an algebraic characterization of transition system equivalences abstract i castellani 1987 j comput system sci 34 210 235 has shown that observation equivalence of transition systems could be characterized by particular reductions systems are equivalent if and only if they can be reduced to the same form moreover every transition system has a minimal reduced form we extend these results to logical equivalence by an algebraic interpretation of temporal logics we characterize logical equivalence of transition systems by particular reductions saturating quasi homomorphisms or their power algebras of sets of states and paths and prove that every power algebra has a minimal reduced form we then offer alternative proofs for logical characterizations of observation equivalence in particular we apply our method to prove m hennessy and c stirling s 1984 lecture notes in comput sci vol 176 pp 301 311 springer verlag new york berlin result that future perfect logic characterizes observation equivalence of generalized transition systems i e systems whose infinite behaviours are restricted by arbitrary fairness constraints

approximating markov processes by averaging normally one thinks of probabilistic transition systems as taking an initial probability distribution over the state space into a new probability distribution representing the system after a transition we however take a dual view of markov processes as transformers of bounded measurable functions this is very much in the same spirit as a predicate transformer view which is dual to the state transformer view of transition systems we redevelop the theory of labelled markov processes from this viewpoint in particular we explore approximation theory we obtain three main results i it is possible to define bisimulation on general measure spaces and show that it is an equivalence relation the logical characterization of bisimulation can be done straightforwardly and generally ii a new and flexible approach to approximation based on averaging can be given this vastly generalizes and streamlines the idea of using conditional expectations to compute approximations iii we show that there is a minimal process bisimulation equivalent to a given process and this minimal process is obtained as the limit of the finite approximants

model categories of diagram spectra working in the category mathcal t of based spaces we give the basic theory of diagram spaces and diagram spectra these are functors mathcal d longrightarrow mathcal t for a suitable small topological category mathcal d when mathcal d is symmetric monoidal there is a smash product that gives the category of mathcal d spaces a symmetric monoidal structure examples include begin enumerate item prespectra as defined classically item symmetric spectra as defined by jeff smith item orthogonal spectra a coordinate free analogue of symmetric spectra with symmetric groups replaced by orthogonal groups in the domain category item gamma spaces as defined by graeme segal item mathcal w spaces an analogue of gamma spaces with finite sets replaced by finite cw complexes in the domain category end enumerate we construct and compare model structures on these categories with the caveat that gamma spaces are always connective these categories and their simplicial analogues are quillen equivalent and their associated homotopy categories are equivalent to the classical stable homotopy category monoids in these categories are strict ring spectra often the subcategories of ring spectra module spectra over a ring spectrum and commutative ring spectra are also model categories when this holds the respective categories of ring and module spectra are quillen equivalent and thus have equivalent homotopy categories this allows interchangeable use of these categories in applications 2000 mathematics subject classification primary 55p42 secondary 18a25 18e30 55u35

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

fixed set systems of equivariant infinite loop spaces we develop machinery enabling us to show that suitable g spaces including the equivariant version of bf are equivariant infinite loop spaces this involves a recognition principle for systems of spaces which behave for mally like the system of fixed sets of a g space that is we give a necessary and sufficient condition for such a system to be equivalent to the fixed set system of an equivariant infinite loop space the advantage of using the language of fixed set systems is that one can frequently replace the system of fixed sets of an ac tual g space by an equivalent formal system which is considerably simpler and which admits the requisite geometry necessary for delooping we also apply this machinery to construct equivariant eilenberg mac lane spaces corresponding to mackey functors

logical vs behavioural specifications abstract there are two fundamentally different approaches for specifying and verifying properties of systems the logical approach makes use of specifications given as formulae of temporal or modal logics and relies on efficient model checking algorithms the behavioural approach exploits various equivalence or refinement checking methods provided the specifications are given in the same formalism as implementations in this paper we provide translations between the logical formalism of calculus and the behavioural formalism of disjunctive modal transition systems the translations preserve structural properties of the input specification and allow us to perform logical operations on the behavioural specifications as well as behavioural compositions on logical formulae the unification of both approaches provides additional methods for component based stepwise design

ccs with priority choice abstract this paper investigates an extension of milner s ccs with a priority choice operator called prisum this operator is very similar to the prialt construct of occam the new binary prisum operator only allows execution of its second component in the case where the environment is not ready to allow the first component to proceed this dependency on the set of actions the environment is ready to perform goes beyond that encountered in traditional ccs its expression leads to a novel operational semantics in which transitions carry ready sets of the environment as well as the normal action symbols from ccs a notion of strong bisimulation is defined on agents with priority via this semantics it is a congruence and satisfies new equational laws including a new expansion law which are shown to be complete for finite agents with prisum the laws are conservative over agents of traditional ccs

equivariant operads string topology and tate cohomology from an operad fancyscript c with an action of a group g we construct new operads using the homotopy fixed point and orbit spectra these new operads are shown to be equivalent when the generalized g tate cohomology of fancyscript c is trivial applying this theory to the little disk operad fancyscript c 2 which is an s 1 operad we obtain variations on getzler s gravity operad which we show governs the chas sullivan string bracket

probabilistic bisimilarity as testing equivalence abstract larsen and skou initiated the study of probabilistic bisimilarity and its characterisation in terms of tests later on van breugel et al showed that for labelled markov processes with continuous state spaces probabilistic bisimilarity nicely coincides with a simple notion of testing equivalence their proof employs advanced machinery from topology in the discrete case of finite state reactive probabilistic processes we prove that coincidence result with an elementary and more accessible proof

integral deligne cohomology for real varieties we develop an integral version of deligne cohomology for smooth proper real varieties for this purpose the role played by singular cohomology in the complex case has to be replaced by the ordinary bigraded gal mathbb c mathbb r equivariant cohomology of lewis et al bull am math soc n s 4 2 208 212 1981 the equivariant counterpart of singular cohomology the theory is aimed at giving more precise information about the 2 primary components of regulators we establish basic properties and give a geometric interpretation for the groups in dimension 2 in weights 1 and 2

the structure of some equivariant thom spectra we show that the equivariant thom spectra moz2 and moz2 do not split as wedges of equivariant eilenberg mac lane spectra as they do nonequivariantly this is done by finding two stage postnikov towers giving these spectra and determining the nontrivial k invariants we also consider the question in what sense is the spectrum moz2 representing unoriented bordism unique

compositionality of hennessy milner logic by structural operational semantics this paper presents a method for the decomposition of hml formulas it can be used to decide whether a process algebra term satisfies a hml formula by checking whether subterms satisfy certain formulas obtained by decomposing the original formula the method uses the structural operational semantics of the process algebra the main contribution of this paper is the extension of an earlier decomposition method for the de simone format from the ph d thesis of larsen in 1986 to more general formats

bisimulation on speed worst case efficiency this paper introduces a novel bi simulation based faster than preorder which relates asynchronous processes where the relative speeds of system components are indeterminate with respect to their worst case timing behavior the study is conducted for a conservative extension of the process algebra ccs called tacs which permits the specification of upper time bounds on action occurrences tacs complements work in plain process algebras which compares asynchronous processes with respect to their functional reactive behavior only and in timed process algebras which focus on analyzing synchronous processes the most unusual contribution is in showing that the proposed faster than preorder coincides with several other preorders two of which consider the absolute times at which actions occur in system runs the paper also develops the semantic theory of tacs by studying congruence properties equational laws and abstractions from internal actions two examples one dealing with mail delivery and one relating two implementations of a simple storage system testify to the practical utility of the new theory

distribution based behavioral distance for nondeterministic fuzzy transition systems modal logics and behavioral equivalences play an important role in the specification and verification of concurrent systems in this paper we first present a new notion of bisimulation for nondeterministic fuzzy transition systems which is distribution based and coarser than state based bisimulation appeared in the literature then we define a distribution based bisimilarity metric as the least fixed point of a suitable monotonic function on a complete lattice which is a behavioral distance and is a more robust way of formalizing behavioral similarity between states than bisimulations we also propose an on the fly algorithm for computing the bisimilarity metric moreover we present a fuzzy modal logic and provide a sound and complete characterization of the bisimilarity metric interestingly this characterization holds for a class of fuzzy modal logics in addition we show the nonexpansiveness of a typical parallel composition operator with respect to the bisimilarity metric which makes compositional verification possible

ccs with hennessy s merge has no finite equational axiomatization this paper confirms a conjecture of bergstra and klop s from 1984 by establishing that the process algebra obtained by adding an auxiliary operator proposed by hennessy in 1981 to the recursion free fragment of milner s calculus of communicating systems is not finitely based modulo bisimulation equivalence thus hennessy s merge cannot replace the left merge and communication merge operators proposed by bergstra and klop at least if a finite axiomatization of parallel composition modulo bisimulation equivalence is desired

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

pin 2 equivariant seiberg witten floer homology and the triangulation conjecture we define pin 2 equivariant seiberg witten floer homology for rational homology 3 spheres equipped with a spin structure the analogue of froyshov s correction term in this setting is an integer valued invariant of homology cobordism whose mod 2 reduction is the rokhlin invariant as an application we show that there are no homology 3 spheres y of rokhlin invariant one such that y y bounds an acyclic smooth 4 manifold by previous work of galewski stern and matumoto this implies the existence of non triangulable high dimensional manifolds

nested semantics over finite trees are equationally hard this paper studies nested simulation and nested trace semantics over the language bccsp a basic formalism to express finite process behaviour it is shown that none of these semantics affords finite in equational axiomatizations over bccsp in particular for each of the nested semantics studied in this paper the collection of sound closed in equations over a singleton action set is not finitely based

statistical mechanical theory of coarsening of spherical droplets abstract a new statistical mechanical theory of diffusion controlled droplet coarsening is presented with the aid of a scaling expansion method a spatial graining is carried out in a manner consistent with an expansion in droplet volume fraction to obtain kinetic equations for a single distribution function of droplets it is shown that there two characteristic stages of coarsening depending on their space time scales an intermediate stage and a late stage in both stages new kinetic equations are systematically derived to order these equations have two terms at order a collisionless drift term and a collision term the collision term is shown to be different from the conventional encounter integral discussed by lifshitz and slyozov since the former is of order and describes distant soft collisions while the latter is of order and describes close hard collisions it is shown in both stages that the mean droplet radius increases as the cube root of the time t 1 3 a scaling behavior of the distribution function is also found in both stages in particular in the late stage this scaling behavior is shown to coincide with that obtained by lifshitz and slysov in the limit o it is also pointed out that a naive expansion in powers of breaks down due to the long range nature of interactions among droplets through diffusions fluctuations around the kinetic equations are also explicitly explored they are shown to be nonthermal fluctuations generated by the soft collision process and to be small especially in the late stage they are shown to obey a linear gaussian markov process satisfying a fluctuation dissipation relation of the second kind

hochschild homology criteria for trivial algebra structures we prove two similar results by quite different methods the first one deals with augmented artinian algebras over a field we characterize the trivial algebra structure on the augmentation ideal in terms of the maximality of the dimensions of the hochschild homology or cyclic homology groups for the second result let x be a 1 connected finite cw complex we characterize the trivial algebra structure on the cohomology algebra of x with coefficients in a fixed field in terms of the maximality of the betti numbers of the free loop space

equivariant vector fields on spheres we address the following question if g is a compact lie group and s m is the unit sphere of an r g module m then how many orthonormal g invariant vector fields can be found on s m we call this number the g field number of m under reasonable hypotheses on m we reduce this question to determining when the difference of two g vector bundles vanishes in a certain subquotient of the kog theory of a real projective space in this general setting we solve the problem for 2 groups for odd order groups and for abelian groups if m also has enough orbit types for example all of them then we solve the problem for arbitrary finite groups we also show that under mild hypotheses on m the g field number depends only on the dimensions of the fixed point sets of m acknowledgements i wish to take this opportunity to express my heartfelt thanks to peter may for his constant guidance and encouragement and for his careful reading of this paper to jim mcclure for many helpful ideas and enlightening conversations and to mel rothenberg for being a one man audience and for all his suggestions and improvements introduction in 1940 hopf 14 and later eckmann 9 observed that a theorem of hurwitz and radon could be used to construct orthonormal vector fields on spheres they showed that if n 2a 1 2c 4d where 0 c s 3 then p n 1 orthonormal vector fields can be constructed on sn where p n 8d 2c is the nth hurwitz radon number twenty years later adams 1 showed that this was best possible there do not exist p n orthonormal vector fields on sn the purpose of this paper is to address the following question if g is a compact lie group and s m is the unit sphere of a real g module m then how many orthonormal g invariant vector fields or g fields can be found on s m we shall call this number the g field number of m previous work has been done on this problem by becker 6 he deals with the case in which g is finite and acts freely on s m he shows that under mild hypotheses the g field number of m depends only on g and the real dimension of m he also shows that it coincides with the e field number of m where 2 is any 2 sylow subgroup of g received by the editors march 22 1982 1980 mathematics subject classification primary 57r25 57s25 secondary 55r25 55r50 the author was tragically killed in an automobile accident on december 23 1981 the editors thank peter may and jim becker for their help in bringing this paper to publication requests for reprints should be addressed to peter may university of chicago 1983 american mathematical society 0002 9947 82 00001355 10 25

divide and congruence ii from decomposition of modal formulas to preservation of delay and weak bisimilarity abstract earlier we presented a method to decompose modal formulas for processes with the internal action and congruence formats for branching and bisimilarity were derived on the basis of this decomposition method the idea is that a congruence format for a semantics must ensure that the formulas in the modal characterisation of this semantics are always decomposed into formulas that are again in this modal characterisation in this follow up paper the decomposition method is enhanced to deal with modal characterisations that contain a modality a to derive congruence formats for delay and weak bisimilarity

ccs expressions finite state processes and three problems of equivalence abstract we examine the computational complexity of testing finite state processes for equivalence in milner s calculus of communicating systems ccs the equivalence problems in ccs are presented as refinements of the familiar problem of testing whether two nondeterministic finite automata nfa are equivalent i e accept the same language three notions of equivalence proposed for ccs are investigated namely observational equivalence strong observational equivalence and failure equivalence we show that observational equivalence can be tested in polynomial time as defined in ccs observational equivalence is the limit of a sequence of successively finer equivalence relations k where 1 is nondeterministic finite automaton equivalence we prove that for each fixed k deciding k is pspace complete we show that strong observational equivalence can be decided in polynomial time by reducing it to generalized partitioning a new combinatorial problem of independent interest finally we demonstrate that testing for failure equivalence is pspace complete even for a very restricted type of process

three logics for branching bisimulation three temporal logics are introduced that induce on labeled transition systems the same identifications as branching bisimulation a behavioral equivalence that aims at ignoring invisible transitions while preserving the branching structure of systems the first logic is an extension of hennessy milner logic with an until operator the second one is another extension of hennessy milner logic which exploits the power of backward modalities the third logic is ctl without the next time operator a relevant side effect of the last characterization is that it sets a bridge between the state and action based approaches to the semantics of concurrent systems

deciding observational congruence of finite state ccs expressions by rewriting abstract we propose a term rewriting approach to verify observational congruence between guarded recursive finite state ccs expressions starting from the complete axiomatization of observational congruence for this subset of ccs a non terminating rewriting relation has been defined this rewriting relation is canonical over a subclass of infinite derivations structured fair derivations which compute all the normal forms the rewriting relation is shown to be complete with respect to the axiomatization by proving that every structured fair derivation computes a term that denotes an r normal process graph the existence of a finite representation for normal forms allows the definition of a rewriting strategy that in a finite number of rewriting steps decides observational congruence of guarded recursive finite state ccs expressions

multiplicativity of the idempotent splittings of the burnside ring and the g sphere spectrum abstract we provide a complete characterization of the equivariant commutative ring structures of all the factors in the idempotent splitting of the g equivariant sphere spectrum including their hill hopkins ravenel norms where g is any finite group our results describe explicitly how these structures depend on the subgroup lattice and conjugation in g algebraically our analysis characterizes the multiplicative transfers on the localization of the burnside ring of g at any idempotent element which is of independent interest to group theorists as an application we obtain an explicit description of the incomplete sets of norm functors which are present in the idempotent splitting of the equivariant stable homotopy category

equivariant cohomology and sheaves abstract ro g graded equivariant cohomology was originally defined by using equivariant spectra in this paper we construct a sheaf version of ro g graded equivariant cohomology theory by introducing a complex of presheaves we obtain an isomorphism theorem of two different cohomology theories we further apply the results to the study of real algebraic varieties

weak and strong fairness in ccs abstract we examine the issue of weak and strong fairness in the framework of milner s ccs our approach is operational we address the problem of giving sets of finite rules for generating all and only the admissible execution sequences when fairness is assumed we achieve our aims by defining two calculi one for weak and the other for strong fairness both calculi are extensions of standard ccs in neither case do we appeal to random assignment or to transformations a distinguishing feature of the weak fair calculus unlike standard approaches which appeal to random assignment is that it does not involve predictive choice

vector bundles over classifying spaces of compact lie groups the completion theorem of atiyah and segal as says that the complex k theory group k bg of the classifying space of any compact lie group g is isomorphic to r g the representation ring completed with respect to its augmentation ideal however the group k bg bg z bu does not directly contain information about vector bundles over the infinite dimensional complex bg itself the purpose of this paper is to compare the grothendieck group of vector bundles over bg which we denote k bg with both k bg and r g the main result is an algebraic description of k bg in terms of the representation rings of certain subgroups of g as one consequence we show that of the natural maps

a fully abstract denotational semantics for the calculus of higher order communicating systems abstract in this paper we study the calculus of higher order communicating systems chocs thomsen proc of popl 89 acm 1989 pp 143 154 inform comput 116 1 1995 38 57 in a denotational setting we present a construction of a denotational semantics for chocs which resides in a domain constructed using the standard constructions of separated sum cartesian product the plotkin power domain constructor and recursively defined domains we show under mild restrictions that the denotational semantics and the operational semantics of chocs are fully abstract we have previously proved using bisimulation arguments that processes as first class objects are powerful enough to simulate recursion however the proof is very long and tedious to demonstrate the power of the denotational approach we use it to obtain a very simple proof of the simulation of recursion result

priority and abstraction in process algebra more than 15 years ago cleaveland and hennessy proposed an extension of the process algebra ccs in which some actions may take priority over others the theory was equipped with a behavioral congruence based on strong bisimulation this article gives a full account of the challenges in and the solutions employed for defining a semantic theory of observation congruence for this process algebra a full abstraction result is presented whose proof relies on a novel approach based on successive approximations for identifying the largest congruence contained in an intuitive but naive equivalence prioritized observation congruence is also characterized equationally for the class of finite processes while its utility for system verification is demonstrated by an illustrative example

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

theory of interaction abstract theory of interaction aims to provide a foundational framework for computation and interaction it proposes four fundamental principles that characterize the common features of all models of computation and interaction these principles suffice to support a model independent treatment of the two most important relationships in computer science the equality between processes and the relative expressiveness between models based on the two relationships the theory of equality the theory of expressiveness and the theory of completeness are developed

divide and congruence from decomposition of modal formulas to preservation of branching and η bisimilarity we present a method for decomposing modal formulas for processes with the internal action t to decide whether a process algebra term satisfies a modal formula one can check whether its subterms satisfy formulas that are obtained by decomposing the original formula the decomposition uses the structural operational semantics that underlies the process algebra we use this decomposition method to derive congruence formats for two weak and rooted weak semantics branching and h bisimilarity

operadic multiplications in equivariant spectra norms and transfers we study homotopy coherent commutative multiplicative structures on equivariant spaces and spectra we define n operads equivariant generalizations of e operads algebras in equivariant spectra over an n operad model homotopically commutative equivariant ring spectra that only admit certain collections of hill hopkins ravenel norms determined by the operad analogously algebras in equivariant spaces over an n operad provide explicit constructions of certain transfers this characterization yields a conceptual explanation of the structure of equivariant infinite loop spaces to explain the relationship between norms transfers and n operads we discuss the general features of these operads linking their properties to families of finite sets with group actions and analyzing their behavior under norms and geometric fixed points a surprising consequence of our study is that in stark contract to the classical setting equivariantly the little disks and linear isometries operads for a general incomplete universe u need not determine the same algebras our work is motivated by the need to provide a framework to describe the flavors of commutativity seen in recent work of the second author and hopkins on localization of equivariant commutative ring spectra

when are prime formulae characteristic abstract in the setting of the modal logic that characterizes modal refinement over modal transition systems boudol and larsen showed that the formulae for which model checking can be reduced to preorder checking that is the characteristic formulae are exactly the consistent and prime ones this paper presents general sufficient conditions guaranteeing that characteristic formulae are exactly the consistent and prime ones it is shown that the given conditions apply to various behavioural relations in the literature in particular characteristic formulae are exactly the prime and consistent ones for all the semantics in van glabbeek s linear time branching time spectrum

quantales finite observations and strong bisimulation abstract it has often been claimed that bisimulation makes distinctions that cannot be observed in practice abramsky and vickers proposed an algebraic framework based on quantales for describing observations on concurrent processes without hidden transitions and used it in order to provide an observational explanation of several process equivalences ranging from hoare trace equivalence to ready simulation we follow their approach and argue that strong bisimulation can be explained in the same way at least in the case of image computable labelled transition systems

diffusion limited droplet coalescence abstract simulations of diffusion limited brownian droplet coalescence have been carried out in which the droplet diffusion coefficients are related to their sizes masses s by d s s for the case d d where d is the droplet dimensionality and d is the dimensionality of the substrate the exponents z and z describing the algebraic growth of the mean droplet size s and the decrease in the number of droplets n are given by z z 1 2 d with no logarithmic corrections for d 2 if d d then for d 2 the growth of s is given by s t ln t 1 1 and the decay of n is given by n t ln t 1 1 for d 2 there are no logarithmic corrections and z z d d d d 2 in all cases the time dependent cluster size distribution can be described in terms of the scaling form n s t s 2 f s s t where ns t is the number of droplets of size s at time t simple scaling arguments indicate that these values obtained for the exponents z and z describing the asymptotic t behavior from computer simulations are exact

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

the equivariant hurewicz map let g be a compact lie group y be a based g space and v be a g representation if v g y is the equivariant homotopy group of y in dimension v and h v g y fis the equivariant ordinary homology group of y with burnside ring coefficients in dimension v then there is an equivariant hurewicz map h v g y h v g y one should not expect this map to be an isomorphism since h v g y must be a module over the burnside ring but v g y need not be however here it is shown that under the obvious connectivity conditions on y this map induces an isomorphism between h v g y and an algebraically defined modification of v g y

completions and fibrations for topological monoids we show that for a certain class of topological monoids there is a homotopy equivalence between the homotopy theoretic group completion m of a monoid m in that class and the topologized grothendieck group m associated to m the class under study is broad enough to include the chow monoids effective cycles associated to a projective algebraic variety and also the infinite symmetric products of finite cw complexes we associate principal fibrations to the completions of pairs of monoids showing the existence of long exact sequences for the naive approach to lawson homology fri91 lf91 a another proof of the eilenberg steenrod axioms for the functors x sp x in the category of finite cw complexes dold thom theorem dt56 is obtained

vanishing theorems for real algebraic cycles we establish the analogue of the friedlander mazur conjecture for teh s reduced lawson homology groups of real varieties which says that the reduced lawson homology of a real quasi projective variety x vanishes in homological degrees larger than the dimension of x in all weights as an application we obtain a vanishing of homotopy groups of the mod 2 topological groups of averaged cycles and a characterization in a range of indices of dos santos real lawson homology as the homotopy groups of the topological group of averaged cycles we also establish an equivariant poincare duality between equivariant friedlander walker real morphic cohomology and dos santos real lawson homology we use this together with an equivariant extension of the mod 2 beilinson lichtenbaum conjecture to compute some real lawson homology groups in terms of bredon cohomology

hecke algebras and cohomotopical mackey functors in this paper we define the concept of the cohomotopical mackey functor which is more general than the usual cohomological mackey functor and show that hecke algebra techniques are applicable to cohomotopical mackey functors our theory is valid for any possibly infinite discrete group some applications to topology are also given

equivariant bundles and cohomology let g be a topological group a an abelian topological group on which g acts continuously and x a g space we define equivariant cohomol ogy groups of x with coefficients in a hlg x a for i 0 which generalize graeme segal s continuous cohomology of the topological group g with coeffi cients in a in particular we have h x a equivalence classes of principal g a bundles over x we show that when g is a compact lie group and a an abelian lie group we have for i 1 h x a hz eg xq x ta where ta is the sheaf of germs of sections of the bundle x x eg x a g x x eg g for i 1 and the trivial action of g on a this is a theorem of lashof may and segal

testing probabilistic equivalence through reinforcement learning checking if a given system implementation respects its specification is often done by proving that the two are equivalent the equivalence is chosen in particular for its computability and of course for its meaning that is for its adequacy with what is observable from the two systems implementation and specification trace equivalence is easily testable decidable from interaction but often considered too weak in contrast bisimulation is accepted as the canonical equivalence for interaction but it is not testable richer than an equivalence is a form of distance it is zero between equivalent systems and it provides an estimation of their difference if the systems are not equivalent our main contribution is to define such a distance in a context where 1 the two systems to be compared have a stochastic behavior 2 the model of one of them e g the implementation is unknown hence our only knowledge is obtained by interacting with it 3 consequently the target equivalence observed when distance is zero must be testable to overcome the problem that the model is unknown we use a reinforcement learning approach that provides powerful stochastic algorithms that only need to interact with the model our second main contribution is a new family of testable equivalences called k moment the weakest of them 1 moment equivalence is trace equivalence as k grows k moment equivalences become finer all remaining as well as their limit weaker than bisimulation we propose a framework to define and test a bigger class of testable equivalences test observation equivalences toes and we show how they can be made coarser or not by tuning some parameters

on the nonexistence of elements of kervaire invariant one we show that the kervaire invariant one elements j 2j 1 2s exist only for j 6 by browder s theorem this means that smooth framed manifolds of kervaire invariant one exist only in dimensions 2 6 14 30 62 and possibly 126 except for dimension 126 this resolves a longstanding problem in algebraic topology

studying equivalences of transition systems with algebraic tools abstract the aim of this paper is twofold on one side we will characterize observational equivalences simulation bisimulation in an algebraic framework on the other side we will deduce by this algebraic framework a new equivalence the skeleton equivalence which is an equivalence situated between trace equivalence and equality of languages in order to characterize simulation equivalence we will define a monad on the category of transition systems we introduce a category of algebras to characterize bisimulation this category turns out to be the stone dual of the category of transition systems moreover this category of algebras seems to be a natural framework to reason about bisimulation equivalence bisimulation corresponds to subalgebras isomorphisms and the minimal transition system in a bisimulation class corresponds to the minimal subalgebra of a given algebra eventually the notion of minimal subalgebra will roughly speaking be factorized as the boolean completion of the skeleton of an algebra so that the concept of skeleton equivalence naturally arises

bialgebraic methods and modal logic in structural operational semantics bialgebraic semantics invented a decade ago by turi and plotkin is an approach to formal reasoning about well behaved structural operational semantics sos an extension of algebraic and coalgebraic methods it abstracts from concrete notions of syntax and system behaviour thus treating various kinds of operational descriptions in a uniform fashion in this paper bialgebraic semantics is combined with a coalgebraic approach to modal logic in a novel general approach to proving the compositionality of process equivalences for languages defined by structural operational semantics to prove compositionality one provides a notion of behaviour for logical formulas and defines an sos like specification of modal operators which reflects the original sos specification of the language this approach can be used to define sos congruence formats as well as to prove compositionality for specific languages and equivalences

three partition refinement algorithms we present improved partition refinement algorithms for three problems lexicographic sorting relational coarsest partition and double lexical ordering our double lexical ordering algorithm uses a new efficient method for unmerging two sorted sets

the quantitative linear time branching time spectrum we present a distance agnostic approach to quantitative verification taking as input an unspecified distance on system traces or executions we develop a game based framework which allows us to define a spectrum of different interesting system distances corresponding to the given trace distance thus we extend the classic linear time branching time spectrum to a quantitative setting parametrized by trace distance we also prove a general transfer principle which allows us to transfer counterexamples from the qualitative to the quantitative setting showing that all system distances are mutually topologically inequivalent

stable maps into free g spaces in this paper we introduce a systematic method for calculating the group of stable equivariant maps x y g 3 18 into a g free space or spectrum y in fact the method applies without restriction on x whenever g is a p group and y is p complete and satisfies standard finiteness assumptions the method is an adams spectral sequence based on a new equivariant coho mology theory c x which we introduce in 1 this spectral sequence is quite calculable and provides a natural generalisation of the classical adams spectral sequence based on ordinary modp cohomology it also geometrically realises certain inverse limits of nonequivariant adams spectral sequences which have been useful in the study of the segal conjecture 19 5 21 9

quaternionic algebraic cycles and reality in this paper we compute the equivariant homotopy type of spaces of algebraic cycles on real brauer severi varieties under the action of the galois group gal c r appropriate stabilizations of these spaces yield two equivariant spectra the first one classifies dupont seymour s quaternionic k theory and the other one classifies an equivariant cohomology theory 3 which is a natural recipient of characteristic classes kh x 3 x for quaternionic bundles over real spaces x

divide and congruence iii from decomposition of modal formulas to preservation of stability and divergence abstract in two earlier papers we derived congruence formats with regard to transition system specifications for weak semantics on the basis of a decomposition method for modal formulas the idea is that a congruence format for a semantics must ensure that the formulas in the modal characterisation of this semantics are always decomposed into formulas that are again in this modal characterisation the stability and divergence requirements that are imposed on many of the known weak semantics have so far been outside the realm of this method stability refers to the absence of a transition we show using the decomposition method how congruence formats can be relaxed for weak semantics that are stability respecting this relaxation for instance brings the priority operator within the range of the stability respecting branching bisimulation format divergence which refers to the presence of an infinite sequence of transitions escapes the inductive decomposition method we circumvent this problem by proving that a congruence format for a stability respecting weak semantics is also a congruence format for its divergence preserving counterpart

parallel kinetic monte carlo simulations of two dimensional island coarsening the results of parallel kinetic monte carlo kmc simulations of island coarsening based on a bond counting model are presented our simulations were carried out both as a test of and as an application of the recently developed semirigorous synchronous sublattice sl algorithm by carrying out simulations over long times and for large system sizes the asymptotic coarsening behavior and scaled island size distribution isd were determined our results indicate that while cluster diffusion and coalescence play a role at early and intermediate times at late times the coarsening proceeds via ostwald ripening in addition we find that the asymptotic scaled isd is significantly narrower and more sharply peaked than the mean field theory prediction the dependence of the scaled isd on coverage is also studied our results demonstrate that parallel kmc simulations can be used to effectively extend the time scale over which realistic coarsening simulations can be carried out in particular for simulations of the late stages of coarsening with system size l 1600 and eight processors a parallel efficiency larger than 80 was obtained these results suggest that the sl algorithm is likely to be useful in the future in parallel kmc simulations of more complicated models of coarsening

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

a complete axiomatisation for observational congruence of finite state behaviours abstract finite state automata with non determinism and silent transitions can be interpreted not as subsets of the free monoid as in classical automata theory but as congruence classes under a congruence relation based upon the notion of weak bisimulation or observational equivalence due to park and milner in this paper a complete axiomatisation for this congruence is presented it extends the previously known complete axiomatisation by hennessy and milner for the case when all computations are finite the extension consists of five simple rules for recursion

higher equivariant excision abstract we develop a theory of goodwillie calculus for functors between g equivariant homotopy theories where g is a finite group we construct j excisive approximations for any finite g set j these combine into a poset the goodwillie tree that extends the classical goodwillie tower we prove convergence results for the tree of a functor on pointed g spaces that commutes with fixed points and we reinterpret the tom dieck splitting as an instance of a more general splitting phenomenon that occurs for the fixed points of the equivariant derivatives of these functors as our main example we describe the layers of the tree of the identity functor in terms of the equivariant spanier whitehead duals of the partition complexes

an algebraic model for rational naive commutative ring so 2 spectra and equivariant elliptic cohomology equipping a non equivariant topological text e infty operad with the trivial g action gives an operad in g spaces for a g spectrum being an algebra over this operad does not provide any multiplicative norm maps on homotopy groups algebras over this operad are called naive commutative ring g spectra in this paper we take g so 2 and we show that commutative algebras in the algebraic model for rational so 2 spectra model rational naive commutative ring so 2 spectra in particular this applies to show that the so 2 equivariant cohomology associated to an elliptic curve c of greenlees topology 44 6 1213 1279 2005 is represented by an text e infty ring spectrum moreover the category of modules over that text e infty ring spectrum is equivalent to the derived category of sheaves over the elliptic curve c with the zariski torsion point topology

weak bisimulation is sound and complete for pctl abstract we investigate weak bisimulation of probabilistic systems in the presence of nondeterminism i e labelled concurrent markov chains lcmc with silent transitions we develop an approach based on allowing convex combinations of computations similar to segala and lynch s use of randomized schedulers the definition of weak bisimulation destroys the additivity property of the probability distributions yielding instead capacities the mathematics behind capacities naturally captures the intuition that when we deal with nondeterminism we must work with bounds on the possible probabilities rather than with their exact values our analysis leads to three new developments we identify a characterization of image finiteness for countable state systems and present a new definition of weak bisimulation for these lcmcs we prove that our definition coincides with that of philippou lee and sokolsky for finite state systems we show that bisimilar states have matching computations the notion of matching involves convex combinations of transitions we study a minor variant of the probabilistic logic pctl the variation arises from an extra path formula to address action labels we show that bisimulation is sound and complete for this variant of pctl this is an extended complete version of a paper that was presented at concur 2002

a transfer homomorphism for compact lie group actions here a space is perfectly normal if it is normal and every open subspace is a countable union of closed subspaces transfer maps for actions of finite groups were defined by floyd 10 and used in particular for studying orbit spaces for actions on contractible spaces when g is a compact lie group acting freely on x then n x h x g is a fiber bundle with fiber g h and the transfer constructed by becker and gottlieb 1 applies in this case so our goal here is to generalize both of these constructions one obvious consequence of the above theorem is that

bigraded equivariant cohomology of real quadrics we give a complete description of the bigraded bredon co homology ring of smooth projective real quadrics with coefficients in the constant mackey functor z these invariants are closely related to the integral motivic cohomology ring which is not known for these va rieties some of the results and techniques introduced can be applied to other geometrically cellular real varieties

equivariant factorization homology of global quotient orbifolds abstract we introduce equivariant factorization homology extending the axiomatic framework of ayala francis to encompass multiplicative invariants of manifolds equipped with finite group actions examples of such equivariant factorization homology theories include bredon equivariant homology and twisted versions of hochschild homology our main result is that equivariant factorization homology satisfies an equivariant version of excision and is uniquely characterised by this property we also discuss applications to representation theory such as constructions of categorical braid group actions

branching time and abstraction in bisimulation semantics in comparative concurrency semantics one usually distinguishes between linear time and branching time semantic equivalences milner s notion of observatin equivalence is often mentioned as the standard example of a branching time equivalence in this paper we investigate whether observation equivalence really does respect the branching structure of processes and find that in the presence of the unobservable action of ccs this is not the case therefore the notion of branching bisimulation equivalence is introduced which strongly preserves the branching structure of processes in the sense that it preserves computations together with the potentials in all intermediate states that are passed through even if silent moves are involved on closed ccs terms branching bisimulation congruence can be completely axiomatized by the single axion scheme a y z y a y z where a ranges over all actions and the usual loaws for strong congruence we also establish that for sequential processes observation equivalence is not preserved under refinement of actions whereas branching bisimulation is for a large class of processes it turns out that branching bisimulation and observation equivalence are the same as far as we know all protocols that have been verified in the setting of observation equivalence happen to fit in this class and hence are also valid in the stronger setting of branching bisimulation equivalence

equivariant fixed point index and fixed point transfer in nonzero dimensions dold s fixed point index and fixed point transfer are generalized for certain coincidence situations namely maps which change the equivariant di mension those invariants change the dimension correspondingly a formula for the index of a situation over a space with trivial group action is exhibited for the transfer a generalization of dold s lefschetz hopf trace formula is proved

a description based on languages of the final non deterministic automaton abstract the study of the behaviour of non deterministic automata has traditionally focused on the languages which can be associated to the different states under this interpretation the different branches that can be taken at every step are ignored however we can also take into account the different decisions which can be made at every state that is the branches that can be taken and these decisions might change the possible future behaviour in this case the behaviour of the automata can be described with the help of the concept of bisimilarity this is the kind of description that is usually obtained when the automata are regarded as labelled transition systems or coalgebras contrarily to what happens with deterministic automata it is not possible to describe the behaviour up to bisimilarity of states of a non deterministic automaton by considering just the languages associated to them in this paper we present a description of a final object for the category of non deterministic automata regarded as labelled transition systems with the help of some structures defined in terms of languages as a consequence we obtain a characterisation of bisimilarity of states of automata in terms of languages and a method to minimise non deterministic automata with respect to bisimilarity of states this confirms that languages can be considered as the natural objects to describe the behaviour of automata

relating strong behavioral equivalences for processes with nondeterminism and probabilities we present a comparison of behavioral equivalences for nondeterministic and probabilistic processes whose activities are all observable in particular we consider trace based testing and bisimulation based equivalences for each of them we examine the discriminating power of three variants stemming from three approaches that differ for the way probabilities of events are compared when nondeterministic choices are resolved via schedulers the first approach compares two resolutions with respect to the probability distributions of all considered events the second approach requires that the probabilities of the set of events of a resolution be individually matched by the probabilities of the same events in possibly different resolutions the third approach only compares the extremal probabilities of each event stemming from the different resolutions the three approaches have very reasonable motivations and when applied to fully nondeterministic processes or fully probabilistic processes give rise to the classical well studied relations we shall see that for processes with nondeterminism and probability they instead give rise to a much wider variety of behavioral relations whose discriminating power is thoroughly investigated here in the case of deterministic schedulers

equivalence notions and model minimization in markov decision processes many stochastic planning problems can be represented using markov decision processes mdps a difficulty with using these mdp representations is that the common algorithms for solving them run in time polynomial in the size of the state space where this size is extremely large for most real world planning problems of interest recent ai research has addressed this problem by representing the mdp in a factored form factored mdps however are not amenable to traditional solution methods that call for an explicit enumeration of the state space one familiar way to solve mdp problems with very large state spaces is to form a reduced or aggregated mdp with the same properties as the original mdp by combining equivalent states in this paper we discuss applying this approach to solving factored mdp problems we avoid enumerating the state space by describing large blocks of equivalent states in factored form with the block descriptions being inferred directly from the original factored representation the resulting reduced mdp may have exponentially fewer states than the original factored mdp and can then be solved using traditional methods the reduced mdp found depends on the notion of equivalence between states used in the aggregation the notion of equivalence chosen will be fundamental in designing and analyzing algorithms for reducing mdps optimally these algorithms will be able to find the smallest possible reduced mdp for any given input mdp and notion of equivalence i e find the minimal model for the input mdp unfortunately the classic notion of state equivalence from non deterministic finite state machines generalized to mdps does not prove useful we present here a notion of equivalence that is based upon the notion of bisimulation from the literature on concurrent processes our generalization of bisimulation to stochastic processes yields a non trivial notion of state equivalence that guarantees the optimal policy for the reduced model immediately induces a corresponding optimal policy for the original model with this notion of state equivalence we design and analyze an algorithm that minimizes arbitrary factored mdps and compare this method analytically to previous algorithms for solving factored mdps we show that previous approaches implicitly derive equivalence relations that we define here

computations in c_ pq bredon cohomology in this paper we compute the ro c pq graded cohomology of c pq orbits we deduce that in all the cases the bredon cohomology groups are a function of the fixed point dimensions of the underlying virtual representations further when thought of as a mackey functor the same independence result holds in almost all cases this generalizes earlier computations of stong and lewis for the group c p the computations of cohomology of orbits are used to prove a freeness theorem the analogous result for the group c p was proved by lewis we demonstrate that certain complex projective spaces and complex grassmannians satisfy the freeness theorem

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