module algebra an axiomatic algebraic calculus of modules is given that is based on the operators combination union export renaming and taking the visible signature four different models of module algebra are discussed and compared

the scaling mean and a law of large permanents abstract in this paper we study two types of means of the entries of a nonnegative matrix the permanental mean which is defined using permanents and the scaling mean which is defined in terms of an optimization problem we explore relations between these two means making use of important results by egorychev and falikman the van der waerden conjecture friedland sinkhorn and others we also define a scaling mean for functions in a much more general context our main result is a law of large permanents a pointwise ergodic theorem for permanental means of dynamically defined matrices that expresses the limit as a functional scaling mean the concepts introduced in this paper are general enough so to include as particular cases certain classical types of means as for example symmetric means and muirhead means as a corollary we reobtain a formula of halasz and szekely for the limit of the symmetric means of a stationary random process

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

specification and proof in membership equational logic this paper is part of a long term effort to increase expressiveness of algebraic specification languages while at the same time having a simple semantic basis on which efficient execution by rewriting and powerful theorem proving tools can be based in particular our rewriting techniques provide semantic foundations for maude s functional sublanguage where they have been efficiently implemented

petri nets are moniods abstract petri nets are widely used to model concurrent systems however their composition and abstraction mechanisms are inadequate we solve this problem in a satisfactory way we start by remarking that place transition petri nets can be viewed as ordinary directed graphs equipped with two algebraic operations corresponding to parallell and sequential composition of transitions a distributive law between the two operations captures a basic fact about concurrency new morphisms are defined mapping single atomic transitions into whole computations thus relating system descriptions at different levels of abstraction categories equipped with products and coproducts corresponding to parallel and nondeterministic compositions are introduced for petri nets with and without initial markings petri net duality is expressed as a duality functor and several new invariants are introduced a tensor product is defined on nets and their category is proved to be symmetric monoidal closed this construction is generalized to a large class of algebraic theories on graphs these results provide a formal basis for expressing the semantics of concurrent languages in terms of petri nets they also provide a new understanding of concurrency in terms of algebraic structures over graphs and categories that should apply to other models besides petri nets and thus contribute to the conceptual unification of concurrency

goal oriented error estimation and adaptivity for fluid structure interaction using exact linearized adjoints we develop duality based a posteriori error estimates for functional outputs of solutions of steady fluid structure interaction problems the crucial complication in obtaining these estimates pertains to the derivation of the coupled dual exact linearized adjoint problem owing to the free boundary character of fluid structure interaction we present two approaches to derive the dual problem in the domain map linearization approach the fluid subproblem is first transformed to a fixed reference domain after which one essentially linearizes with respect to the domain transformation map in the shape linearization approach fluid unknowns are fixed in the current configuration and a very weak formulation of the fluid subproblem is then linearized using shape derivative techniques we show that the dual problems correspond to coupled fluid structure problems with nonstandard coupling conditions furthermore we present numerical experiments that demonstrate the consistency of the dual based error estimates and their usefulness in goal oriented adaptive mesh refinement

scalings of matrices satisfying line product constraints and generalizations abstract a scaling of a nonnegative matrix a is a matrix having the form a uav where u and v are square diagonal matrices which have positive diagonal elements if the matrix a is square and v u 1 we call a a symmetric scaling of a we consider two problems the first concerns the identification of a scaling of a given nonnegative matrix with prescribed row and column products the second concerns the problem of finding a symmetric scaling of a given nonnegative square matrix whose row products equal the corresponding column products for each of these two scaling problems we characterize the solutions in terms of a nonlinear convex optimization problem we use the characterization to demonstrate that feasibility of either scaling problem is equivalent to the existence of a matrix satisfying the target property and having the same pattern as the given matrix we establish uniqueness of solutions to either scaling problem whenever it is feasible and we develop algorithms for computing the desired unique scalings in the cases where the problem are feasible

initial and final algebra semantics for data type specifications two characterization theorems we prove that those data types which may be defined by conditional equation specifications and final algebra semantics are exactly the cosemicomputable data types those data types which are effectively computable but whose inequality relations are recursively enumerable and we characterize the computable data types as those data types which may be specified by conditional equation specifications using both initial algebra semantics and final algebra semantics numerical bounds for the number of auxiliary functions and conditional equations required are included in both theorems

applications of an inequality in information theory to matrices abstract if x and y are nonnegative vectors of order n and if n i 1 x i n i 1 y i then a well known inequality asserts that n i 1 x x i i n i 1 y x i i with equality if and only if x y in this paper various situations are considered where this inequality can be applied to obtain inequalities concerning nonnegative matrices in particular inequalities are proved concerning nonnegative matrices which are diagonally equivalent permanents and functions more general than the permanent and diagonal products and circuit products of nonnegative matrices

institutional semantics for many valued logics we develop many valued logic including a generic abstract model theory over a fully abstract syntax we show that important many valued logic model theories such as traditional first order many valued logic and fuzzy multi algebras may be conservatively embedded into our abstract framework our development is technically based upon the so called theory of institutions of goguen and burstall and may serve as a template for defining at hand many valued logic model theories over various concrete syntaxes or from another perspective to combine many valued logic with other logical systems we also show that our generic many valued logic abstract model theory enjoys a couple of important institutional model theory properties that support the development of deep model theory methods

d1ad2 theorems for multidimensional matrices abstract a new technique for proving d 1 ad 2 theorems is given also a generalization of d 1 ad 2 theorems to multidimensional matrices is indicated

on the complexity of general matrix scaling and entropy minimization via the ras algorithm given an n m nonnegative matrix a a ij and positive integral vectors r e n and c e m having a common one norm h the r c scaling problem is to obtain positive diagonal matrices x and y if they exist such that xay has row and column sums equal to r and c respectively the entropy minimization problem corresponding to a is to find an n m matrix z z ij having the same zero pattern as a the sum of whose entries is a given number h its row and column sums are within given integral vectors of lower and upper bounds and such that the entropy function consisting of the sum of the terms z ij ln z ij a ij is minimized when the lower and upper bounds coincide matrix scaling and entropy minimization are closely related in this paper we present several complexity bounds for the e approximate r c scaling problem polynomial in n m h 1 e and ln v v where v and v are the largest and the smallest positive entries of a respectively these bounds although not polynomial in ln 1 1 e not only provide alternative complexities for the polynomial time algorithms but could result in better overall complexities in particular our theoretical analysis supports the practicality of the well known ras algorithm in our analysis we obtain bounds on the norm of scaling vectors which will be used in deriving not only some of the above complexities but also a complexity for square nonnegative matrices having positive permanent in particular our results extend nontrivially many bounds for the doubly stochastic scaling of square nonnegative matrices previously given by kalantari and khachiyan to the case of general r c scaling finally we study a more general entropy minimization problem where row and column sums are constrained to lie in prescribed intervals and the sum of all entries is also prescribed balinski and demange described an ras type algorithm for its continuous version but did not analyze its complexity we show that this algorithm produces an 1 e approximate solution within complexity polynomial in n m h v v and 1 1 e

on the scaling of multidimensional matrices abstract elementary proofs are given for theorems of bapat and raghavan on the scaling of nonnegative multidimensional matrices theorems of sinkhorn and of brualdi parter and schneider are derived as corollaries for positive two dimensional matrices hilbert s projective metric and a theorem of g birkhoff are used to prove that sinkhorn s original iterative procedure converges geometrically the ratio of convergence is estimated from the given data

an axiomatic approach to structuring specifications in this paper we develop an axiomatic approach to structured specifications in which both the underlying logical system and corresponding institution of the structured specifications are treated as abstract institutions which means two levels of institution independence this abstract axiomatic approach provides a uniform framework for the study of structured specifications independently from any actual choice of specification building operators and moreover it unifies the theory and the model oriented approaches within this framework we develop concepts and results about abstract structured specifications such as co limits model amalgamation compactness interpolation sound and complete proof theory and pushout style parameterization with sharing all of them in a top down manner dictated by the upper level of institution independence

specification of abstract dynamic data types a temporal logic approach abstract a concrete dynamic data type is just a partial algebra with predicates such that for some of the sorts there is a special predicate defining a transition relation an abstract dynamic data type ad dt is an isomorphism class of such algebras to obtain specifications for ad dt s we propose a logic which combines many sorted first order logic with branching time combinators we consider both an initial and a loose semantics for our specifications and give sufficient conditions for the existence of the initial models then we discuss structured specifications and implementation

hydrodynamic singular regimes in 1 1 kinetic models and spectral numerical methods classical results from spectral theory of stationary linear kinetic equations are applied to efficiently approximate two physically relevant weakly nonlinear kinetic models a model of chemotaxis involving a biased velocity redistribution integral term and a vlasov fokker planck vfp system both are coupled to an attractive elliptic equation producing corresponding mean field potentials spectral de compositions of stationary kinetic distributions are recalled based on a variation of case s elementary solutions for the first model and on a sturm liouville eigenvalue problem for the second one well balanced godunov schemes with strong stability properties are deduced moreover in the stiff hydrodynamical scaling an hybridized algorithm is set up for which asymptotic preserving properties can be established under mild restrictions on the computational grid several numerical validations are displayed including the consistency of the vfp model with burgers hopf dynamics on the velocity field after blowup of the macroscopic density into dirac masses

interval constrained matrix balancing abstract we define two interval constrained matrix balancing problems the models encompass several known formulations of problems that appear in regional input output analysis estimation of traffic over transportation and telecommunications networks and estimation of social accounting matrices we develop primal dual row action algorithms for the solution of these models and establish their convergence both algorithms generalize existing scaling algorithms for equality constrained matrix balancing problems one of the algorithms is a generalization of the well known procedure for matrix balancing called ras that can handle the range constraints and is thus called range ras the structure of the problem makes the algorithm suitable for implementation on massively parallel computers details of our implementation on a connection machine cm 2 are given numerical results for the solution of problems of size up to 500 500 are given and the performance of the algorithm is compared with that of ras

ultraproducts and possible worlds semantics in institutions we develop possible worlds kripke semantics at the categorical abstract model theoretic level provided by the so called institutions our general abstract modal logic framework provides a method for systematic kripke semantics extensions of logical systems from computing science and logic we also extend the institution independent method of ultraproducts of r diaconescu institution independent ultraproducts fundamenta informaticae 55 3 4 2003 321 348 to possible worlds semantics and prove a fundamental preservation result for abstract modal satisfaction as a consequence we develop a generic compactness result for possible worlds semantics

strings chains and ropes following antman amer math mon 87 1980 pp 359 370 we advocate a more physically realistic and systematic derivation of the wave equation suitable for a typical undergraduate course in partial differential equations to demonstrate the utility of this derivation three applications that follow naturally are described strings hanging chains and jump ropes

order sorted algebra i equational deduction for multiple inheritance overloading exceptions and partial operations abstract this paper generalizes many sorted algebra msa to order sorted algebra osa by allowing a partial ordering relation on the set of sorts this supports abstract data types with multiple inheritance in roughly the sense of object oriented programming several forms of polymorphism and overloading partial operations as total on equationally defined subsorts exception handling and an operational semantics based on term rewriting we give the basic algebraic constructions for osa including quotient image product and term algebra and we prove their basic properties including quotient homomorphism and initiality theorems the paper s major mathematical results include a notion of osa deduction a completeness theorem for it and an osa birkhoff variety theorem we also develop conditional osa including initiality completeness and mckinsey malcev quasivariety theorems and we reduce osa to conditional msa which allows lifting many known msa results to osa retracts which intuitively are left inverses to subsort inclusions provide relatively inexpensive run time error handling we show that it is safe to add retracts to any osa signature in the sense that it gives rise to a conservative extension a final section compares and contrasts many different approaches to osa this paper also includes several examples demonstrating the flexibility and applicability of osa including some standard benchmarks like stack and list as well as a much more substantial example the number hierarchy from the naturals up to the quaternions

generalized scalings satisfying linear equations abstract we unify and generalize a broad class of problems referred in the literature as scaling problems by extending the applicability of a formulation suggested recently by bapat and raghavan specifically let a r n b r m and c r m n be given where a is strictly positive a c scaling of the vector a is defined to be a vector a r n with a i a i m k 1 u c kj k for some strictly positive vector u r m the problem of finding a c scaling of the vector a which satisfies the linear system cx b will be called a generalized scaling problem in this paper it is shown that previously studied matrix scaling problems e g finding scalings with prespecified row sums and column sums or finding scalings with row sums equaling the corresponding column sums or finding scalings of multidimensional matrices with prespecified margins are special instances of generalized scaling problems generalized scaling problems are reduced to convex optimization problems and the reduction is used to characterize solutions to develop necessary and sufficient conditions for their existence to establish uniqueness results and to characterize approximate solutions

elan from a rewriting logic point of view elan implements computational systems a concept that combines two first class entities rewrite rules and rewriting strategies elan can be used either as a logical framework or to describe and execute deterministic as well as non deterministic rule based processes with the general goal to make precise a rewriting logic based semantics of elan this paper has three contributions a presentation of the concepts of rules and strategies available in elan an expression of rewrite rules with matching conditions in conditional rewriting logic and finally an enrichment mechanism of a rewrite theory into a strategy theory in conditional rewriting logic

a rewriting based inference system for the nrl protocol analyzer and its meta logical properties the nrl protocol analyzer npa is a tool for the formal specification and analysis of cryptographic protocols that has been used with great effect on a number of complex real life protocols one of the most interesting of its features is that it can be used to reason about security in face of attempted attacks on low level algebraic properties of the functions used in a protocol indeed it has been used successfully to either reproduce or discover a number of such attacks in this paper we give for the first time a precise formal specification of the main features of the npa inference system its grammar based techniques for invariant generation and its backwards reachability analysis method this formal specification is given within the well known rewriting framework so that the inference system is specified as a set of rewrite rules modulo an equational theory describing the behavior of the cryptographic algorithms involved we then use this formalization to prove some important meta logical properties about the npa inference system including the soundness and completeness of the search algorithm and soundness of the grammar generation algorithm the formalization and soundness and completeness theorems not only provide also a better understanding of the npa as it currently operates but provide a modular basis which can be used as a starting point for increasing the types of equational theories it can handle

pushout complements and basic concepts of grammars in toposes abstract an existence theorem of pushout complements is given in an elementary topos by using category theory of binary relations called relational calculus and it is also shown more explicitly in the category of directed graphs which is a typical example of toposes as an application moreover an embedding theorem and church rosser theorem on grammars derivations in a topos are proved

positive diagonal scaling of a nonnegative tensor to one with prescribed slice sums abstract in this paper we give necessary and sufficient conditions on a nonnegative tensor to be diagonally equivalent to a tensor with prescribed slice sums these conditions are variations of bapat raghavan and franklin lorenz conditions

infinite hypergraphs i basic properties abstract basic properties of the category of infinite directed hyperedge labelled hypergraphs are studied an algebraic structure is given which enables us to describe such hypergraphs by means of infinite expressions it is then shown that two expressions define the same hypergraphs if and only if they are congruent with respect to some rewriting system these results will be used in the second part of this paper to solve systems of recursive equations on hypergraphs and characterize their solutions

semantic foundations for generalized rewrite theories rewriting logic rl is a logic of actions whose models are concurrent systems rewrite theories involve the specification of equational theories of data and state structures together with a set of rewrite rules that model the dynamics of concurrent systems since its introduction more than one decade ago rl has attracted the interest of both theorists and practitioners who have contributed in showing its generality as a semantic and logical framework and also as a programming paradigm the experimentation conducted in these years has suggested that some significant extensions to the original definition of the logic would be very useful in practice these extensions may develop along several dimensions like the choice of the underlying equational logic the kind of side conditions allowed in rewrite rules and operational concerns for the execution of certain rewrites in particular the maude system now supports subsorting and conditional sentences in the equational logic for data and also frozen arguments to block undesired nested rewrites moreover it allows equality and membership assertions in rule conditions in this paper we give a detailed presentation of the inference rules model theory and completeness of such generalized rewrite theories our results provide a mathematical semantics for maude and a foundation for formal reasoning about maude specifications

partial evaluation and ω completeness of algebraic specifications abstract suppose p x y is a program with two arguments whose first argument has a known value c but whose second argument is not yet known partial evaluation of p c y results or rather should result in a specialized residual program p c y in which as much as possible has been computed on the basis of c in the literature on partial evaluation this is often more or less loosely expressed by saying that partial evaluation amounts to making maximal use of incomplete information in this paper a precise meaning is given to this notion in the context of equational logic initial algebra specification and term rewriting systems if maximal propagation of incomplete information is to be achieved within this context as a first step it is necessary to add equations to the algebraic specification in question until it is complete if ever the basic properties of complete specifications are discussed and some examples of complete specifications as well as of specifications that do not have a finite complete enrichment are given

penalized maximum likelihood estimation the baum welch algorithm diagonal balancing of symmetric matrices and applications to training acoustic data we study penalized maximum likelihood estimation methods for nonparametric density estimation and propose their use in training acoustic models for speech recognition several algorithms for the numerical solution of the optimization problems that we encounter are proposed and analyzed

order independence and factor convergence in iterative scaling abstract we prove two results concerning iterative scaling which have been claimed but not proved by other authors in the field iterative scaling is a procedure which begins with a probability measure q on a finite set x and a finite set of partition constraints on x it produces a sequence of iterates p0 q p1 pt in which each pt t 62 0 is an adjustment scaling of pt 1 to fit a single set of prescribed partition constraints under fairly general hypotheses the iterates pt converge to the unique probability p which simultaneously satisfies the given constraints and is exponentially equivalent to the starting measure q or equivalently which minimizes the i divergence d p q over all probabilities p on x which satisfy the constraints the first main result theorem 3 1 states that the convergence of iterative scaling to the unique limit is independent of the order in which the adjustments for the prescribed partition constraints are made provided each adjustment is made infinitely many times the second main result theorem 4 2 is that under certain commonly satisfied conditions each factor of the exponential form being built up within the algorithm one factor for each partition constraint converges separately a third group of results sections 5 6 provides an account of the relationship between the probability measures which satisfy all of the constraints and those which are exponentially equivalent to q

observational congruences for dynamically reconfigurable tile systems the sos formats that ensure that bisimilarity is a congruence tail in the presence ot structural axioms on states dynamic bisimulation introduced to characterize the coarsest congruence for ccs which is also a weak bisimulation reconciles the bisimilarity is a congruence property with structural axioms and also with the specification of open ended systems where states can be reconfigured at runtime we show that the compositional framework offered by tile logic handles structural axioms and specifications of reconfigurable systems successfully this allows for a finitary presentation of dynamic context closure as internalized in the tile language the case study of the calculus illustrates the main features of our approach moreover duality is exploited to model a second kind of reconfiguration dynamic specialization

interpolation in grothendieck institutions it is well known that interpolation properties of logics underlying specification formalisms play an important rule in the study of structured specifications they have also many other useful logical consequences in this paper we solve the interpolation problem for grothendieck institutions which have recently emerged as an important mathematical structure underlying heterogenous multilogic specification our main result can be used in the applications in several different ways it can be used to establish interpolation properties for multi logic grothendieck institutions but also to lift interpolation properties from unsorted logics to their many sorted variants the importance of the latter resides in the fact that unlike other structural properties of logics many sorted interpolation is a non trivial generalisation of unsorted interpolation the concepts results and the applications discussed in this paper are illustrated with several examples from conventional logic and algebraic specification theory

functorial theory of parameterized specifications in a general specification framework abstract a general specification framework based on the notion of indexed categories is introduced in order to study the structural aspects of specifications independent of the underlying logics similar to institutions this concept of specification frames allows to formulate a unified structural theory of various kinds of algebraic specifications which have been studied separately in the literature before in contrast to institutions we do not require to have satisfaction relations and conditions which allows to handle also behavioural specifications and semantics and various concepts of constraints in this framework in this framework we generalize the well known theory of parameterized algebraic specifications with initial semantics from the equational case to specification frames satisfying mainly three basic axioms the existence of pushouts free constructions and amalgamation moreover an axiomatic treatment of restriction is presented which allows to study in addition to refinement also implementations of parameterized specifications including restrictions finally we present an axiomatic framework for functorial semantics which opens the way to apply the theory not only to initial semantics but also to other kinds of functorial semantics including final and specific kinds of loose semantics

conditional rewriting logic as a unified model of concurrency abstract rewriting with conditional rewrite rules modulo a set e of structural axioms provides a general framework for unifying a wide variety of models of concurrency concurrent rewriting coincides with logical deduction in conditional rewriting logic a logic of actions whose models are concurrent systems this logic is sound and complete and has initial models in addition to general models interpreted as concurrent systems which provide a more operational style of semantics more restricted semantics with an incresingly denotational flavor such as preorder poset cpo and standard algebraic models appear as special cases of the model theory this permits dealing with operational and denotational issues within the same model theory and logic a programming language called maude whose modules are rewriting logic theories is defined and given denotational and operational semantics maude provides a simple unification of concurrent programming with functional and object oriented programming and supports high level declarative programming of concurrent systems

the completeness of the algebraic specification methods for computable data types the following fundamental theorem about the adequacy of the algebraic specification methods for data abstractions is proved let a be a data type with n subtypes then a is computable if and only if a possesses an equational specification involving at most 3 n 1 hidden operators and 2 n 1 axioms which defines it under initial and final algebra semantics simultaneously

completion of a set of rules modulo a set of equations abstract church rosser properties are first presented depending on an arbitrary relation r an equivalence relation e and a reduction relation r e used to compute normal forms of r modulo e terminating rewriting systems operating on equational congruence classes of terms of a free algebra are then considered in this framework the church rosser property is proved decidable for a very general reduction relation which may take into account the left linearity of rules for efficiency reasons under the only assumption of existence of a complete and finite unification algorithm for the underlying equational theory whose congruence classes are assumed to be finite this extends previous results by lankford and ballantyne peterson and stickel huet jouannaud a general completion procedure for mixed sets of rules and equations is then presented that generalizes and improves peterson and stickel s one in addition to computing a church rosser set of rules when it terminates it yields a semi decision pro

generalized incompressible flows multi marginal transport and sinkhorn algorithm starting from brenier s relaxed formulation of the incompress ible euler equation in terms of geodesics in the group of measure preserving diffeomorphisms we propose a numerical method based on sinkhorn s algorithm for the entropic regularization of optimal transport we also make a detailed comparison of this entropic regular ization with the so called bredinger entropic interpolation problem see 1 numerical results in dimension one and two illustrate the feasibility of the method

tile formats for located and mobile systems abstract standard sos formats are limited in their ability to define the operational semantics of process calculi with concurrency causality and mobility and with bound names and name generation mechanisms in this paper we describe a general approach based on the tile model to the definition of the operational semantics of process calculi by providing tile systems for located ccs and asynchronous calculus we demonstrate that the proposed approach is more suited than sos to provide a uniform treatment of concurrency and mobility within a compositional framework

strict coherence of conditional rewriting modulo axioms conditional rewriting modulo axioms with rich types makes specifications and declarative programs very expressive and succinct and is used in all well known rule based languages however the current foundations of rewriting modulo axioms have focused for the most part on the unconditional and untyped case the main purpose of this work is to generalize the foundations of rewriting modulo axioms to the conditional order sorted case a related goal is to simplify such foundations in particular even in the unconditional case the notion of strict coherence proposed here makes rewriting modulo axioms simpler and easier to understand properties of strictly coherent conditional theories like operational equi termination of the r b and r b relations and general conditions for the conditional churchrosser property modulo b are also studied

relating casl with other specification languages the institution level in this work we investigate various specification languages and their relation to casl the recently developed common algebraic specification language in particular we consider the languages larch obj3 and functional cafeobj act one asf and hep theories as well as various sublanguages of casl all these languages are translated to an appropriate sublanguage of casl the translation mainly concerns the level of specification in the small the logics underlying the languages are formalized as institutions and representations among the institutions are developed however it is also considered how these translations interact with specification in the large thus we obtain on the one hand translations of any of the above mentioned specification languages to an appropriate sublanguage of casl this allows us to take libraries and case studies that have been developed for other languages and re use them in casl on the other hand we set up institution representations going from the casl institution and some of its subinstitutions to simpler subinstitutions given a theorem proving tool for such a simpler subinstitution with the help of a representation it can also be used for a more complex institution thus first order theorem provers and conditional term rewriting tools become usable for casl

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

on complexity of matrix scaling abstract line sun scaling problem for a nonnegative matrix a is to find positive definite diagonal matrices y z which result in prescribed row and column sums of the scaled matrix yaz the matrix balancing problem for a nonnegative square matrix a is to find a positive definite diagonal matrix x such that the row sums in the scaled matrix xax are equal to the corresponding column sums we demonstrate that versions of both these problems same as those of other scaling problems for non negative multiindex arrays can be reduced to a specific geometric programming problem for the latter problem we develop a polynomial time algorithm thus deriving polynomial time solvability of a number of generic scaling problems for nonnegative multiindex arrays our results extend those previously known for the problems of matrix balancing 3 and of double stochastic scaling of a square nonnegative matrix 2

methods for scaling to doubly stochastic form abstract new methods for scaling square nonnegative matrices to doubly stochastic form are described a generalized version of the convergence theorem of sinkhorn and knopp 1967 is proved and applied to show convergence for these new methods tests indicate that one of the new methods has significantly better average and worst case behavior than the sinkhorn knopp method for one of the 3 3 examples of marshall and olkin 1968 sk requires 130 times as many operations as the new algorithm to achieve row and column sums 1 10 5

a comparative study of algorithms for matrix balancing the problem of adjusting the entries of a large matrix to satisfy prior consistency requirements occurs in economics urban planning statistics demography and stochastic modeling these problems are called matrix balancing problems we describe five applications of matrix balancing and compare the algorithmic and computational performance of balancing procedures that represent the two primary approaches for matrix balancing matrix scaling and nonlinear optimization the algorithms we study are the ras algorithm a diagonal similarity scaling algorithm and a truncated newton algorithm for network optimization we present results from computational experiments with large scale problems based on producing consistent estimates of social accounting matrices for developing countries

some fundamental algebraic tools for the semantics of computation part 2 signed and abstract theories les theories algebriques dans le sens de lawvere sont abstraites en ce qui concerne les presentations operation donnee ni equations particulieres ne sont determinees par la classe d isomorphisme d une theorie de ce fait pas meme les rangs ou le nombre total d operations ne sont determines ce degre d abstraction n est pas approprie a la specification des concepts de programmation on a donc donne une signature particuliere

entropy in linear programs this paper treats entropy constrained linear programs from modelling as well as computational aspects the optimal solutions to linear programs with one additional entropy constraint are expressed in terms of lagrange multipliers conditions for uniqueness are given sensitivity and duality are studied the newton kantorovich method is used to obtain a locally convergent iterative procedure related problems based on maximum entropy or minimum information are discussed

scalings of matrices which have prespecified row sums and column sums via optimization abstract the problem of scaling a matrix so that it has given row and column sums is transformed into a convex minimization problem in particular we use this transformation to characterize the existence of such scaling or corresponding approximations we obtain new results as well as new streamlined proofs of known results

a class of onto multifunctions a convex valued upper continuous multifunction with pointed closed convex domain is proved to be onto if there is a selection with certain coercive properties and if the selection for each point lies in the affine hull of the smallest face of the domain containing the point the proof uses a piecewise affine homotopy construction we apply the onto theorem to an approximation of a network of servers and show that arbitrary congestion levels can be realized with appropriate arrival levels

matrix scaling a geometric proof of sinkhorn s theorem abstract matrix scaling problems have been extensively studied since sinkhorn established in 1964 the following result any positive square matrix of order n is diagonally equivalent to a unique doubly stochastic matrix of order n and the diagonal matrices which take part in the equivalence are unique up to scalar factors we present a new elementary proof of the existence part of sinkhorn s theorem which is based on well known geometrical interpretations of doubly stochastic matrices and left and right multiplication by diagonal matrices

matrix scaling entropy minimization and conjugate duality ii the dual problem we present a matrix scaling problem calledtruncated scaling and describe applications arising in economics urban planning and statistics we associate a dual pair of convex optimization problems to the scaling problem and prove that the existence of a solution for the truncated scaling problem is characterized by the attainment of the infimum in the dual optimization problem we show that optimization problems used by bacharach 1970 bachem and korte 1979 eaves et al 1985 marshall and olkin 1968 and rothblum and schneider 1989 to study scaling problems can be derived as special cases of the dual problem for truncated scaling we present computational results for solving truncated scaling problems using dual coordinate descent thereby showing that truncated scaling provides a framework for modeling and solving large scale matrix scaling problems

foundations of logic programming in hybrid logics with user defined sharing abstract the present contribution advances an abstract notion of hybrid logic by supplementing the definition of institution with an additional structure to extract frames the foundation of logic programming is set in the general framework proposed by defining the basic concepts such as horn clause query and solution and proving fundamental results such as the existence of initial model of horn clauses and herbrand s theorem the abstract results are then applied to hybrid logics with user defined sharing where the possible worlds share a common domain and the variables used for quantification are interpreted uniformly across the worlds

on the existence of free models in abstract algebraic institutions abstract to provide a formal framework for discussing specifications of abstract data types we restrict the notion of institution due to goguen and burstall 1984 which formalises the concept of a logical system for writing specifications and deal with abstract algebraic institutions these are institutions equipped with a notion of submodel which satisfy a number of technical conditions our main results concern the problem of the existence of free constructions in abstract algebraic institutions we generalise a characterization of algebraic specification languages that guarantee the existence of reachable initial models for any consistent set of axioms given by mahr and makowsky 1984 then the more general problem of the existence of free functors left adjoints to forgetful functors for any theory morphism is analysed we give a construction of a free model of a theory over a model of a subtheory with respect to an arbitrary theory morphism which requires only the existence of initial models this yields a characterization of strongly liberal abstract algebraic institutions we also show how to specialise there characterisation results for the partial algebras

relaxed models for rewriting logic we modify the definition of the models for rewrite theories by replacing the equality of functors defined by e equal terms with the equality via a natural isomorphism called natural symmetry the relaxation process can be adapted by relaxing all or only a part of the equations and by relaxing the state structure and implicitly the computation structure or just the computation structure we also consider the subclasses of c coherent models where c is a set of equations specifying a collection of commutative symmetry diagrams the result is a wide palette of model classes which offers more flexibility in modeling concurrent systems

iterative bregman projections for regularized transportation problems this article details a general numerical framework to approximate so lutions to linear programs related to optimal transport the general idea is to introduce an entropic regularization of the initial linear program this regularized problem corresponds to a kullback leibler bregman di vergence projection of a vector representing some initial joint distribu tion on the polytope of constraints we show that for many problems related to optimal transport the set of linear constraints can be split in an intersection of a few simple constraints for which the projections can be computed in closed form this allows us to make use of iterative bregman projections when there are only equality constraints or more generally bregman dykstra iterations when inequality constraints are in volved we illustrate the usefulness of this approach to several variational problems related to optimal transport barycenters for the optimal trans port metric tomographic reconstruction multi marginal optimal trans port and in particular its application to brenier s relaxed solutions of in compressible euler equations partial un balanced optimal transport and optimal transport with capacity constraints

entropic approach to interior point solution of linear programs we present a maxentropic approach for obtaining interior suboptimal solutions to a linear programming problem not necessarily in karmarkar s canonical form each suboptimal solution lies in the relative interior set of feasible solutions we present an application to the problem of obtaining reconstructions of minimal weighted l 1 norm of a function from the knowledge of a few of its fourier coefficients

structural induction in institutions abstract we develop a general logic independent structural induction proof method at the level of abstract institutions this provides a solid and uniform mathematical foundation to induction proof methodologies for a wide variety of actual logic based formal specification frameworks our development is based technically upon an axiomatic approach to substitutions within institution theory

observational logic constructor based logic and their duality observability and reachability are important concepts for formal software development while observability concepts are used to specify the required observable behavior of a program or system reachability concepts are used to describe the underlying data in terms of datatype constructors in this paper we first reconsider the observational logic institution which provides a logical framework for dealing with observability then we develop in a completely analogous way the constructor based logic institution which formalizes a novel treatment of reachability both institutions are tailored to capture the semantically correct realizations of a specification from either the observational or the reachability point of view we show that there is a methodological and even formal duality between both frameworks in particular we establish a correspondence between observer operations and datatype constructors observational and constructor based algebras fully abstract and reachable algebras and observational and inductive consequences of specifications the formal duality between the observability and reachability concepts is established in a category theoretic setting

a finite element boundary element method for large displacement fluid structure interaction with potential flow this work concerns the interaction of light membrane structures enclosing incompressible fluids large displacements and collapsed boundaries initially slender subdomains are characteristic of this class of problems a finite element boundary element fe be coupled discretization is presented as an enabling technology addressing these challenges by avoiding volumetric meshing as required by arbitrary lagrangian eulerian or immersed boundary type methods the presented formulation includes a compatibility condition to which a physical interpretation is given and a regularizing bending stiffness observed to be necessary from both the theoretical well posedness and numerical stability point of view a cheap contact load is designed to deal with possibly complex geometries reusing already computed discrete boundary element kernels numerical experiments show the capabilities of the proposed scheme

reflection in conditional rewriting logic we recall general metalogical axioms for a reflective logic based on the notion of a universal theory that is a theory that can simulate the deductions of all other theories in a class of theories of interest including itself we then show that conditional rewriting logic is reflective generalizing in two stages first to the unsorted conditional case and then to the many sorted conditional case the already known result for unconditional and unsorted rewriting logic reflection in rewriting logic metalogical foundations and metaprogramming applications csli publications 2000 this work should be seen as providing foundations for many useful applications of rewriting logic reflection the results presented here have greatly influenced the design of the maude language which implements rewriting logic and supports its reflective capabilities and have been used as a theoretical foundation for applications such as internal rewrite strategies reflective design of theorem proving tools module algebra and metaprogramming and metareasoning in metalogical frameworks

equational rules for rewriting logic in addition to equations and rules we introduce equational rules that are oriented while having an equational interpretation correspondence between operational behavior and intended semantics is guaranteed by a property of coherence which can be checked by examination of critical pairs and linearity conditions we present applications of this theory to three examples where the rewrite relation is interpreted respectively as equality transition and deduction

a causal semantics for ccs via rewriting logic we consider two operational semantics for ccs defined in the literature the first exploits proved transition systems pts and the second rewriting logic rl we show that the interleaving interpretation of both semantics agree in that they define the same transitions and exhibit the same non deterministic structure in addition we study causality in ccs computations we recall its treatment via pts exhibiting the notion of causality presented in the literature and we show how to recast it in the rl semantics via suitable axioms also in this case the two semantics agree

bisimilarity of open terms traditionally in process calculi relations over open terms i e terms with free process variables are defined as extensions of closed term relations two open terms are related if and only if all their closed instantiations are related working in the context of bisimulation in this paper we study a different approach we define semantic models for open terms so called conditional transition systems and define bisimulation directly on those models it turns out that this can be done in at least two different ways one giving rise to de simone s formal hypothesis bisimilarity and the other to a variation which we call hypothesis preserving bisimilarity denoted fh and hp respectively for open terms we have strict inclusions fh c hp c ci the latter denoting the standard closed instance extension for closed terms the three coincide each of these relations is a congruence in the usual sense we also give an alternative characterisation of hp in terms of nonconditional transitions as substitution closed bisimilarity denoted sb finally we study the issue of recursion congruence we prove that each of the above relations is a congruence with respect to the recursion operator however for ci this result holds under more restrictive conditions than for fh and hp

some fundamental algebraic tools for the semantics of computation part 3 indexed categories abstract this paper presents indexed categories which model uniformly defined families of categories and suggests that they are a useful tool for the working computer scientist an indexed category gives rise to a single flattened category as a disjoint union of its component categories plus some additional morphisms similarly an indexed functor which is a uniform family of functors between the components categories induces a flattened functor between the corresponding flattened categories under certain assumptions flattened categories are co complete if all their components are and flattened functors have left adjoints if all their components do several examples are given although this paper is part 3 of the series some fundamental algebraic tools for the semantics of computation it is entirely independent of parts 1 and 2

a semantic approach to interpolation craig interpolation is investigated for various types of formulae by shifting the focus from syntactic to semantic interpolation we generate prove and classify a series of interpolation results for first order logic a few of these results non trivially generalize known interpolation results all the others are new we also discuss some applications of our results to the theory of institutions and of algebraic specifications and a craig robinson version of these results

on expressive completeness of duration and mean value calculi the standard way of lifting a binary relation r from closed terms of an algebra to open terms is to define its closed instance extension r ci which holds for a given pair of open terms if and only if r holds for all their closed instantiations in this paper we study alternatives for the case of strong bisimulation we define semantic models for open terms so called conditional transition systems and define bisimulation directly on those models it turns out that this can be done in at least two different ways giving rise to formal hypothesis bisimulation sim fh due to de simone and hypothesis preserving bisimilarity sim hp for open terms we have strict inclusions sim fh subset sim hp subset sim ci for closed terms the three relations coincide we show that each of these relations is a congruence in the usual sense and we give an alternative characterisation of sim hp in terms of non conditional transitions finally we study the issue of recursive congruence we give general theorems for the congruence of each of the above variants with respect to the recursion combinator where however the results we achieve for sim fh and sim hp hold in a more general setting than the one for sim ci

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

reflection in membership equational logic many sorted equational logic horn logic with equality and rewriting logic we show that the generalized variant of formal systems where the underlying equational specifications are membership equational theories and where the rules are conditional and can have equations memberships and rewrites in the conditions is reflective we also show that membership equational logic many sorted equational logic and horn logic with equality are likewise reflective these results provide logical foundations for reflective languages and tools based on these logics

the contraction mapping approach to the perron frobenius theory why hilbert s metric the perron frobenius theorem says that if a is a nonnegative square matrix some power of which is positive then there exists an x0 such that anx anx converges to xn for all x 0 there are many classical proofs of this theorem all depending on a connection between positively of a matrix and properties of its eigenvalues a more modern proof due to garrett birkhoff is based on the observation that every linear transformation with a positive matrix may be viewed as a contraction mapping on the nonnegative orthant this observation turns the perron frobenius theorem into a special ease of the banach contraction mapping theorem furthermore it applies equally to linear transformations which are positive in a much more general sense the metric which birkhoff used to show that positive linear transformations correspond to contraction mappings is known as hilbert s projective metric the definition of this metric is rather complicated it is therefore natural to try to define another less complicated m

on fuzzification of topological categories this paper shows that l m fuzzy topology of u hohle t kubiak and a sostak is an instance of a general fuzzification procedure for topological categories which amounts to the construction of a new topological category from a given one this fuzzification procedure motivates a partial dualization of the machinery of tower extension of topological constructs of d zhang thereby providing the procedure of tower extension of topological categories with the help of this dualization we arrive at the meta mathematical result that the concept of l m fuzzy topology and the notion of approach space of r lowen are dual to each other

matrix scaling entropy minimization and conjugate duality i existence conditions abstract we have four primary objectives in this paper first we introduce a problem called truncated matrix scaling that generalizes two well studied matrix scaling problems diagonal similarity scaling and fixed row column equivalence scaling second we derive necessary and sufficient conditions for the attainment of the infimum in the fenchel dual of a class of convex optimization problems third we show that existence of a solution for truncated matrix scaling is equivalent to the attainment of the infimum in a corresponding dual optimization problem we thereby derive necessary and sufficient conditions for the existence of a solution for truncated matrix scaling fourth we derive known existence conditions for similarity and equivalence scaling from the conditions for truncated matrix scaling

characterizing specification languages which admit initial semantics abstract the paper proposes an axiomatic approach to specification languages and introduces notions of reducibility and equivalence as tools for their study and comparison algebraic specification languages are characterized up to equivalence they are shown to be limited in expressive power by implicational languages

an extension of a theorem of darroch and ratcliff in loglinear models and its application to scaling multidimensional matrices abstract let c c ij be an m n matrix with real entries let b be any nonzero m vector let k c b 0 be bounded let x x 1 x 2 x n y y 1 y 2 y n be two nonnegative vectors with y k and x j 0 y j 0 for any coordinate j then it is shown that there exists a k and positive numbers z 1 z 2 z m such that j x j m i 1 z c ij i for all j th theorem slightly generalizes a theorem of darroch and ratcliff in loglinear models with a completely different proof technique the proof relies on an extension of a topological theorem of kronecker to set valued maps and the duality theorem of linear programming many theorems in scaling of matrices and multidimensional matrices are direct consequences of this theorem the main idea is to associate a suitable zero one matrix of transportation with any multidimensional matrix some motivations for scaling applications are also discussed

a theorem of the alternative for multihomogeneous functions and its relationship to diagonal scaling of matrices abstract we prove that given a multihomogeneous function satisfying some initial conditions either it has a certain nonnegative zero over a given subspace or an associated logarithmic barrier function has a constrained stationary point under convexity precisely one of these conditions is satisfied the main ingredients of the proof are the derivation of significant properties of the constrained stationary points of the logarithmic barrier function and their relationship to corresponding points of an associated karmarkar potential function corollaries of the theorem include a duality for karmarkar s canonical linear program which happens to be a stronger version of gordan s theorem a more general duality than an existing one concerning the diagonal scaling of symmetric matrices also shown to be a stronger version of gordan s theorem and a diagonal scalability result for a class of multihomogeneous polynomials which is more general than a previously known result on the scalability of positive multidimensional matrices we also give an algorithmic proof of the theorem of the alternative through a projective algorithm which is a generalization of a modified karmarkar linear programming algorithm and in the context of nonnegative matrix scaling becomes a variant of the well known ras algorithm

on on graph rewritings abstract in 1984 raoult has given a description of graph rewriting his description is operational despite the similarity which his constructions have to the category theoretic concept of a pushout we describe a modification to raoult s description of graph rewriting which allows the reduction of a redex to be described as a pushout in a category of graphs where morphisms are not required to preserve graph structure our description can also handle term rewrite rules whose right hand sides consist of a variable raoult specifically excludes such rules from his treatment rules of this form include the k combinator the identity function selector functions for extracting components of data structures and the conditional we prove the correctness of this implementation of term rewriting

on pairs of multidimensional matrices abstract recently bapat applied a topological theorem of kronecker and generalized a theorem of sinkhorn on positive matrices here we give an alternative proof of a slightly stronger version of his generalization this proof combines kakutani s fixed point theorem and the duality theorem of linear programming and gives yet another proof of a theorem of bacharach and menon on pairs of nonnegative matrices

modular specification of process algebras abstract this paper proposes a modular approach to the algebraic specification of process algebras this is done by means of the notion of a module the simplest modules are building blocks of operators and axioms each block describing a feature of concurrency in a certain semantical setting these modules can then be combined by means of a union operator an export operator allowing to forget some operators in a module an operator h changing semantics by taking homomorphic images and an operator s which takes subalgebras these operators enable us to combine modules in a subtle way when the direct combination would be inconsistent we give a presentation of equational logic infinitary conditional equational logic of which we also prove the completeness and first order logic and show how the notion of a formal proof of a formula from a theory can be generalized to that of a proof of a formula from a module this module logic is then applied in process algebra we show how auxiliary process algebra operators can be hidden when this is needed moreover we demonstrate how new process combinators can be defined in terms of more elementary ones in a clean way as an illutration of our approach we specify some fifo queues and verify several of their properties

on graph rewritings abstract the purpose of the present paper is twofold firstly show that it is possible to rewrite graphs in a way equivalent to and in fact slightly more powerful than that of ehrig pfender and schneider 1973 which has since then been developed mainly by the berlin school our method consists in using a single push out of partial morphisms and is described in section 3 section 1 is devoted to the elementary definitions concerning graphs and related terms section 2 contains the set theoretic prerequisites for the sequel but the proofs have been moved into an appendix for easier reading secondly we indicate in section 4 why this method is not really fit for rewriting graphs that represent collapsed terms i e sharing common subterms and we introduce pushouts of total functions which are not morphisms everywhere on their domain this method is connected to the classical rewriting of the corresponding terms the adequacy of these new rewriting rules is then tested to prove a local confluence criterion a la knuth bendix 1970 in section 5 the proof of which turns out to be very short