally compact hausdorff spacex in a previous article we showed that there is a bijection z f between the collection of exterior equivalence classes of locally inner actions g aut a and the collection of principalgab bundlesz together with continuous functionsf x h2 g t in this paper we compute the crossed productsa gin terms of the dataz f andc h

d continuous causal nets a model of non sequential processes we propose a model of non sequential processes and study its properties the model is called d continuous causal nets ccn s and is based on a class of petri nets a causal net is essentially a partially ordered set of conditions and events which represents a fragment of the history of a concurrent system d continuity is a generalization of dedekind s definition of the continuity completeness of the reals which is applicable to both totally and partially ordered sets as also to both dense and discrete structures we develop a number of properties of our model and discuss why these might be useful properties for a non sequential process to have

an asychronous model for distributed systems french resume la modelisation des systemes distribues est un sujet qui a deja fait couler beaucoup d encre on presente ici un nouveau modele qui s inspire de la theorie des langages son originalite par rapport aux modeles developpes dans ce cadre est le refus de representer le parallelisme par l intercalage des actions concurrents les idees fortes reprises ici sont issues des langages csp et estelle il s agit principalement de l independance totale des processus en dehors des synchronisations ces dernieres etant des rendez vous un element du modele distribue sera essentiellement un vecteur d histories une pour chaque processus et un ensemble de synchronisations une fois le modele defini on introduit les notions de longueur concatenation ordre prefixe borne superieure et produit infini le modele distribue est ainsi muni de toutes les operations necessaires au developpement aise de semantiques enfin on montre que la partie finitaire du modele distribue est isomorphe au monoide partiellement commutatif mpc on donne alors les bases d une extension infinitaire du mpc

pointwise unitary automorphism groups abstract let a g be a separable c dynamical system in which g is abelian and a has continuous trace the action is said to pointwise unitary if for each in a there is a covariant representation u of the system a g it is shown that for pointwise unitary actions the spectrum a g of the crossed product is a locally compact hausdorff space and the restriction map res which takes u in a g to maps a g onto a furthermore res induces a homeomorphism of a g g onto a these results lead to a characterization of crossed products a g with continuous trace when a has continuous trace and g acts freely on a this happens precisely when the action of g on a is also proper this extends green s characterization of free and proper transformation groups finally it is shown that the results have applications to the problem of determining the dual topology on a locally compact group

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

a nice labelling for tree like event structures of degree 3 we address the problem of finding nice labellings for event structures of degree 3 we develop a minimum theory by which we prove that the index of an event structure of degree 3 is bounded by a linear function of the height the main theorem of the paper states that event structures of degree 3 whose causality order is a tree have a nice labelling with 3 colors we exemplify how to use this theorem to construct upper bounds for the index of other event structures of degree 3

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

contextual petri nets asymmetric event structures and processes we present an event structure semantics for contextual nets an extension of p t petri nets where transitions can check for the presence of tokens without consuming them read only operations a basic role is played by asymmetric event structures a generalization of winskel s prime event structures where symmetric conflict is replaced by a relation modelling asymmetric conflict or weak causality used to represent a new kind of dependency between events arising in contextual nets extending winskel s seminal work on safe nets the truly concurrent event based semantics of contextual nets is given at categorical level via a chain of coreflections leading from the category sw cn of semi weighted contextual nets to the category dom of finitary prime algebraic domains first an unfolding construction generates from a contextual net a corresponding occurrence contextual net from where an asymmetric event structure is extracted then the configurations of the asymmetric event structure endowed with a suitable order are shown to form a finitary prime algebraic domain we also investigate the relation between the proposed unfolding semantics and several deterministic process semantics for contextual nets in the literature in particular the domain obtained via the unfolding is characterized as the collection of the deterministic processes of the net endowed with a kind of prefix ordering 2001 elsevier science

true concurrency probabilistic models markov nets and a law of large numbers we introduce the model of markov nets a probabilistic extension of safe petri nets under the true concurrency semantics this means that traces not firing sequences are given a probability this model builds upon our previous work on probabilistic event structures we use the notion of a branching cell for event structures and show that the latter provides an adequate conception of local state for nets we prove a law of large numbers lln for markov nets which constitutes the main contribution of the paper this lln allows for the characterization in a quantitative way of the asymptotic behavior of markov nets

transformation group c algebras with continuous trace we obtain several results characterizing when transformation group c algebras have continuous trace these results can be stated most succinctly when g l is second countable and the stability groups are contained in a fixed abelian subgroup in this case c g q has continuous trace if and only if the stability groups vary continuously on r and compact subsets of q are wandering in an appropriate sense in general we must assume that the stability groups vary continuously and if g j is not second countable that the natural maps of g s onto g x are homeomorphisms for each x then c g 0 has continuous trace if and only if compact subsets of 0 are wandering and an additionai c algebra constructed from the stability groups and 0 has continuous trace

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

model checking games for fixpoint logics with partial order models in this paper we introduce model checking games that allow local second order power on sets of independent transitions in the underlying partial order models where the games are played since the interleaving semantics of such models is not considered some problems that may arise when using interleaving representations are avoided and new decidability results for partial order models of concurrency are achieved the games are shown to be sound and complete and therefore determined while in the interleaving case they coincide with the local model checking games for the m calculus in a partial order setting they verify properties of a number of fixpoint modal logics that can specify in concurrent systems with partial order semantics several properties not expressible with the m calculus the games underpin a novel decision procedure for model checking all temporal properties of a class of infinite and regular event structures thus improving in terms of temporal expressive power previous results in the literature

on the spectrum of two different fractional operators in this paper we deal with two non local operators that are both well known and widely studied in the literature in connection with elliptic problems of fractional type more precisely for a fixed s 0 1 we consider the integral definition of the fractional laplacian given by where c n s is a positive normalizing constant and another fractional operator obtained via a spectral definition that is where e i i are the eigenfunctions and the eigenvalues of the laplace operator in with homogeneous dirichlet boundary data while a i represents the projection of u on the direction e i the aim of this paper is to compare these two operators with particular reference to their spectrum in order to emphasize their differences

a trace semantics for petri nets a generalization of the notion of trace is proposed this enables us to associate with each petri net a single behavioural object namely a poset of generalized traces a characterization is given of the trace languages defined by petri nets we show that the general event structures of winskel and the stable event structures can also be characterized in terms of our trace languages one consequence is that in this framework stable event structures general event structures and petri nets constitute a strictly ascending chain in terms of expressive power

strength of convergence in non free transformation groups let g x be a transformation group where the group g does not necessarily act freely on the space x we investigate the extent to which the action of g may fail to be proper stability subgroups are used to define new notions of strength of convergence in the orbit space and of measure accumulation along orbits by using the representation theory of the associated crossed product c algebra we show that these notions are equivalent under certain conditions

symmetry of minimizers for some nonlocal variational problems abstract we present a new approach to study the symmetry of minimizers for a large class of nonlocal variational problems this approach which generalizes the reflection method is based on the existence of some integral identities we study the identities that lead to symmetry results the functionals that can be considered and the function spaces that can be used then we use our method to prove the symmetry of minimizers for a class of variational problems involving the fractional powers of laplacian for the generalized choquard functional and for the standing waves of the davey stewartson equation

petr nets algebras morphisms and compositionality abstract it is shown how a category of petri nets can be viewed as a subcategory of two sorted algebras over multisets this casts petri nets in a familiar framework and provides a useful idea of morphism on nets different from the conventional definition the morphisms here respect the behaviour of nets the categorical constructions which result provide a useful way to synthesise nets and reason about nets in terms of their components for example various forms of parallel composition of petri nets arise naturally from the product in the category this abstract setting makes plain a useful functor from the category of petri nets to a category of spaces of invariants and provides insight into the generalisations of the basic definition of petri nets for instance the coloured and higher level nets of kurt jensen arise through a simple modification of the sorts of the algebras underlying nets further it provides a smooth formal relation with other models of concurrency such as milner s calculus of communicating systems ccs and hoare s communicating sequential processes csp though this is only indicated in this paper

stable trace automata vs full trace automata trace automata provide a well studied model for systems with concurrent behavior which is usually given by associated domains of finite or infinite computation systems several authors in the literature have characterized order theoretically these domains which are typically particular scott domains in most of these investigations the question remain open when such a domain can be obtained from some finite automaton in this paper it is shown that finite stable trace automata and finite full trace automata give rise to the same class of coherent di domains the proof of this result involves combinatorial means from graph theory colorings and ramsey s theorem

regularity of the obstacle problem for a fractional power of the laplace operator given a function and s 0 1 we will study the solutions of the following obstacle problem u in r n s u 0i nr n s u x 0 for those x such that u x x lim x u x 0 we show that when is c 1 s or smoother the solution u is in the space c 1 for every s in the case where the contact set u is convex we prove the optimal regularity result u c 1 s when is only c 1 for a s we prove that our solution u is c 1 for every c 2006 wiley periodicals inc

fractional laplacians on domains a development of hormander s theory of μ transmission pseudodifferential operators abstract let p be a classical pseudodifferential operator of order m c on an n dimensional c manifold 1 for the truncation p to a smooth subset there is a well known theory of boundary value problems when p has the transmission property preserves c and is of integer order the calculus of boutet de monvel many interesting operators such as for example complex powers of the laplacian with z are not covered they have instead the transmission property defined in hormander s books mapping x n c into c in an unpublished lecture note from 1965 hormander described an l 2 solvability theory for transmission operators departing from vishik and eskin s results we here develop the theory in l p sobolev spaces 1 p in a modern setting it leads to not only fredholm solvability statements but also regularity results in full scales of sobolev spaces s the solution spaces have a singularity at the boundary that we describe in detail we moreover obtain results in holder spaces which radically improve recent regularity results for fractional laplacians

a logic for true concurrency we propose a logic for true concurrency whose formulae predicate about events in computations and their causal dependencies the induced logical equivalence is hereditary history preserving bisimilarity and fragments of the logic can be identified which correspond to other true concurrent behavioural equivalences in the literature step pomset and history preserving bisimilarity standard hennessy milner logic and thus interleaving bisimilarity is also recovered as a fragment we also propose an extension of the logic with fixpoint operators thus allowing to describe causal and concurrency properties of infinite computations this work contributes to a rational presentation of the true concurrent spectrum and to a deeper understanding of the relations between the involved behavioural equivalences

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

membership problems for regular and context free trace languages abstract trace languages have been introduced in order to describe the behaviour of concurrent systems in the same way as usual formal languages do for sequential system they can be defined as subsets of a free partially commutative monoid and a theory of trace languages can be developed generalizing the usual formal languages theory in this paper the time complexity of membership problems for regular and context free trace languages is investigated it is proved that the membership problem for context free trace languages can be solved in time o bm n where is the dimension of the greatest clique of the concurrency relation c and bm n is the time required for multiplying two arbitrary n n boolean matrices for regular trace languages our method gives an algorithm which requires o n time finally the uniform membership problem is shown to be np complete

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

neumann conditions for the higher order s fractional laplacian δ su with s 1 abstract in this paper we study a variational neumann problem for the higher order fractional laplacian s s 1 in the process we introduce some nonlocal neumann boundary conditions that appear in a natural way from a gauss like integration formula

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

building continuous webbed models for system f we present here a large family of concrete models for girard and reynolds polymorphism system f in a noncategorical setting the family generalizes the construction of the model of barbanera and berardi tech report university of turin 1997 hence it contains complete models for f a complete model for system f preprint june 1998 and we conjecture that it contains models which are complete for f it also contains simpler models the simplest of them e2 being a second order variant of the engeler plotkin model e all the models here belong to the continuous semantics and have underlying prime algebraic domains all have the maximum number of polymorphic maps the class contains models which can be viewed as two intertwined compatible webbed models of untyped calculus in the sense of berline from computations to foundations the calculus and its webbed models revised version theoret comput sci 86 pp to appear but it is much larger than this finally many of its models might he read as two intertwined strict intersection type systems

functorial models for petri nets we show that although the algebraic semantics of place transition petri nets under the collective token philosophy can be fully explained in terms of strictly symmetric monoidal categories the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality we introduce the notion of pre nets to overcome this obtaining a fully satisfactory categorical treatment where the operational semantics of nets yields an adjunction this allows us to present a uniform logical description of net behaviors under both the collective and the individual token philosophies in terms of theories and theory morphisms in partial membership equational logic moreover since the universal property of adjunctions guarantees that colimit constructions on nets are preserved in our algebraic models the resulting semantic framework has good compositional properties

process versus unfolding semantics for place transition petri nets in the last few years the semantics of petri nets has been investigated in several different ways apart from the classical token game one can model the behaviour of petri nets via non sequential processes via unfolding constructions which provide formal relationships between nets and domains and via algebraic models which view petri nets as essentially algebraic theories whose models are monoidal categories in this paper we show that these three points of view can be reconciled in our formal development a relevant role is played by cdecocc a category of occurrence nets appropriately decorated to take into account the history of tokens the structure of decorated occurrence nets at the same time provides natural unfoldings for place transition pt nets and suggests a new notion of processes the decorated processes which induce on petri nets the same semantics as that of unfolding in addition we prove that the decorated processes of a net can be axiomatized as the arrows of a symmetric monoidal category which therefore provides the aforesaid unification

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