the novikov conjecture for algebraic k theory of the group algebra over the ring of schatten class operators abstract in this paper we prove the algebraic k theory novikov conjecture for group algebras over the ring of schatten class operators the main technical tool in the proof is an explicit construction of the connes chern character

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

equivalence of deterministic top down tree to string transducers is decidable we prove that equivalence of deterministic top down tree to string transducers is decidable thus solving a long standing open problem in formal language theory we also present efficient algorithms for subclasses for linear transducers or total transducers with unary output alphabet over a given top down regular domain language as well as for transducers with the single use restriction these results are obtained using techniques from multi linear algebra for our main result we introduce polynomial transducers and prove that for these validity of a polynomial invariant can be certified by means of an inductive invariant of polynomial ideals this allows us to construct two semi algorithms one searching for a certificate of the invariant and one searching for a witness of its violation via a translation into polynomial transducers we thus obtain that equivalence of general y dt transducers is decidable in fact our translation also shows that equivalence is decidable when the output is not in a free monoid but in a free group

the m calculus as an assertion language for fairness arguments abstract various principles of proof have been proposed to reason about fairness this paper addresses for the first time the question in what formalism such fairness arguments can be couched to wit we prove that park s monotone first order calculus augmented with constants for all recursive ordinals can serve as an assertion language for proving fair termination of do loops in particular the weakest precondition for fair termination of a loop w r t some postcondition is definable in it the relevance of this result to proving eventualities in the temporal logic formalism of manna and pnuelis in foundations of computer science iv part 2 math centre tracts vol 159 math centrum amsterdam 1983 is discussed

homotopy theory of associative rings a kind of unstable homotopy theory on the category of associative rings without unit is developed there are the notions of fibrations homotopy in the sense of karoubi path spaces puppe sequences etc one introduces the notion of a quasi isomorphism or weak equivalence for rings and shows that similar to spaces the derived category obtained by inverting the quasi isomorphisms is naturally left triangulated also homology theories on rings are studied these must be homotopy invariant in the algebraic sense meet the mayer vietoris property and plus some minor natural axioms to any functor from rings to pointed simplicial sets a homology theory is associated in a natural way if and fibrations are the gl fibrations one recovers karoubi villamayor s functors kvi i 0 if is quillen s k theory functor and fibrations are the surjective homomorphisms one recovers the non negative homotopy k theory in the sense of weibel technical tools we use are the homotopy information for the category of simplicial functors on rings and the bousfield localization theory for model categories the machinery developed in the paper also allows to give another definition for the triangulated category kk constructed by cortinas and thom g cortinas a thom bivariant algebraic k theory preprint math kt 0603531 the latter category is an algebraic analog for triangulated structures on operator algebras used in kasparov s kk theory

determinism and non determinism in pdl abstract the main purpose of this paper is to consider a variant of propositional dynamic logic pdl in which the natural program concepts while do od and if then else fi are basic and in which is the only non deterministic program concept dropping leads to the known system strict propositional dynamic logic spdl the main result of this paper is that spdl is weaker than pdl it is pointed out however that by extending spdl by propositional assignments a system called propositional program logic ppl is obtained which has the same expressive power as pdl

semantic models for total correctness and fairness assertional s rings are introduced to provide an algebraic setting in which the finite and infinite behavior of nondeterministic programs can be expressed and reasoned about this includes expressing the fair infinite behavior of nondeterministic iterative programs and reasoning about termination under various fairness assumptions we also address the question of when the reasoning techniques are semantically complete

kk theory for banach algebras ii equivariance and green julg type theorems abstract we extend the definition of the bivariant k theory kk ban from plain banach algebras to banach algebras equipped with an action of a locally compact hausdorff group g we also define a natural transformation from lafforgue s theory kk g ban into the new equivariant theory overcoming some technical difficulties that are particular to the equivariant case the categorical framework allows us to systematically define a descent homomorphism and to prove a green julg theorem a dual version of it and a generalised version that involves the action of a proper g space we also include a naive poincare duality theorem

alternating states for dual nondeterminism in imperative programming the refinement calculus of back morgan morris and others is based on monotone predicate transformers weakest preconditions where conjunctions stand for demonic choices between commands and disjunctions for angelic choices arbitrary monotone predicate transformers cannot be modelled by relational semantics but can be modelled by so called multirelations results of morris indicate however that the natural domain for the combination of demonic and angelic choice is the free distributive completion fdc of the state space the present paper provides a new axiomatization and more explicit construction of the fdc of an arbitrary ordered set the fdc concept is self dual but the construction is not we therefore determine the duality function from the fdc to the dual of the fdc of the dual ordered set the elements of the fdc are classified according to their conjunctivity and disjunctivity the theory is applied to imperative programming with operators for sequential composition and demonic and angelic choice the theory based on the fdc is shown to be equivalent to a weakest precondition theory for up closed predicates if the order is discrete i e the equality relation the fdc turns out to be the domain of the choice semantics of back and von wright whereas up closed multirelations are functions towards this domain

graver basis and proximity techniques for block structured separable convex integer minimization problems we consider n fold 4 block decomposable integer programs which simultaneously generalize n fold integer programs and two stage stochastic integer programs with n scenarios in previous work hemmecke et al in integer programming and combinatorial optimization springer berlin 2010 it was proved that for fixed blocks but variable n these integer programs are polynomial time solvable for any linear objective we extend this result to the minimization of separable convex objective functions our algorithm combines graver basis techniques with a proximity result hochbaum and shanthikumar in j acm 37 843 862 1990 which allows us to use convex continuous optimization as a subroutine

k theorie bivariante pour les algebres de banach et conjecture de baum connes je suis parvenu dans ma these a construire une k theorie bivariante pour les algebres de banach cela m a permis de demontrer la conjecture de baum connes pour les groupes de lie semi simples et les groupes reductifs p adiques ainsi que pour les sous groupes discrets de type fini de sl 3 f avec f une extension finie de q p et pour les sous groupes discrets cocompacts de sp n 1 sl 3 r et sl 3 c j ai aussi demontre une conjecture analogue a la conjecture de baum connes pour les algebres l 1 et plus generalement toutes les bonnes completions des sous groupes fermes des groupes de lie semi simples et des groupes reductifs p adiques

looping vs repeating in dynamic logic two extensions of propositional dynamic logic for dealing with infinite computations lpdl and rpdl are compared in expressive power the first is obtained by adding the assertion loop for any program meaning contains an infinite computation and the second by adding repeat meaning can be repeated indefinitely while repeat can be used to encode loop and hence lpdl rpdl it is shown here that the converse fails thus lpdl

constructive design of a hierarchy of semantics of a transition system by abstract interpretation we construct a hierarchy of semantics by successive abstract interpretations starting from the maximal trace semantics of a transition system we derive the big step semantics termination and nontermination semantics plotkin s natural smyth s demoniac and hoare s angelic relational semantics and equivalent nondeterministic denotational semantics with alternative powerdomains to the egli milner and smyth constructions d scott s deterministic denotational semantics the generalized and dijkstra s conservative liberal predicate transformer semantics the generalized total and hoare s partial correctness axiomatic semantics and the corresponding proof methods all the semantics are presented in a uniform fixpoint form and the correspondences between these semantics are established through composable galois connections each semantics being formally calculated by abstract interpretation of a more concrete one using kleene and or tarski fixpoint approximation transfer theorems copyright 2002 elsevier science b v

comparative metric semantics for concurrent prolog abstract this paper shows the equivalence of two semantics for a version of concurrent prolog with non flat guards an operational semantics based on a transition system and a denotational semantics which is a metric semantics the domains are metric spaces we do this in the following manner first a uniform language l is considered that is a language where the atomic actions have arbitrary interpretations for this language we define an operational and a denotational semantics and we prove that the denotational semantics is correct with respect to the operational semantics this result relies on banach s fixed point theorem techniques stemming from imperative languages are used then we show how to translate a concurrent prolog program to a program in l by selecting certain basic sets for l and then instantiating the interpretation function for the atomic actions in this way we induce the two semantics for concurrent prolog and the equivalence between the two semantics

nondeterministic extensions of untyped λ calculus the main concern of this paper is the interplay between functionality and nondeterminism we ask whether the analysis of parallelism in terms of sequentiality and nondeterminism which is usual in the algebraic treatment of concurrency remains correct in the presence of functional application and abstraction we argue in favour of a distinction between nondeterminism and parallelism due to the conjunctive nature of the former in contrast to the disjunctive character of the latter this is the basis of our analysis of the operational and denotational semantics of the nondeterministic calculus which is the classical calculus plus a choice operator and of our election of bounded indeterminacy as the semantic counterpart of conjunctive nondeterminism this leads to operational semantics based on the idea of must preorder coming from the classical theory of solvability and from the theory of process algebras to characterize this relation we build a model using the inverse limit construction over nondeterministic algebras and we prove it fully abstract using a generalization of bohm trees we further prove conservativity theorems for the equational theory of the model and for other theories related to nondeterministic calculus with respect to classical theories

optimization with multivariate conditional value at risk constraints for many decision making problems under uncertainty it is crucial to develop risk averse models and specify the decision makers risk preferences based on multiple stochastic performance measures or criteria incorporating such multivariate preference rules into optimization models is a fairly recent research area existing studies focus on extending univariate stochastic dominance rules to the multivariate case however enforcing multivariate stochastic dominance constraints can often be overly conservative in practice as an alternative we focus on the widely applied risk measure conditional value at risk cvar introduce a multivariate cvar relation and develop a novel optimization model with multivariate cvar constraints based on polyhedral scalarization to solve such problems for finite probability spaces we develop a cut generation algorithm where each cut is obtained by solving a mixed integer problem we show that a multivariate cvar constraint reduces to finitely many univariate cvar co

bivariant algebraic k theory we show how methods from k theory of operator algebras can be applied in a completely algebraic setting to define a bivariant m1 stable homotopy invariant excisive k theory of algebras over a fixed unital ground ring h a b 7 kk a b which is universal in the sense that it maps uniquely to any other such theory it turns out kk is related to c weibel s homotopy algebraic k theory kh we prove that if h is commutative and a is central as an h bimodule then kk h a kh a we show further that some calculations from operator algebra kk theory such as the exact sequence of pimsner voiculescu carry over to algebraic kk

optimization with reference based robust preference constraints we propose an optimization model using a novel robust preference relationship reference based almost stochastic dominance rsd the concept of rsd addresses the two problems in utility based dec

a fully abstract semantics for concurrent constraint programming a compositional and fully abstract semantics for concurrent constraint programming is developed it is the first fully abstract semantics which takes into account both non determinism infinite computations and fairness we present a simple concurrent constraint programming language whose semantics is given by a set of reduction rules augmented with fairness requirements in the fully abstract semantics we consider two aspects of a trace viz the function computed by the trace the functionality and the set of input and output data the limit of the trace we then derive the fully abstract semantics from the set of traces using a closure operation we give two proofs of full abstraction the first relies on the use of a syntactically infinite context the second proof requires only a finite context but assumes as input a representation of the function to be computed by the context finally we examine the algebraic properties of the programming language with respect to the fully abstract semantics it turns out that the non deterministic selection operation can be defined using operations derived from parallel composition and the usual set theoretic operations on sets of traces

frontiers of stochastically nondominated portfolios we consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution we propose mean risk models that are solvable by linear programming and generate portfolios whose returns are nondomi nated in the sense of second order stochastic dominance next we develop a specialized parametric method for recovering the entire mean risk efficient frontiers of these models and we illustrate its operation on a large data set involving thousands of assets and real izations the problem of optimizing a portfolio of finitely many assets is a classical problem in theoretical and computational finance since the seminal work of markowitz 1952 it is generally agreed that portfolio performance should be measured in two distinct dimen sions the mean describing the expected return and the risk which measures the uncer tainty of the return in the mean risk approach we select from the universe of all possible portfolios those that are efficient for a given value of the mean they minimize the risk or equivalently for a given value of risk they maximize the mean such an approach has many advantages it allows one to formulate the problem as a parametric optimization problem and it facilitates the trade off analysis between mean and risk markowitz used the variance of the return as the measure of the risk it is easy to compute and it reduces the portfolio selection problem to a parametric quadratic pro gramming problem one can however construct simple counterexamples that show the imperfection of the variance as the risk measure it treats over performance equally as under performance and more importantly its use may suggest a portfolio that is always outperformed by another portfolio the use of the semivariance rather than the variance was already recommended by markowitz 1959 but even in this case significant deficien cies remain as we shall explain another theoretical approach to the portfolio selection problem is that of stochastic dominance see whitmore and findlay 1978 levy 1992 the usual first order defi nition of stochastic dominance gives a partial order in the space of real random variables more important from the portfolio point of view is the notion of second order dominance which is also defined as a partial order but which is equivalent to this statement a random variable y dominates the random variable z if e u y e u z for all nondecreasing concave functions u for which these expected values are finite thus no risk averse decision marker will prefer a portfolio with return z over a portfolio with return y while

kk theoretic duality for proper twisted actions let mathcal a be a smooth continuous trace algebra with a riemannian manifold spectrum x equipped with a smooth action by a discrete group g such that g acts on x properly and isometrically then mathcal a 1 rtimes g is kk theoretically poincare dual to big mathcal a hat otimes c 0 x c tau x big rtimes g where mathcal a 1 is the inverse of mathcal a in the brauer group of morita equivalence classes of continuous trace algebras equipped with a group action we deduce this from a strengthening of kasparov s duality theorem as applications we obtain a version of the above poincare duality with x replaced by a compact g manifold m and poincare dualities for twisted group algebras if the group satisfies some additional properties related to the dirac dual dirac method for the baum connes conjecture

precise interprocedural dependence analysis of parallel programs it is known that interprocedural detection of copy constants and elimination of faint code in parallel programs are undecidable problems if base statements are assumed to execute atomically we show that these problems become decidable if this assumption is abandoned so the unrealistic idealization from program verification atomic execution of base statements introduced in order to simplify matters actually increases the difficulty of these problems from the point of view of program analysis amazingly these problems become more tractable if we adopt a less idealized more realistic model of execution we introduce an effective abstract domain of antichains of dependence traces that allows us to perform a precise interprocedural dependence analysis in non atomically executing parallel programs the main idea is to trace sequences of dependences exhibited successively by program executions we define operations on antichains of dependence traces and show that they precisely abstract the corresponding operations on sets of non atomic program executions using these operations we can analyze dependences by means of an abstract interpretation of constraint systems that characterize sets of program executions of interest the result of the dependence analysis can in turn be used to detect all copy constants and to eliminate faint code while the run time of the algorithms is exponential in the number of program variables it is polynomial in the program size hence they are polynomial time algorithms if the number of program variables is bounded in order to justify their overall exponential run time we show that both detection of copy constants and elimination of faint code are intractable np hard even when the atomic execution idealization is abandoned this holds already for parallel programs without loops or procedures

proof systems for infinite behaviours abstract we introduce several generalizations of testing to behaviours of communicating processes analyse the logical complexity of the testing equivalences and establish on that basis a connection with proof systems

from stochastic dominance to mean risk models semideviations as risk measures abstract two methods are frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches the former is based on an axiomatic model of risk averse preferences but does not provide a convenient computational recipe the latter quantifies the problem in a lucid form of two criteria with possible trade off analysis but cannot model all risk averse preferences in particular if variance is used as a measure of risk the resulting mean variance markowitz model is in general not consistent with stochastic dominance rules this paper shows that the standard semideviation square root of the semivariance as the risk measure makes the mean risk model consistent with the second degree stochastic dominance provided that the trade off coefficient is bounded by a certain constant similar results are obtained for the absolute semideviation and for the absolute and standard deviations in the case of symmetric or bounded distributions in the analysis we use a new tool the outcome risk o r diagram which appears to be particularly useful for comparing uncertain outcomes

stochastic programs with first order dominance constraints induced by mixed integer linear recourse we propose a new class of stochastic integer programs whose special features are dominance constraints induced by mixed integer linear recourse for these models we establish closedness of the constraint set mapping with the underlying probability measure as a parameter in the case of finite probability spaces the models are shown to be equivalent to large scale block structured mixed integer linear programs we propose a decomposition algorithm for the latter and discuss computational results

decomposition methods in stochastic programming stochastic programming problems have very large dimension and characteristic structures which are tractable by decomposition we review basic ideas of cutting plane methods augmented lagrangian and splitting methods and stochastic decomposition methods for convex polyhedral multi stage stochastic programming problems

lipschitzian properties and stability of a class of first order stochastic dominance constraints considering first order stochastic dominance constraints for random variables arising as optimal values of stochastic programs with linear recourse verifiable sufficient conditions for metric regularity are presented a growth condition developed in r henrion and w romisch math program 84 1999 pp 55 88 has a crucial role in the analysis of the present paper implications regarding stability and sensitivity of optimal values and optimal solutions of stochastic optimization problems involving the dominance constraints considered conclude the paper

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

full abstraction and recursion the question of extending semantic models for a programming language without recursion to a larger language supporting recursion is of fundamental importance if one wants to develop a modular approach to building models in our previous work 14 we showed how to extend models for a language without recursion to models for a language in which unnested recursion was supported via simultaneous systems of recursive equations in that setting we proved that modest assumptions about the models enabled us to lift adequacy and full abstraction for the models of the base language to analogous results for the models of the extended language in this paper we tackle similar problems for languages with explicit recursion operators starting with a base language l we define what it means for an ordered denotational model for l to be order adequate and strongly order fully abstract with respect to an ordered operational model for l by freely adding identifiers x x and recursion operators x for each x x we obtain an extended language l x in which we single out the sublanguage l c of closed terms we then give general conditions which ensure that an ordered operational model o l o and a related order adequate and strongly order fully abstract denotational model d l d can be extended to an ordered operational model o c l c o and a related ordered denotational model d c l c d which also is order adequate and strongly order fully abstract

optimization with stochastic dominance constraints we introduce stochastic optimization problems involving stochastic dominance constraints we develop necessary and sufficient conditions of optimality and duality theory for these models and show that the lagrange multipliers corresponding to dominance constraints are concave nondecreasing utility functions the models and results are illustrated on a portfolio optimization problem

while programs with nondeterministic assignments and the logic alna abstract in this paper unbounded countable nondeterminism allowed by adding nondeterministic assignments to while programs is studied first their semantical properties that are expressible in the language of alna algorithmic logic for while programs with nondeterministic assignments are considered wellfoundedness as well as bounded and unbounded nondeterminism for the considered class of programs are shown to be expressible in the language of alna a characterization of the wellfounded while computation trees is obtained via a notion of approximation by computation trees of suitable if then else programs no use of ordinals has been necessary to that aim the logic alna is proved to be sound and complete

a continuous semantics for unbounded nondeterminism abstract nondeterminism is introduced into an ordinary iterative programming language by treating procedure calls as nondeterministic assignment statements the effect of such assignment statements is assumed to be determined solely by the entry exit specifications of the corresponding procedures the nondeterminism which this approach yields is not necessarily bounded the paper discusses the problem of defining a denotational semantic for programming languages with this kind of possibly unbounded nondeterminism as an additional constraint the semantics is required to be continuous in the sense that the underlying semantic algebra is continuous it is shown how such a continuous semantics for unbounded nondeterminism can be derived from a simple operational semantics based on program execution trees

on specifications theories and models with higher types we discuss the mathematical foundations of specifications theories and models with higher types higher type theories are presented by specifications either using the language of cartesian closure or a typed calculus we prove equivalence of both the specification methods the main result being the equivalence of cartesian closure and a typed calculus then we investigate intensional and extensional models the distinction is similar to that between algebras and models we prove completeness of higher type theories with regard to intensional models as well as existence of free intensional models for extensional models we prove that completeness and existence of an initial models implies that the theory itself already is the initial model as a consequence intensional models seem to be better suited for the purposes of data type specification

equivariant algebraic kk theory and adjointness theorems abstract we introduce an equivariant algebraic kk theory for g algebras and g graded algebras we study some adjointness theorems related with crossed product trivial action induction and restriction in particular we obtain an algebraic version of the green julg theorem which gives us a computational tool

cut generation for optimization problems with multivariate risk constraints we consider a class of stochastic optimization problems that features benchmarking preference relations among random vectors representing multiple random performance measures criteria of interest given a benchmark random performance vector preference relations are incorporated into the model as constraints which require the decision based random vector to be preferred to the benchmark according to a relation based on multivariate conditional value at risk cvar or second order stochastic dominance ssd we develop alternative mixed integer programming formulations and solution methods for cut generation problems arising in optimization under such multivariate risk constraints the cut generation problems for cvar and ssd based models involve the epigraphs of two distinct piecewise linear concave functions which we refer to as reverse concave sets we give the complete linear description of the linearization polytopes of these two non convex substructures we present computational results that show the effectiveness of our proposed models and methods

on the logic of unity abstract the unity approach to specification design and verification of parallel programs expounded by chandy and misra 1988 contains a programming notation and a programming logic to express and prove properties of unity programs for progress properties there is a basic notion leads to which comes in two versions one version here called leads to explicitly expresses progress of fair execution sequences of a unity program another prima facie stronger version here called is defined by infinitary closure conditions from the more elementary notion ensures this version is used in the actual proofs of program properties given in chandy and misra 1988 in this paper these notions are investigated from a foundational point of view a principle of transfinite induction for is introduced and it is proved that every true leads to proposition can be obtained by application of one single instance of this principle semantic completeness of w r t its intended semantics leads to is a corollary aspects of the complexity and computational power of unity are analyzed the halting problem for fair executions of unity programs is shown to be 1 1 complete and it is proved that a nondeterministic numerical function is computable by a unity program if and only if its graph is 1 1 and its halting set is a 1 1 subset of its domain in order to retain completeness of the principle of transfinite induction for arbitrarily large recursive ordinals are needed as heights of well founded relations a formalized finitary proof system for is introduced and proved syntactically correct and complete relative to the set of true 1 1 sentences of a second order assertion language more precisely the well founded relation itself and the auxiliary assertions used can be expressed in a first order language it is only the hypothesis of well foundedness which has to be expressed by a 1 1 formula in view of the 1 1 completeness phenomenon this result is best possible

kk theory for banach algebras i the non equivariant case abstract kkban is a bivariant k theory for banach algebras that has reasonable homological properties a product and is morita invariant in a very general sense we define it here by a universal property and ensure its existence in a rather abstract manner using triangulated categories the definition ensures that there is a natural transformation from lafforgue s theory kkban into it so that one can take products of elements in kkban that lie in kkban

on time stochastic dominance induced by mixed integer linear recourse in multistage stochastic programs abstract we propose in this work a new multistage risk averse strategy based on time stochastic dominance tsd along a given horizon it can be considered as a mixture of the two risk averse measures based on first and second order stochastic dominance constraints induced by mixed integer linear recourse respectively given the dimensions of medium sized problems augmented by the new variables and constraints required by this new risk measure it is unrealistic to solve the problem up to optimality by plain use of mip solvers in a reasonable computing time at least instead of it decomposition algorithms of some type should be used we present an extension of our branch and fix coordination algorithm so named bfc tsd where a special treatment is given to cross scenario group constraints that link variables from different scenario groups a broad computational experience is presented by comparing the risk neutral approach and the tested risk averse strategies the performance of the new version of the bfc algorithm versus the plain use of a state of the art mip solver is also reported

excision in cyclic homology and in rational algebraic k theory for a precise definition see 1 below by replacing everywhere k by k q one obtains the corresponding notion in rational algebraic k theory the above definition has an obvious counterpart for cyclic homology and algebras over a fixed field in the case of a general commutative ground ring k some restrictions on the class of allowable extensions seem inevitable due to the well known limitations of cyclic homology considered as a homology functor for algebras not flat over a ground ring an extension of k algebras will be called pure if it is pure as an extension of k modules in the sense of p m cohn 6 cf also appendix a 3 below the class of pure extensions contains e g i extensions which admit a k module splitting ii extensions a e r s with s flat over k in fact one among the several possible characterizations of purity says that an extension is pure if and only if the underlying extension of k modules is an inductive limit of split extensions see theorem a 4 of appendix a below everywhere in this paper the word excision used in the context of cyclic homology will mean excision with respect to the class of pure extensions the second purpose of the present paper is to give a complete characterization of the class of algebras possessing the excision property in cyclic homology before stating the corresponding result we need the following definition let us

homotopy classification of leavitt path algebras abstract in this paper we address the classification problem for purely infinite simple leavitt path algebras of finite graphs over a field l each graph e has associated a leavitt path l algebra l e there is an open question which asks whether the pair k 0 l e 1 l e consisting of the grothendieck group together with the class 1 l e of the identity is a complete invariant for the classification up to algebra isomorphism of those leavitt path algebras of finite graphs which are purely infinite simple we show that k 0 l e 1 l e is a complete invariant for the classification of such algebras up to polynomial homotopy equivalence to prove this we further develop the study of bivariant algebraic k theory of leavitt path algebras started in a previous paper and obtain several other results of independent interest

a relation algebraic model of robust correctness we propose a new and uniform abstract relational approach to demonic nondeterminism and robust correctness similar to hoare s chaos semantics it is based on a specific set of relations on flat lattices this set forms a complete lattice furthermore we deal with the refinement of programs among other things we show the correctness of the unfold fold method for demonic nondeterminism and robust correctness as refinement relation and investigate relationships to dijkstra s wp calculus and morgan s specification statement authors abstract

second order stochastic dominance constrained portfolio optimization theory and computational tests abstract due to the definition of second order stochastic dominance ssd in terms of utility theory portfolio optimization with ssd constraints is of major practical interest we contribute to the field in two ways first we present a self contained theory with some new results and new proofs of known results second we perform a set of tests for computational efficiency we provide new and simple arguments for the formulation of ssd constraints in a mathematical programming framework for many individuals an ssd constraint may seem too severe wherefore various relaxations assd have been proposed we introduce yet another relaxation directional ssd where a candidate portfolio is admissible if a step from the benchmark in the direction of the candidate yields a dominating portfolio optimal step size depends on individual preferences reflected by the objective function we compare computational efficiency of seven approaches for sd constrained portfolio problems including ssd and assd constrained cases

interpretations of recursion under unbounded nondeterminacy abstract a language is constructed that supports arbitrary atomic statements composition alternatives and mutual recursion in the presence of unbounded nondeterminacy the concept of interpretation is defined axiomatically by operational means a standard interpretation is constructed which is proved to be the smallest interpretation with respect to the egli milner ordering the corresponding weakest precondition and weakest liberal precondition are characterized as smallest and largest preparator functions we characterize the interpretations which upon divergence cannot deliver unjustified meaningful values these interpretations form a spectrum that ranges from standard semantics over various forms of fair semantics to the so called friendly semantics where error is signalled only if divergence can become inevitable after finitely many steps we determine the corresponding preparator functions

transforming semantics by abstract interpretation in 1997 cousot introduced a hierarchy where semantics are related with each other by abstract interpretation in this field we consider the standard abstract domain transformers devoted to refine abstract domains in order to include attribute independent and relational information respectively the reduced product and power of abstract domains as domain operations to systematically design and compare semantics of programming languages by abstract interpretation we first prove that natural semantics can be decomposed in terms of complementary attribute independent observables leading to an algebraic characterization of the symmetric structure of the hierarchy moreover we characterize some structural property of semantics such as their compositionality in terms of simple abstract domain equations this provides an equational presentation of most well known semantics which is parametric on the observable and structural property of the semantics making it possible to systematically derive abstract semantics e g for program analysis as solutions of abstract domain equations

making abstract interpretations complete completeness is an ideal although uncommon feature of abstract interpretations formalizing the intuition that relatively to the properties encoded by the underlying abstract domains there is no loss of information accumulated in abstract computations thus complete abstract interpretations can be rightly understood as optimal we deal with both pointwise completeness involving generic semantic operations and least fixpoint completeness completeness and fixpoint completeness are shown to be properties that depend on the underlying abstract domains only our primary goal is then to solve the problem of making abstract interpretations complete by minimally extending or restricting the underlying abstract domains under the weak and reasonable hypothesis of dealing with continuous semantic operations we provide constructive characterizations for the least complete extensions and the greatest complete restrictions of abstract domains as far as fixpoint completeness is concerned for merely monotone semantic operators the greatest restrictions of abstract domains are constructively characterized while it is shown that the existence of least extensions of abstract domains cannot be in general guaranteed even under strong hypotheses these methodologies which in finite settings give rise to effective algorithms provide advanced formal tools for manipulating and comparing abstract interpretations useful both in static program analysis and in semantics design a number of examples illustrating these techniques are given

determinism and looping in combinatory pdl abstract in this paper some propositional modal logics of programs are considered based on the system cpdl combinatory pdl an extension of pdl with proper names for states these proper names are atomic formulae which are satisfied at exactly one state in each model among other things e g decidability and finite model property results a version of streett s conjecture that his axioms do axiomatize the infinite repeating construct repeat is established with respect to cpdl

dual stochastic dominance and related mean risk models we consider the problem of constructing mean risk models which are consistent with the second degree stochastic dominance relation by exploiting duality relations of convex analysis we develop the quantile model of stochastic dominance for general distributions this allows us to show that several models using quantiles and tail characteristics of the distribution are in harmony with the stochastic dominance relation we also provide stochastic linear programming formulations of these models

propositional dynamic logic of looping and converse is elementarily decidable propositional dynamic logic is a formal system for reasoning about the before after behavior of regular program schemes an extension of propositional dynamic logic which includes both an infinite looping construct and a converse or backtracking construct is considered and it is proved that the satisfiability problem for this logic is elementarily decidable in order to establish this result deterministic two way automata on infinite trees are defined and it is shown how they can be simulated by nondeterministic one way automata the satisfiability problem for propositional dynamic logic of looping and converse is then reduced to the emptiness problem for these two way automata

a logic of recursion abstract moschovakis 1984 in computation and proof theory y richter et al eds lect notes in math vol 1104 pp 289 362 springer verlag berlin raised a question to find a logic of recursion related to recursion structures as denotational models of the language of recursion investigated in the same paper we give a positive answer to this question the logic of recursion presented in our paper is a first order many sorted logic cf girard in press proof theory and logical complexity vol 2 bibliopolis napoli modified in order to deal with function symbols interpreted as partial functions and extended with the operators abstraction r recursion i iteration along the ordinal numbers the operators and r are already present in moschovakis languages of recursion the use of the operator i together with first order many sorted logic is needed for obtaining the completeness theorem

optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints we consider a new class of optimization problems involving stochastic dominance constraints of second order we develop a new splitting approach to these models optimality conditions and duality theory these results are used to construct special decomposition methods

two stage stochastic programming under multivariate risk constraints with an application to humanitarian relief network design in this study we consider two classes of multicriteria two stage stochastic programs in finite probability spaces with multivariate risk constraints the first stage problem features multivariate stochastic benchmarking constraints based on a vector valued random variable representing multiple and possibly conflicting stochastic performance measures associated with the second stage decisions in particular the aim is to ensure that the decision based random outcome vector of interest is preferable to a specified benchmark with respect to the multivariate polyhedral conditional value at risk or a multivariate stochastic order relation in this case the classical decomposition methods cannot be used directly due to the complicating multivariate stochastic benchmarking constraints we propose an exact unified decomposition framework for solving these two classes of optimization problems and show its finite convergence we apply the proposed approach to a stochastic network design problem in the context of pre disaster humanitarian logistics and conduct a computational study concerning the threat of hurricanes in the southeastern part of the united states the numerical results provide practical insights about our modeling approach and show that the proposed algorithm is computationally scalable

effective transformations on infinite trees with applications to high undecidability dominoes and fairness elementary translations between various kinds of recursive trees are presented it is shown that trees of either finite or countably infinite branching can be effectively put into one one correspondence with infinitely branching trees in such a way that the infinite paths of the latter correspond to the p abiding infinite paths of the former here p can be any member of a very wide class of properties of infinite paths for many properties the converse holds too two of the applications involve a the formulation of large classes of highly undecidable variants of classical computational problems and in particular easily describable domino problems that are iii 1 1 complete and b the existence of a general method for proving termination of nondeterministic or concurrent programs under any reasonable notion of fairness

a note on second order stochastic dominance constraints induced by mixed integer linear recourse we introduce stochastic integer programs with second order dominance constraints induced by mixed integer linear recourse closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived for discrete probability measures large scale block structured mixed integer linear programming equivalents to the dominance constrained stochastic programs are identified for these models a decomposition algorithm is proposed and tested with instances from power optimization

comparison between algebraic and topological k theory of locally convex algebras abstract this paper is concerned with the algebraic k theory of locally convex c algebras stabilized by operator ideals and its comparison with topological k theory we show that if l is locally convex and j a frechet operator ideal then all the different variants of topological k theory agree on the completed projective tensor product l j and that the obstruction for the comparison map k l j k top l j to be an isomorphism is absolute algebraic cyclic homology we prove the existence of an exact sequence theorem 6 2 1 we show that cyclic homology vanishes in the case when j is the ideal of compact operators and l is a frechet algebra whose topology is generated by a countable family of sub multiplicative seminorms and admits an approximate right or left unit which is totally bounded with respect to that family theorem 8 3 3 this proves the generalized version of karoubi s conjecture due to mariusz wodzicki and announced in his paper m wodzicki algebraic k theory and functional analysis in first european congress of mathematics vol ii paris 1992 in progr math vol 120 birkhauser basel 1994 pp 485 496 we also consider stabilization with respect to a wider class of operator ideals called sub harmonic every frechet ideal is sub harmonic but not conversely for example the schatten ideal l p is sub harmonic for all p 0 but is frechet only if p 1 we prove a variant of the exact sequence above which essentially says that if a is a c algebra and j is sub harmonic then the obstruction for the periodicity of k a c j is again cyclic homology theorem 7 1 1 this generalizes to all algebras a result of wodzicki for h unital algebras announced in m wodzicki algebraic k theory and functional analysis in first european congress of mathematics vol ii paris 1992 in progr math vol 120 birkhauser basel 1994 pp 485 496 the main technical tools we use are the diffeotopy invariance theorem of cuntz and the second author which we generalize in theorem 6 1 6 and the excision theorem for infinitesimal k theory due to the first author

stability and sensitivity of optimization problems with first order stochastic dominance constraints we analyze the stability and sensitivity of stochastic optimization problems with stochastic dominance constraints of first order we consider general perturbations of the underlying probability measures in the space of regular measures equipped with a suitable discrepancy distance we show that the graph of the feasible set mapping is closed under rather general assumptions we obtain conditions for the continuity of the optimal value and upper semicontinuity of the optimal solutions as well as quantitative stability estimates of lipschitz type furthermore we analyze the sensitivity of the optimal value and obtain upper and lower bounds for the directional derivatives of the optimal value the estimates are formulated in terms of the dual utility functions associated with the dominance constraints

ten years of hoare s logic a survey part ii nondeterminism a survey of various results concerning the use of hoare s logic in proving correctness of nondeterministic programs is presented various proof systems together with the example proofs are given and the corresponding soundness and completeness proofs of the systems are discussed programs allowing bounded and countable nondeterminism are studied proof systems deal with partial and total correctness freedom of failure and the issue of fairness the paper is a continuation of part i by apt 1981 where various results concerning hoare s approach to proving correctness of sequential programs are presented

reasoning about infinite computations we investigate extensions of temporal logic by connectives defined by finite automata on infinite words we consider three different logics corresponding to three different types of acceptance conditions finite looping and repeating for the automata it turns out however that these logics all have the same expressive power and that their decision problems are all pspace complete we also investigate connectives defined by alternating automata and show that they do not increase the expressive power of the logic or the complexity of the decision problem