hascasl integrated higher order specification and program development we lay out the design of hascasl a higher order extension of the algebraic specification language casl that serves both as a wide spectrum language for the rigorous specification and development of software in particular but not exclusively in modern functional programming languages and as an expressive standard language for higher order logic distinctive features of hascasl include partial higher order functions higher order subtyping shallow polymorphism and an extensive type class mechanism moreover hascasl provides dedicated specification support for monad based functional imperative programming with generic side effects including a monad based generic hoare logic

on multiple solutions for berman s problem we study berman s problemsubjects to the conditions f 0 f 0 f 1 f 1 1 0 which arises from the study of laminar flows in channels with porous walls positive negative re denotes the case of suction injection flows preliminary numerical studies indicated the existence of three different types of solutions and a small portion of mathematical evidence was provided in this paper we are able to show that there exist connected sets in the re k plane on which different types of solutions occur in particular our result verifies that the problem possesses all three types of suction solutions for sufficiently large re moreover the limiting injection solution is also obtained

closed action calculi action calculi provide a framework for capturing many kinds of interactive behaviour by focussing on the primitive notion of names we introduce a name free account of action calculi called the closed action calculi and show that there is a strong correspondence between the original presentation and the name free presentation we also add free names plus natural axioms to the closed world and show that the abstraction operator can be constructed as a derived operator our results show that in some sense names are inessential however the purpose of action calculi is to understand formalisms which mimic the behaviour of interactive systems perhaps more significantly therefore these results highlight the important presentational role that names play

coalgebras in functional programming and type theory this is a survey article on the use of coalgebras in functional programming and type theory it presents the basic theory underlying the implementation of coinductive types families and predicates it gives an overview of the application of corecursive methods to the study of general recursion formal power series tabulations of functions on inductive data it also sketches some advanced topics in the study of the solutions to non guarded corecursive equations and the design of non standard type theory

a theory of binding structures and applications to rewriting abstract in this paper we present a theory of binding structures and give examples of its application to rewriting we define the set of binding structures as an abstract algebra and define a general notion of parameterized homomorphism a variety of operations on binding structures are presented as homomorphisms and a collection of properties useful for developing applications is given three applications are presented a generalized notion of term rewriting a theory of unification for binding structures and a set of structures and primitive rules intended to serve as a basis for design of rewriting components for quantified first order reasoning systems

monoidal indeterminates and categories of possible worlds given any symmetric monoidal category c a small symmetric monoidal category s and a strong monoidal functor j s c we construct c x j s the polynomial category with a system of freely adjoined monoidal indeterminates x i j w natural in w s as a special case we construct the free co affine category symmetric monoidal category with initial unit on a given small symmetric monoidal category we then exhibit all the known categories of possible worlds used to treat languages that allow for dynamic creation of new variables locations or names as instances of this construction and explicate their associated universality properties as an application of the resulting characterization of o w oles s category of possible worlds we present an o w indexed lawvere theory of many sorted storage generalizing the single sorted one introduced by j power and we describe explicitly an associated monad of typed block algebras for local storage

boolean restriction categories and taut monads a boolean category is a restriction category if and only if it has one exception and all morphisms are deterministic in the category of sets taut monads are precisely the boolean ones it follows that collection monad types in haskell inherit an assertion calculus based on dynamic logic

monad transformers as monoid transformers the incremental approach to modular monadic semantics constructs complex monads by using monad transformers to add computational features to a pre existing monad a complication of this approach is that the operations associated to the pre existing monad need to be lifted to the new monad in a companion paper by jaskelioff the lifting problem has been addressed in the setting of system email protected here we recast and extend those results in a category theoretic setting we abstract and generalize from monads to monoids in a monoidal category and from monad transformers to monoid transformers the generalization brings more simplicity and clarity and opens the way for lifting of operations with applicability beyond monads

a first order logic of effects abstract in this paper we describe some of our progress towards an operational implementation of a modern programming logic the logic is inspired by the variable type systems of feferman and is designed for reasoning about imperative functional programs the logic goes well beyond traditional programming logics such as hoare s logic and dynamic logic in its expressibility yet is less problematic to encode into higher order logics the main focus of the paper is to present an axiomatization of the base first order theory

monad as modality abstract in 1989 eugenio moggi proposed a categorical framework for program semantics based on the notion of a strong monad he showed that various kinds of computation can be modeled in his framework on the other hand strong monads are not suited for the categorical semantics of traditional modal logics according to these observations moggi thought that the curryhoward correspondence would not hold between programs and constructive proofs in modal logics however contrary to his view we can show that proofs in a certain kind of modal logics are actually considered as programs in this paper first we shall introduce the notion of an l strong monad which is a generalization of strong monads using this new notion we can generalize moggi s semantics preserving soundness and completeness with respect to his equational logic next we shall show that l strong monads give a sound and complete semantics of a constructive version of s4 modal logic finally we present a method to extract a monad based imperative functional program from a proof in the modal logic interestingly this method can also be understood in terms of l strong monads

a threshold of ln n for approximating set cover given a collection f of subsets of s 1 n setcover is the problem of selecting as few as possiblesubsets from f such that their union covers s and maxk cover is the problem of selecting k subsets from f such that their union has maximum cardinality both these problems arenp hard we prove that 1 o 1 ln n is a threshold below which setcover cannot be approximated efficiently unless np has slightlysuperpolynomial time algorithms this closes the gap up to low orderterms between the ratio of approximation achievable by the greedyalogorithm which is 1 o 1 lnn and provious results of lund and yanakakis that showed hardness ofapproximation within a ratio of log 2 n 2s0 72 ln n for max k cover we show an approximationthreshold of 1 1 e up tolow order terms under assumption that p np

a bisimulation for type abstraction and recursion we present a bisimulation method for proving the contextual equivalence of packages in calculus with full existential and recursive types unlike traditional logical relations either semantic or syntactic our development is elementary using only sets and relations and avoiding advanced machinery such as domain theory admissibility and tt closure unlike other bisimulations ours is complete even for existential types the key idea is to consider sets of relations instead of just relations as bisimulations

a coinductive calculus for asynchronous side effecting processes we present an abstract framework for concurrent processes in which atomic steps have generic side effects handled according to the principle of monadic encapsulation of effects processes in this framework are potentially infinite resumptions modelled using final coalgebras over the monadic base as a calculus for such processes we introduce a concurrent extension of moggi s monadic meta language of effects we establish soundness and completeness of a natural equational axiomatization of this calculus our main result is a corecursion scheme that is explicitly definable over the base language and provides flexible expressive means for the definition of new operators on processes such as parallel composition moreover we present initial results on verification methods for generic side effecting processes

information based objective functions for active data selection learning can be made more efficient if we can actively select particularly salient data points within a bayesian learning framework objective functions are discussed that measure the expected informativeness of candidate measurements three alternative specifications of what we want to gain information about lead to three different criteria for data selection all these criteria depend on the assumption that the hypothesis space is correct which may prove to be their main weakness

a generalization of nash s theorem with higher order functionals the recent theory of sequential games and selection functions by escardo oliva is extended to games in which players move simultaneously the nash existence theorem for mixed strategy equilibria of finite games is generalized to games defined by selection functions a normal form construction is given which generalizes the game theoretic normal form and its soundness is proved minimax strategies also generalize to the new class of games and are computed by the berardi bezem coquand functional studied in proof theory as an interpretation of the axiom of countable choice

combining effects sum and tensor we seek a unified account of modularity for computational effects we begin by reformulating moggi s monadic paradigm for modelling computational effects using the notion of enriched lawvere theory together with its relationship with strong monads this emphasises the importance of the operations that produce the effects effects qua theories are then combined by appropriate bifunctors on the category of theories we give a theory for the sum of computational effects which in particular yields moggi s exceptions monad transformer and an interactive input output monad transformer we further give a theory of the commutative combination of effects their tensor which yields moggi s side effects monad transformer finally we give a theory of operation transformers for redefining operations when adding new effects we derive explicit forms for the operation transformers associated to the above monad transformers

on the asymptotic solution of a high order nonlinear ordinary differential equation we examine berman s similarity solution for steady flow of a viscous incompressible fluid in a channel driven by suction or injection of the fluid through the channel walls we convert the two point boundary value problem for the similarity function into an initial value problem in which the position of the upper channel wall and the reynolds number are determined as part of the solution and consider two cases in the first case equal suction or injection takes place at each wall and solutions are sought that are symmetrical about the mid line of the channel in the second case fluid can pass through only the upper channel wall in each case analysis of a single initial value problem yields two distinct solutions one corresponding to injection the other to suction and our analysis is valid in the limit of large suction or injection the injection solutions are well known for the first symmetrical case the suction solution has previously been given only incompletely while for the second case the asymptotic structure of the solution for large suction has been an open problem we complement our asymptotics with numerical integrations of the ordinary differential equation governing the similarity function and find excellent agreement between the two

robust optimization of contaminant sensor placement for community water systems we present a series of related robust optimization models for placing sensors in municipal water networks to detect contaminants that are maliciously or accidentally injected we formulate sensor placement problems as mixed integer programs for which the objective coefficients are not known with certainty we consider a restricted absolute robustness criteria that is motivated by natural restrictions on the uncertain data and we define three robust optimization models that differ in how the coefficients in the objective vary under one set of assumptions there exists a sensor placement that is optimal for all admissible realizations of the coefficients under other assumptions we can apply sorting to solve each worst case realization efficiently or we can apply duality to integrate the worst case outcome and have one integer program the most difficult case is where the objective parameters are bilinear and we prove its complexity is np hard even under simplifying assumptions we consider a relaxation that provides an approximation giving an overall guarantee of near optimality when used with branch and bound search we present preliminary computational experiments that illustrate the computational complexity of solving these robust formulations on sensor placement applications

domain semantics of possibility computations the purpose of this paper is to introduce a kind of computational model called possibility computation to deal with non determinism both its denotational and logical semantics in the framework of domain theory are established and their equivalence is verified in this approach the denotational semantics will be set up by assigning to programs possibility state transformers i e scott continuous functions from the domain of input states to the possibility powerdomain of the codomain of final states this possibility powerdomain of a dcpo will consist of all possibility valuations ordered pointwise of this dcpo the logical semantics will be given by fuzzy predicate transformers introduced by the first author and jung following dijkstra s predicate transformers two semantics equivalence will be verified in terms of the integration of fuzzy predicates with respect to possibility valuations the categorical monad of the possibility powerdomain will be investigated

on the existence of solutions of an equation arising in the theory of laminar flow in a uniformly porous channel with injection we establish the existence of concave solutions of berman s equation which describes the laminar flow in channels with injection through porous walls it is found that the unique concave solutions exist for all injection reynolds number r 0

a best possible heuristic for the k center problem in this paper we present a 2 approximation algorithm for the k center problem with triangle inequality this result is best possible since for any 2 the existence of approximation algorithm would imply that p np it should be noted that no approximation algorithm for any constant has been reported to date linear programming duality theory provides interesting insight to the problem and enables us to derive in o e log e time a solution with value no more than twice the k center optimal value a by product of the analysis is an o e algorithm that identifies a dominating set in g2 the square of a graph g the size of which is no larger than the size of the minimum dominating set in the graph g the key combinatorial object used is called a strong stable set and we prove the np completeness of the corresponding decision problem

combining algebraic effects with continuations we consider the natural combinations of algebraic computational effects such as side effects exceptions interactive input output and nondeterminism with continuations continuations are not an algebraic effect but previously developed combinations of algebraic effects given by sum and tensor extend with effort to include commonly used combinations of the various algebraic effects with continuations continuations also give rise to a third sort of combination that given by applying the continuations monad transformer to an algebraic effect we investigate the extent to which sum and tensor extend from algebraic effects to arbitrary monads and the extent to which felleisen et al s c operator extends from continuations to its combination with algebraic effects to do all this we use dubuc s characterisation of strong monads in terms of enriched large lawvere theories

sequential games and optimal strategies this article gives an overview of recent work on the theory of selection functions we explain the intuition behind these higher type objects and define a general notion of sequential game whose optimal strategies can be computed via a certain product of selection functions several instances of this game are considered in a variety of areas such as fixed point theory topology game theory higher type computability and proof theory these examples are intended to illustrate how the fundamental construction of optimal strategies based on products of selection functions permeates several research areas

generic weakest precondition semantics from monads enriched with order we devise a generic framework where a weakest precondition semantics in the form of indexed posets is derived from a monad whose kleisli category is enriched by posets it is inspired by jacobs recent identification of a categorical structure that is common in various predicate transformers but adds generality in the following aspects 1 different notions of modality such as may vs must are captured by eilenberg moore algebras 2 nested alternating branching like in games and in probabilistic systems with nondeterministic environments is modularly modeled by a monad on the eilenberg moore category of another

continuity spaces reconciling domains and metric spaces abstract we use continuity spaces a common refinement of posets and metric spaces to develop a general theory of semantic domains which includes metric spaces and domains of cpo s as special cases and provides the appropriate tools for producing new examples which may be suitable for modeling language constructs that occur in concurrent and probabilistic programming our proposal for a general notion of semantic domain is a symmetrically compact continuity space where is a value quantale we show that the category of symmetrically compact continuity spaces with continuous maps has many of the key properties required of a category of domains and that it captures in a natural way the traditional examples in general the category will not be cartesian closed however powerdomains do exist and by adapting a construction of suenderhauf to continuity spaces we show that they define a computational monad in the sense of moggi

existence of solutions for berman s equation from laminar flows in a porous channel with suction abstract we study the berman problem re 2 k re 0 d d subject to the conditions 0 0 1 1 1 0 which arises from laminar flows in a porous channel with suction the existence of nonnegative concave solutions for each re is verified by applying a topological method with an a priori estimate the uniqueness for small re is also shown

coalgebraic semantics for timed processes we give a coalgebraic formulation of timed processes and their operational semantics we model time by a monoid called a time domain and we model processes by timed transition systems which amount to partial monoid actions of the time domain or equivalently coalgebras for an evolution comonad generated by the time domain all our examples of time domains satisfy a partial closure property yielding a distributive law of a monad for total monoid actions over the evolution comonad and hence a distributive law of the evolution comonad over a dual comonad for total monoid actions we show that the induced coalgebras are exactly timed transition systems with delay operators we then integrate our coalgebraic formulation of time qua timed transition systems into turi and plotkin s formulation of structural operational semantics in terms of distributive laws we combine timing with action via the more general study of the combination of two arbitrary sorts of behaviour whose operational semantics may interact we give a modular account of the operational semantics for a combination induced by that of each of its components our study necessitates the investigation of products of comonads in particular we characterise when a monad lifts to the category of coalgebras for a product comonad providing constructions with which one can readily calculate

stable power domains abstract in the category of stable dcpo s free constructions w r t algebraic theories exist from this we obtain various stable power domain constructions after handling their properties in general we concentrate on the stable plotkin power construction for continuous ground domains it is explicitly described in terms of saturated compact sets in case of algebraic ground domains this description is isomorphic to buneman s lossless power domains

general bounds for incremental maximization we propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems the defining characteristic of our framework is that the cardinality support of the solution is bounded by a value k in mathbb n that grows over time and we allow the solution to be extended one element at a time we investigate the best possible competitive ratio of such an incremental solution i e the worst ratio over all k between the incremental solution after k steps and an optimum solution of cardinality k we consider a large class of problems that contains many important cardinality constrained maximization problems like maximum matching knapsack and packing covering problems we provide a general 2 618 competitive incremental algorithm for this class of problems and we show that no algorithm can have competitive ratio below 2 18 in general in the second part of the paper we focus on the inherently incremental greedy algorithm that increases the objective value as much as possible in each step this algorithm is known to be 1 58 competitive for submodular objective functions but it has unbounded competitive ratio for the class of incremental problems mentioned above we define a relaxed submodularity condition for the objective function capturing problems like maximum weighted d dimensional matching maximum weighted b matching and a variant of the maximum flow problem we show a general bound for the competitive ratio of the greedy algorithm on the class of problems that satisfy this relaxed submodularity condition our bound generalizes the tight bound of 1 58 slightly beyond sub modular functions and yields a tight bound of 2 313 for maximum weighted b matching our bound is also tight for a more general class of functions as the relevant parameter goes to infinity note that our upper bounds on the competitive ratios translate to approximation ratios for the underlying cardinality constrained problems and our bounds for the greedy algorithm carry over both

robust submodular observation selection in many applications one has to actively select among a set of expensive observations before making an informed decision for example in environmental monitoring we want to select locations to measure in order to most effectively predict spatial phenomena often we want to select observations which are robust against a number of possible objective functions examples include minimizing the maximum posterior variance in gaussian process regression robust experimental design and sensor placement for outbreak detection in this paper we present the submodular saturation algorithm a simple and efficient algorithm with strong theoretical approximation guarantees for cases where the possible objective functions exhibit submodularity an intuitive diminishing returns property moreover we prove that better approximation algorithms do not exist unless np complete problems admit efficient algorithms we show how our algorithm can be extended to handle complex cost functions incorporating non unit observation cost or communication and path costs we also show how the algorithm can be used to near optimally trade off expected case e g the mean square prediction error in gaussian process regression and worst case e g maximum predictive variance performance we show that many important machine learning problems fit our robust submodular observation selection formalism and provide extensive empirical evaluation on several real world problems for gaussian process regression our algorithm compares favorably with state of the art heuristics described in the geostatistics literature while being simpler faster and providing theoretical guarantees for robust experimental design our algorithm performs favorably compared to sdp based algorithms c 2008 andreas krause h brendan mcmahan carlos guestrin and anupam gupta krause mcmahan guestrin and gupta

precoder design for physical layer multicasting this paper studies the instantaneous rate maximization and the weighted sum delay minimization problems over a k user multicast channel where multiple antennas are available at the transmitter as well as at all the receivers motivated by the degree of freedom optimality and the simplicity offered by linear precoding schemes we consider the design of linear precoders using the aforementioned two criteria we first consider the scenario wherein the linear precoder can be any complex valued matrix subject to rank and power constraints we propose cyclic alternating ascent based precoder design algorithms and establish their convergence to respective stationary points simulation results reveal that our proposed algorithms considerably outperform known competing solutions we then consider a scenario in which the linear precoder can be formed by selecting and concatenating precoders from a given finite codebook of precoding matrices subject to rank and power constraints we show that under this scenario the instantaneous rate maximization problem is equivalent to a robust submodular maximization problem which is strongly np hard we propose a deterministic approximation algorithm and show that it yields a bicriteria approximation for the weighted sum delay minimization problem we propose a simple deterministic greedy algorithm which at each step entails approximately maximizing a submodular set function subject to multiple knapsack constraints and establish its performance guarantee

a syntactic theory of sequential state abstract the assignment statement is a ubiquitous building block of programming languages in functionally oriented programming languages the assignment is the facility for modeling and expressing state changes given that functional languages are directly associated with the equational calculus theory it is natural to wonder whether this syntactic proof system is extensible to imperative variants of functional languages including state variables and side effects in this paper we show that such an extension exists and that it satisfies variants of the conventional consistency and standardization theorems with a series of examples we also demonstrate the system s capabilities for reasoning about imperative functional programs and illustrate some of its advantages over alternative models

formal security proofs with minimal fuss we show how implicit computational complexity can be used in order to increase confidence in game based security proofs in cryptography for this purpose we extend cslr a probabilistic lambda calculus with a type system that guarantees the existence of a probabilistic polynomial time bound on computations this allows us to define cryptographic constructions feasible adversaries security notions computational assumptions game transformations and game based security proofs in a unified framework we also show that the standard practice of cryptographers ignoring that polynomial time turing machines cannot generate all uniform distributions is actually sound we illustrate our calculus on cryptographic constructions for public key encryption and pseudorandom bit generation

strong normalization from weak normalization in typedλ calculi for some typed calculi it is easier to prove weak normalization than strong normalization techniques to infer the latter from the former have been invented over the last twenty years by nederpelt klop khasidashvili karr de groote and kfoury and wells however these techniques infer strong normalization of one notion of reduction from weak normalization of amore complicatednotion of reduction this paper presents a new technique to infer strong normalization of a notion of reduction in a typed calculus from weak normalization of thesamenotion of reduction the technique is demonstrated to work on some well known systems including second order calculus and the system of positive recursive types it gives hope for a positive answer to the barendregt geuvers conjecture stating that every pure type system which is weakly normalizing is also strongly normalizing the paper also analyzes the relationship between the techniques mentioned above and reviews in less detail other techniques for proving strong normalization

full abstractness for a functional concurrent language with higher order value passing we study an applied typed call by value calculus which in addition to the usual types for higher order functions contains an extra type called proc for processes the constructors for terms of this type are similar to those found in standard process calculi such as ccs we first give an operational semantics for this language in terms of a labelled transition system which is then used to give a behavioural preorderbased on contexts the expression n dominates m if in every appropriate context if m can produce a boolean value then so can n

robust monotone submodular function maximization we consider a robust formulation introduced by krause et al j artif intell res 42 427 486 2011 of the classical cardinality constrained monotone submodular function maximization problem and give the first constant factor approximation results the robustness considered is w r t adversarial removal of up to tau elements from the chosen set for the fundamental case of tau 1 we give a deterministic 1 1 e 1 vartheta m approximation algorithm where m is an input parameter and number of queries scale as o n m 1 in the process we develop a deterministic 1 1 e 1 vartheta m approximate greedy algorithm for bi objective maximization of two monotone submodular functions generalizing the ideas and using a result from chekuri et al in focs 10 ieee pp 575 584 2010 we show a randomized 1 1 e epsilon approximation for constant tau and epsilon le frac 1 tilde varomega tau making o n 1 epsilon 3 queries further for tau ll sqrt k we give a fast and practical 0 387 algorithm finally we also give a black box result result for the much more general setting of robust maximization subject to an independence system

a theory of bisimulation for a fragment of concurrent ml with local names concurrent ml is an extension of standard ml with calculus like primitives for multithreaded programming cml has a reduction semantics but to date there has been no labelled transition system semantics provided for the entire language in this paper we present a labelled transition semantics for a fragment of cml called vcml which includes features not covered before dynamically generated local channels and thread identifiers we show that weak bisimilarity for vcml is a congruence and coincides with barbed bisimulation congruence we also provide a variant of sangiorgi s normal bisimulation for vcml and show that this too coincides with bisimilarity

comparing logics for rewriting the large diffusion of concurrent and distributed systems has spawned in recent years a variety of new formalisms equipped with features for supporting an easy specification of such systems the aim of our paper is to analyze three proposals namely rewriting logic action calculi and tile logic chosen among those formalisms designed for the description of rule based systems for each of these logics we first try to understand their foundations then we briefly sketch some applications the overall goal of our work is to find out a common layout where these logics can be recast thus allowing for a comparison and an evaluation of their specific features

an equational notion of lifting monad we introduce the notion of an equational lifting monad a commutative strong monad satisfying one additional equation valid for monads arising from partial map classifiers we prove that any equational lifting monad has a representation by a partial map classifier such that the kleisli category of the former fully embeds in the partial category of the latter thus equational lifting monads precisely capture the equational properties of partial maps as induced by partial map classifiers the representation theorem also provides a tool for transferring nonequational properties of partial map classifiers to equational lifting monads it is proved using a direct axiomatization of kleisli categories of equational lifting monads this axiomatization is of interest in its own right

robust discrete optimization and network flows we propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution and is computationally tractable both practically and theoretically in particular when both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty we propose a robust integer programming problem of moderately larger size that allows controlling the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation when only the cost coefficients are subject to uncertainty and the problem is a 0 1 discrete optimization problem on n variables then we solve the robust counterpart by solving at most n 1 instances of the original problem thus the robust counterpart of a polynomially solvable 0 1 discrete optimization problem remains polynomially solvable in particular robust matching spanning tree shortest path matroid intersection etc are polynomially solvable we also show that the robust counterpart of an np hard approximable 0 1 discrete optimization problem remains approximable finally we propose an algorithm for robust network flows that solves the robust counterpart by solving a polynomial number of nominal minimum cost flow problems in a modified network

a formal abstract framework for modelling and testing complex software systems the contribution of this paper is twofold first it defines a unified framework for modelling abstract components as well as a formalization of integration rules to combine their behaviour this is based on a coalgebraic definition of components which is a categorical representation allowing the unification of a large family of formalisms for specifying state based systems second it studies compositional conformance testing i e checking whether an implementation made of correct interacting components combined with integration operators conforms to its specification

combining a monad and a comonad we give a systematic treatment of distributivity for a monad and a comonad as arises in giving category theoretic accounts of operational and denotational semantics and in giving an intensional denotational semantics we do this axiomatically in terms of a monad and a comonad in a 2 category giving accounts of the eilenberg moore and kleisli constructions we analyse the eight possible relationships deducing that two pairs are isomorphic but that the other pairs are all distinct we develop those 2 categorical definitions necessary to support this analysis

lifting results for categories of algebras in this paper we present results that provide an abstract setting for the construction and interpretation of categories of algebras appearing in various semantic examples including those related to scott domains and cartesian closed categories a methodology is introduced that lifts adjoint pairs on categories with monads to categories whose objects are algebras for these monads results are achieved by exploiting prior work on kleisli liftings and the existence of key isomorphisms while applicable to domain theory and the semantics of partiality the construction at work is considerably more general and is applicable to other settings as well

cut free gentzen calculus for multimodal ck this paper extends previous work on the modal logic ck as a reference system both proof theoretically and model theoretically for a correspondence theory of constructive modal logics first the fundamental nature of ck is discussed and compared with the intuitionistic modal logic ik which is traditionally taken to be the base line then it is shown that ck admits of a cut free gentzen sequent calculus g ck which has i a local interpretation in constructive kripke models and ii does not require explicit world labels finally the paper demonstrates how non classical modal logics such as ik cs4 cl or email protected s deontic system of 2 sequents arise as theories of ck presented both as special rules and as frame classes

clustering to minimize the maximum intercluster distance the problem of clustering a set of points so as to minimize the maximum intercluster distance is studied an o kn approximation algorithm where n is the number of points and k is the number of clusters that guarantees solutions with an objective function value within two times the optimal solution value is presented this approximation algorithm succeeds as long as the set of points satisfies the triangular inequality we also show that our approximation algorithm is best possible with respect to the approximation bound if pz np

the category theoretic solution of recursive domain equations recursive specifications of domains plays a crucial role in denotational semantics as developed by scott and strachey and their followers the purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place the idea is to follow the well known analogy between partial orders and categories generalizing from least fixed points of continuous functions over cpos to initial ones of continuous functors over omega categories to apply these general ideas we introduce wand s bf o categories where the morphism sets have a partial order structure and which include almost all the categories occurring in semantics the idea is to find solutions in a derived category of embeddings and we give order theoretic conditions which are easy to verify and which imply the needed categorical ones the main tool is a very general form of the limit colimit coincidence remarked by scott in the concluding section we outline how compatibilit

near optimal sensor placements in gaussian processes theory efficient algorithms and empirical studies when monitoring spatial phenomena which can often be modeled as gaussian processes gps choosing sensor locations is a fundamental task there are several common strategies to address this task for example geometry or disk models placing sensors at the points of highest entropy variance in the gp model and a d or e optimal design in this paper we tackle the combinatorial optimization problem of maximizing the mutual information between the chosen locations and the locations which are not selected we prove that the problem of finding the configuration that maximizes mutual information is np complete to address this issue we describe a polynomial time approximation that is within 1 1 e of the optimum by exploiting the submodularity of mutual information we also show how submodularity can be used to obtain online bounds and design branch and bound search procedures we then extend our algorithm to exploit lazy evaluations and local structure in the gp yielding significant speedups we also extend our approach to find placements which are robust against node failures and uncertainties in the model these extensions are again associated with rigorous theoretical approximation guarantees exploiting the submodularity of the objective function we demonstrate the advantages of our approach towards optimizing mutual information in a very extensive empirical study on two real world data sets

learning from minimum entropy queries in a large committee machine in supervised learning the redundancy contained in random examples can be avoided by learning from queries using statistical mechanics we study learning from minimum entropy queries in a large tree committee machine the generalization error decreases exponentially with the number of training examples providing a significant improvement over the algebraic decay for random examples the connection between entropy and generalization error in multi layer networks is discussed and a computationally cheap algorithm for constructing queries is suggested and analysed

the oscillatory channel flow with large wall injection in the presence of smallamplitude pressure oscillations the linearized navierstokes equations are solved to obtain an accurate description of the timedependent field in a channel having a rectangu

similarity solutions of steady flows in a channel with accelerating walls abstract we study the boundary layer equation f r ff f 2 0 subject to the conditions f 0 f 0 f 1 f 1 1 0 and f 1 f 1 f 1 f 1 1 0 respectively which arises from the study of two dimensional steady flows in a channel with two equally accelerating walls or one accelerating wall the preliminary classification of possible solutions was introduced by cox 1 in this paper we are able to verify the existence of families of solutions as indicated from the numerical computations moreover multiple solutions for some positive r and local uniqueness are also obtained

modelling environments in call by value programming languages in categorical semantics there have traditionally been two approaches to modelling environments one by use of finite products in cartesian closed categories the other by use of the base categories of indexed categories with structure each requires modifications in order to account for environments in call by value programming languages there have been two more general definitions along both of these lines the first generalising from cartesian to symmetric premonoidal categories the second generalising from indexed categories with specified structure to categories in this paper we investigate environments in call by value languages by analysing a fine grain variant of moggi s computational calculus giving two equivalent sound and complete classes of models one given by closed freyd categories which are based on symmetric premonoidal categories the other given by closed categories

on the algebraic structure of declarative programming languages we develop an algebraic framework logic programming doctrines for the syntax proof theory operational semantics and model theory of horn clause logic programming based on indexed premonoidal categories our aim is to provide a uniform framework for logic programming and its extensions capable of incorporating constraints abstract data types features imported from other programming language paradigms and a mathematical description of the state space in a declarative manner we define a new way to embed information about data into logic programming derivations by building a sketch like description of data structures directly into an indexed category of proofs we give an algebraic axiomatization of bottom up semantics in this general setting describing categorical models as fixed points of a continuous operator

a new foundation for finitary corecursion and iterative algebras abstract this paper contributes to a generic theory of behaviour of finite state systems systems are coalgebras with a finitely generated carrier for an endofunctor on a locally finitely presentable category their behaviour gives rise to the locally finite fixpoint lff a new fixpoint of the endofunctor the lff exists provided that the endofunctor is finitary and preserves monomorphisms is a subcoalgebra of the final coalgebra i e it is fully abstract w r t behavioural equivalence and it is characterized by two universal properties as the final locally finitely generated coalgebra and as the initial fg iterative algebra instances of the lff are regular languages rational streams rational formal power series regular trees etc moreover we obtain e g realtime deterministic resp non deterministic context free languages constructively s algebraic formal power series in general the behaviour of finite coalgebras under the coalgebraic language semantics arising from the generalized powerset construction by silva bonchi bonsangue and rutten and the monad of courcelle s algebraic trees

categories of rough sets and textures abstract it is known that the theories of rough sets and fuzzy sets have successful applications in computing textures as a theoretical model provide a new perspective for both rough sets and fuzzy sets indeed recent papers have shown that there is a natural link between rough sets and textures while a texture is an alternative point set based setting for fuzzy sets relations are representatives of information systems and induce approximation operators therefore the first step for the categorical discussions on rough sets involves the category rel of sets and relations in this context we observe that power sets and pairs of rough set approximation operators form a category denoted by r apr in particular we prove that r apr is isomorphic to a full subcategory of the category cdrtex whose objects are complemented textures and morphisms are complemented direlations therefore cdrtex may be regarded as a suitable abstract model of rough set theory here we show that r apr and cdrtex are new examples of dagger symmetric monoidal categories

powersets of terms and composite monads composing various powerset functors with the term monad gives rise to the concept of generalized terms this in turn provides a technique for handling many valued sets of terms in a framework of variable substitutions thus being the prerequisite for categorical unification in many valued logic programming using an extended notion of terms as constructions of monads involve complicated calculations with natural transformations proofs are supported by a graphical approach that provides a useful tool for handling various conditions such as those well known for distributive laws

the lambda context calculus extended version we present the lambda context calculus this simple lambda calculus features variables arranged in a hierarchy of strengths such that substitution of a strong variable does not avoid capture with respect to abstraction by a weaker variable this allows the calculus to express both capture avoiding and capturing substitution instantiation the reduction rules extend the vanilla lambda calculus in a simple and modular way and preserve the look and feel of a standard lambda calculus with explicit substitutions good properties of the lambda calculus are preserved the lamcc is confluent and a natural injection into the lamcc of the untyped lambda calculus exists and preserves strong normalisation we discuss the calculus and its design with full proofs in the presence of the hierarchy of variables functional binding splits into a functional abstraction l lambda and a name binder new we investigate how the components of this calculus interact with each other and with the reduction rules with examples in two more extended case studies we demonstrate how global state can be expressed and how contexts and contextual equivalence can be naturally internalised using function application

a fully abstract denotational semantics for the π calculus this paper describes the construction of two set theoretic denotational models for the p calculus the models are obtained as initial solutions to domain equations in a functor category by associating with each syntactic construct of the p calculus a natural transformation over these models we obtain two interpretations for the language we also show that these models are fully abstract with respect to natural behavioural preorders over terms in the language by this we mean that two terms are related behaviourally if and only if their interpretations in the model are related the behavioural preorders are the standard versions of may and must testing adapted to the p calculus

on the call by value cps transform and its semantics we investigate continuations in the context of idealized call by value programming languages on the semantic side we analyze the categorical structures that arise from continuation models of call by value languages on the syntactic side we study the call by value continuation passing transformation as a translation between equational theories among the novelties are an unusually simple axiomatization of control operators and a strengthened completeness result with a proof based on a delaying transform

premonoidal categories as categories with algebraic structure we develop the study of premonoidal categories specifically we reconcile premonoidal categories with the usual study of categories with algebraic structure by adding a little extra structure we further give a notion of closedness for a premonoidal category with such extra structure and show that every premonoidal category fully embeds into a closed one

a combinatorial strongly polynomial algorithm for minimizing submodular functions this paper presents a combinatorial polynomial time algorithm for minimizing submodular functions answering an open question posed in 1981 by grotschel lovasz and schrijver the algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter the resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the length of the largest absolute function value the paper also presents a strongly polynomial version in which the number of steps is bounded by a polynomial in the size of the underlying set independent of the function values

eilenberg moore algebras for stochastic relations we investigate the category of eilenberg moore algebras for the giry monad associated with stochastic relations over polish spaces with continuous maps as morphisms the algebras are identified as the positive convex structures on the base space the forgetful functor assigning a positive convex structure the underlying polish space has the stochastic powerdomain as its left adjoint

vortical and acoustical mode coupling inside a porous tube with uniform wall suction this paper considers the oscillatory motion of gases inside a long porous tube of the closed open type in particular the focus is placed on describing an analytical solution for the internal acoustico vortical coupling that arises in the presence of appreciable wall suction this unsteady field is driven by longitudinal oscillatory waves that are triggered by small unavoidable fluctuations in the wall suction speed under the assumption of small amplitude oscillations the time dependent governing equations are linearized through a regular perturbation of the dependent variables further application of the helmholtz vector decomposition theorem enables us to discriminate between acoustical and vortical equations after solving the wave equation for the acoustical contribution the boundary driven vortical field is considered the method of matched asymptotic expansions is then used to obtain a closed form solution for the unsteady momentum equation developing from flow decomposition an exact series expansion is also derived and shown to coincide with the numerical solution for the problem the numerically verified end results suggest that the asymptotic scheme is capable of providing a sufficiently accurate solution this is due to the error associated with the matched asymptotic expansion being smaller than the error introduced in the navier stokes linearization a basis for comparison is established by examining the evolution of the oscillatory field in both space and time the corresponding boundary layer behavior is also characterized over a range of oscillation frequencies and wall suction velocities in general the current solution is found to exhibit features that are consistent with the laminar theory of periodic flows by comparison to the sexl profile in nonporous tubes the critically damped solution obtained here exhibits a slightly smaller overshoot and depth of penetration these features may be attributed to the suction effect that tends to attract the shear layers closer the wall

notions of computation and monads abstract the calculus is considered a useful mathematical tool in the study of programming languages since programs can be identified with terms however if one goes further and uses conversion to prove equivalence of programs then a gross simplification is introduced programs are identified with total functions from values to values that may jeopardise the applicability of theoretical results in this paper we introduce calculi based on a categorical semantics for computations that provide a correct basis for proving equivalence of programs for a wide range of notions of computation

the semantics of second order lambda calculus abstract in the second order polymorphic typed lambda calculus lambda abstraction over type variables leads to terms denoting polymorphic functions straightforward cardinality considerations show that a naive set theoretic interpretation of the calculus is impossible we give two definitions of semantic models for this language and prove them equivalent our syntactical environment model definition and a more algebraic combinatory model definition for the polymorphic calculus correspond to analogous model definitions for untyped lambda calculus soundness and completeness theorems are proved using the environment model definition we verify that some specific interpretations of the calculus proposed in the literature indeed yield models in our sense

generalized submodular cover problems and applications the greedy approach has been successfully applied in the past to produce logarithmic ratio approximations to np hard problems under certain conditions the problems for which these conditions hold are known as submodular cover problems the current paper3extends the applicability of the greedy approach to wider classes of problems the usefulness of our extensions is illustrated by giving new approximate solutions for two different types of problems the first problem is that of finding the spanning tree of minimum weight among those whose diameter is bounded by d a logarithmic ratio approximation algorithm is given for the cases of d 4 and 5 this approximation ratio is also proved to be the best possible unless p np the second type involves some known and new center selection problems for which new logarithmic ratio approximation algorithms are given again it is shown that the ratio must be at least logarithmic unless p np

asymmetric k center is log n hard to approximate in the asymmetric k center problem the input is an integer k and a complete digraph over n points together with a distance function obeying the directed triangle inequality the goal is to choose a set of k points to serve as centers and to assign all the points to the centers so that the maximum distance of any point from its center is as small as possible we show that the asymmetric k center problem is hard to approximate up to a factor of log n o 1 unless np dtime nlog log n since an o log n approximation algorithm is known for this problem this resolves the asymptotic approximability of asymmetric k center this is the first natural problem whose approximability threshold does not polynomially relate to the known approximation classes we also resolve the approximability threshold of the metric symmetric k center problem with costs

a fully abstract semantics for a higher order functional language with nondeterministic computation abstract this paper presents a functional programming language based on moggi s monadic metalanguage in the first part of this paper we show how the language can be regarded as a monad on a category of signatures and that the resulting category of algebras is equivalent to the category of computationally cartesian closed categories in the second part we extend the language to include a nondeterministic operational semantics and show that the lower powerdomain semantics is fully abstract for may testing

on the complexity of a class of combinatorial optimization problems with uncertainty we consider a robust minmax regret version of the problem of selecting p elements of minimum total weight out of a set of m elements with uncertainty in weights of the elements we present a polynomial algorithm with the order of complexity o min p m p 2m for the case where uncertainty is represented by means of interval estimates for the weights we show that the problem is np hard in the case of an arbitrary finite set of possible scenarios even if there are only two possible scenarios this is the first known example of a robust combinatorial optimization problem that is np hard in the case of scenario represented uncertainty but is polynomially solvable in the case of the interval representation of uncertainty

robust experimental design for multivariate generalized linear models a simple heuristic is proposed for constructing robust experimental designs for multivariate generalized linear models the method is based on clustering a set of local optimal designs a method for finding local d optimal designs using available resources is also introduced clustering with its simplicity and minimal computation needs is demonstrated to outperform more complex and sophisticated methods