linear logical relations and observational equivalences for session based concurrency we investigate strong normalization confluence and behavioral equality in the realm of session based concurrency these interrelated issues underpin advanced correctness analysis in models of structured communications the starting point for our study is an interpretation of linear logic propositions as session types for communicating processes proposed in prior work strong normalization and confluence are established by developing a theory of logical relations defined upon a linear type structure our logical relations remain remarkably similar to those for functional languages we also introduce a natural notion of observational equivalence for session typed processes strong normalization and confluence come in handy in the associated coinductive reasoning as applications we prove that all proof conversions induced by the logic interpretation actually express observational equivalences and explain how type isomorphisms resulting from linear logic equivalences are realized by coercions between interface types of session based concurrent systems

on the boundedness and continuity of the spectral factorization mapping it is known that the spectral factorization mapping is bounded but not continuous on l infty the space of essentially bounded measurable functions on the unit circle in this article we study the spectral factorization mapping on decomposing banach algebras the most important example of a decomposing banach algebra is the wiener algebra the space of all absolutely convergent fourier series it is shown that the spectral factorization mapping is locally lipschitz continuous but not bounded on all decomposing banach algebras in consideration an application is given to the construction of approximate normalized coprime factorization

a connection between normalized coprime factorizations and linear quadratic regulator theory given a transfer matrix described by a minimal state space triple a method is given for computing state space realizations for the numerator and denominator of a normalized stable right coprime factorization for the transfer matrix the method involves the solution of an algebraic riccati equation it allows the use of existing computational state space algorithms in finding normalized stable right coprime factorizations and avoids explicit calculations of spectral factors

controllability and observability of linear retarded systems in banach spaces abstract controllability and observability are studied for linear retarded systems in a banach space x both the x exact and the x approximate controllability are considered and a number of necessary and sufficient conditions in terms of the coefficient operators and or the fundamental solution are presented various corresponding concepts for observability are introduced and the duality between controllability and observability is clarified an applicable condition for the x approximate controllability and the x observability is established under the assumptions that the control is a finite dimensional one and the system of generalized eigenspaces is projectively complete the condition is stated in terms of eigenvectors and controllers

boundary optimal lq control of coupled hyperbolic pdes and odes this contribution addresses the development of a linear quadratic lq regulator for a set of hyperbolic pdes coupled with a set of odes through the boundary the approach is based on an infinite dimensional hilbert state space description of the system and the well known operator riccati equation ore in order to solve the optimal control problem the ore is converted to a set of matrix riccati equations the feedback operator is found by solving the resulting matrix riccati equations the performance of the designed control policy is assessed by applying it to a system of interconnected continuous stirred tank reactor cstr and a plug flow reactor pfr through a numerical simulation

an arithmetic for polynomial time computation we define a restriction lha of heyting arithmetic ha with the property that all extracted programs are feasible the restrictions consist in linearity and ramification requirements

the role of polymorphism in the characterisation of complexity by soft types soft type assignment systems sta sta and sta b characterise by means of reduction of terms computation in complexity classes ptime np and pspace respectively all these systems are inspired by linear logic and include polymorphism similar to the one of system f we show that the presence of polymorphism gives the undecidability of typechecking and type inference we also show that reductions in decidable monomorphic versions of these systems also capture the same complexity classes in a way sufficient for the traditional complexity theory the translations we propose show in addition that the monomorphic systems to serve as a programming language require some metalanguage support since the program which operates on data has form and type which depend on the size of the input

linear and affine logics with temporal spatial and epistemic operators a temporal spatial epistemic intuitionistic linear logic tseill is introduced and the completeness theorem for this logic is proved with respect to kripke semantics tseill has three temporal modal operators f any time in the future n next time and p past some spatial modal operators li locations two epistemic modal operators k know and k and a linear modal operator exponential a basic normal modal intuitionistic affine logic bial and its normal extensions are also defined and the completeness theorems for these logics are proved with respect to kripke semantics in the proposed semantic framework of these normal extensions a simple correspondence can be given between frame conditions and lemmon scott axioms a dynamic intuitionistic affine logic dial is proposed as an affine version of test free dynamic logic and the completeness theorem for this logic is shown with respect to kripke semantics finally some intuitive interpretations such as resource and informational interpretations are given for the proposed logics and semantics by using these logics semantics and interpretations various kinds of fine grained resource sensitive reasoning can be expressed

linear logic and elementary time a subsystem of linear logic elementary linear logic is defined and shown to represent exactly elementary recursive functions its choicest part consists in reducing the deductive power of the exponential also known as the bang which in linear logic is in charge of controlling duplication in the cut elimination process

transient wave propagation in constant and linear strain finite elements this paper deals with transient wave propagation in a semi infinite rod which is represented by constant or linear strain finite elements having two different element sizes after assembling the system matrices a matrix differential equation is obtained and integrated numerically two different types of end condition prescribed axial force and displacement are considered the corresponding results are displayed in figures and the oscillations in the numerical solution are discussed the results reveal spurious reflections due to the change in the element size

phase semantics for light linear logic light linear logic girard inform comput 14 1998 175 204 is a refinement of the propositions as types paradigm to polynomial time computation a semantic setting for the underlying logical system is introduced here in terms of fibred phase spaces strong completeness is established with a purely semantic proof of cut elimination as a consequence a number of mathematical examples of fibred phase spaces are presented that illustrate subtleties of light linear logic

on strong normalization and type inference in the intersection type discipline we introduce a new unification procedure for the type inference problem in the intersection type discipline it is well known that type inference in this case should succeed exactly for the strongly normalizing expressions we give a proof for the strong normalization result in the intersection type discipline which we obtain by putting together some well known results and proof techniques our proof uses a variant of klop s extended l calculus for which it is shown that strong normalization is equivalent to weak normalization this is proved here by means of a finiteness of developments theorem obtained following de vrijer s combinatory technique the main property of this extended calculus is uniformity i e weak and strong normalizabilities coincide the strong normalizability result is therefore a consequence of the fact first established by coppo and dezani for the l calculus that typability implies weak normalizability we then show that the unification process which is the basis for type inference exactly corresponds to reduction in the extended l calculus finally we show that our notion of unification allows us to compute a principal typing for any typable l expression

bounded linear logic a modular approach to polynomial time computability typing is a way of describing the interactive behavior of algorithms usual typing systems are mainly concerned with input output specifications e g given terms f a b and a a the computation of f a by normalization yields a result of type b however one can dream of more refined typings that would not only ensure ethereal termination but would for instance yield feasible resource bounds it seems that time complexity does not lend itself naturally to modular manipulation we seek something more primitive

robust stabilization bibo stability distance notions and robustness optimization abstract this paper studies robust stabilization of both linear shift invariant causal systems in an lp setting and linear time invariant causal continuous time systems in an lp p 1 or setting two key technical results in the paper establish the existence of lp and lp stable normalized coprime factorizations for discrete time and continuous time systems respectively which have coprime factorizations as lp and lp stable operators several distance measures for systems are then introduced including the graph metric the function the gap between the graphs of the systems and the projection gap it is shown that these distance measures lead to the weakest convergence notions for systems for which closed loop stability is a robust property the function can be computed using the dahleh pearson theory for l1 l1 optimal control robustness optimization in a directed p function is shown to be closely related to robustness optimization for bibo stable normalized coprime factor perturbations this result connects the stability margin of dahleh for coprime factor perturbations to the function these considerations are further supported by a robustness result in terms of the projection gap

brief papers new results in state estimation and regulation an alternative technique to design linear state estimators and regulators is presented this technique is based on transfer matrix considerations the optimal regulator or estimator gain is obtained via spectral factorization and the solution of a simple equation in polynomial matrices this approach provides further insight displays the duality of estimation and control nicely and bridges the state space and frequency domain techniques the resulting design procedure is computationally attractive and particularly simple for system matrices in the observer or controller canonical form

plane elastic waves in meshes of bilinear finite elements elastic wave propagation in a two dimensional grid of finite elements having uniform size is investigated only bilinear finite elements of rectangular shape are considered however the elastic wave is assumed to propagate in an arbitrary direction numerical calculations are made to find out the representability of finite elements and the suitability of the lumped masses formulation

linear types and non size increasing polynomial time computation we propose a linear type system with recursion operators for inductive datatypes which ensures that all definable functions are polynomial time computable the system improves upon previous such systems in that recursive definitions can be arbitrarily nested in particular no predicativity or modality restrictions are made

robustness analysis for feedback interconnections of distributed systems via integral quadratic constraints a framework is established for directly accommodating feedback interconnections of unstable distributed parameter transfer functions in robust stability analysis via integral quadratic constraints iqcs this involves transfer function homotopies that are continuous in a gap metric sense as such the development includes the extension of gap metric concepts to an irrational setting and the study of uncertainty set connectedness in these terms the main iqc based robust stability result is established for constantly proper transfer functions in the callier desoer algebra i e finitely many unstable poles and a constant limit at infinity problems of structured robust stability analysis and robust performance analysis are considered to illustrate use of the main result several numerical examples are also presented these include stability analysis of an autonomous system with uncertain time delay and a closed loop control system accounting for both the gain and phase characteristics of the distributed parameter uncertainty associated with the nominal rational plant model used for controller synthesis

light types for polynomial time computation in lambda calculus we present a polymorphic type system for lambda calculus ensuring that well typed programs can be executed in polynomial time dual light affine logic dlal dlal has a simple type language with a linear and an intuitionistic type arrow and one modality it corresponds to a fragment of light affine logic lal we show that contrarily to lal dlal ensures good properties on lambda terms and not only on proof nets subject reduction is satisfied and a well typed term admits a polynomial bound on the length of any of its beta reduction sequences we also give a translation of lal into dlal and deduce from it that all polynomial time functions can be represented in dlal

a semantic measure of the execution time in linear logic we give a semantic account of the execution time i e the number of cut elimination steps leading to the normal form of an untyped mell net we first prove that 1 a net is head normalizable i e normalizable at depth 0 if and only if its interpretation in the multiset based relational semantics is not empty and 2 a net is normalizable if and only if its exhaustive interpretation a suitable restriction of its interpretation is not empty we then give a semantic measure of execution time we prove that we can compute the number of cut elimination steps leading to a cut free normal form of the net obtained by connecting two cut free nets by means of a cut link from the interpretations of the two cut free nets these results are inspired by similar ones obtained by the first author for the untyped lambda calculus

spectral factorization and lq optimal regulation for multivariable distributed systems a necessary and sufficient condition is proved for the existence of a bistable spectral factor with entries in the distributed proper stable transfer function algebra x1d49c in the context of distributed multivariable convolution systems with no delays a by product is the existence of a normalized coprime fraction of the transfer function of such a possibly unstable system with entries in the algebra of fractions over x1d49c we next study semigroup state space systems sgb with bounded sensing and control having a transfer function with entries in and consider its standard lq optimal regulation problem having an optimal state feedback operator k0 for a system sgb a formula is given relating any spectral factor of a transfer function coprime fraction power spectral density to k0 a by product is the description of any normalized coprime fraction of the transfer function in terms of k0 finally we describe an alternative way of finding the solution operator k0 of the lq problem using spectral factor

characterizing polynomial and exponential complexity classes in elementary lambda calculus abstract in this paper an implicit characterization of the complexity classes k exp and k fexp for k 0 is given by a type assignment system for a stratified calculus where types for programs are witnesses of the corresponding complexity class types are formulae of elementary linear logic ell and the hierarchy of complexity classes k exp is characterized by a hierarchy of types

paths based criteria and application to linear logic subsystems characterizing polynomial time abstract several variants of linear logic have been proposed to characterize complexity classes in the proofs as programs correspondence light linear logic lll ensures a polynomial bound on reduction time and characterizes in this way polynomial time p t i m e in this paper we study the complexity of linear logic proof nets and propose three semantic criteria based on context semantics stratification dependence control and nesting stratification alone entails an elementary time bound the three criteria entail together a polynomial time bound these criteria can be used to prove the complexity soundness of several existing variants of linear logic we define a decidable syntactic subsystem of linear logic s d n l l we prove that the proof nets of sdnll satisfy the three criteria which implies that s d n l l is sound for p t i m e several previous subsystems of linear logic characterizing polynomial time lll m l 4 maximal system of ms are embedded in s d n l l proving its p t i m e completeness

principal type scheme and unification for intersection type discipline abstract the intersection type discipline for the calculus itd is an extension of the classical functionality theory of curry in the itd a term satisfying a given property has a principal type scheme in an extended meaning i e there is a type scheme deducible for it from which all and only the type schemes deducible for it are reachable by means of suitable operations the problem of finding the principal type scheme for a term if it exists is semidecidable in the paper a procedure is shown building the principal type scheme of a term through the construction of the most general unifier for intersection type schemes

the decidability of the intensional fragment of classical linear logic intensional classical linear logic mell is proved decidable intensional interlinear logic rll is proved decidable we adapt kripke s method used to prove decidability for some relevance logics the semi relevant rll emerges as a logic superior to mell in this context triple and double inductive proofs of cut theorems are explained in some detail the intensional fragment of classical propositional linear logic combines modalities with contraction free relevance logic adding modalized versions of the thinning and contraction rules this paper provides a proof of the decidability of this logic based on a sequent calculus formulation some related logics and some other fragments of linear logic are also shown decidable

on discrete spectral factorizations a unified approach state space formulas for all key spectral factorizations appearing in the discrete time h sup 2 h sup infinity optimization are summarized the factorization problems are categorized into three groups solutions are constructed by finding special coprime factors of a given transfer matrix using the associated discrete algebraic riccati equation solution procedures for the three groups are in general the same which may lead to yield to a unified approach

linear quadratic optimal control of hereditary differential systems infinite dimensional riccati equations and numerical approximations recent theory of infinite dimensional riccati equations is applied to the linear quadratic optimal control problem for hereditary differential systems and it is shown that for most such problems the operator solutions of the riccati equations are of trace class i e nuclear with special attention to trace norm convergence an abstract approximation theory is developed and applied to a particular approximation scheme numerical examples are given problems on both finite and infinite time intervals are studied for both the hereditary system and the approximating systems in the infinite time problem characteristic equations are derived for the closed loop eigenvalues and formulas for the corresponding eigenvectors are given

linear logic by levels and bounded time complexity we give a new characterization of elementary and deterministic polynomial time computation in linear logic through the proofs as programs correspondence girard s seminal results concerning elementary and light linear logic achieve this characterization by enforcing a stratification principle on proofs using the notion of depth in proof nets here we propose a more general form of stratification based on inducing levels in proof nets by means of indices which allows us to extend girard s systems while keeping the same complexity properties in particular it turns out that girard s systems can be recovered by forcing depth and level to coincide a consequence of the higher flexibility of levels with respect to depth is the absence of boxes for handling the paragraph modality we use this fact to propose a variant of our polytime system in which the paragraph modality is only allowed on atoms and which may thus serve as a basis for developing lambda calculus type assignment systems with more efficient typing algorithms than existing ones

analytic controllability of time dependent quantum control systems the question of controllability is investigated for a quantum control system in which the hamiltonian operator components carry explicit time dependence which is not under the control of an external agent we consider the general situation in which the state moves in an infinite dimensional hilbert space a drift term is present and the operators driving the state evolution may be unbounded however considerations are restricted by the assumption that there exists an analytic domain dense in the state space on which solutions of the controlled schrodinger equation may be expressed globally in exponential form the issue of controllability then naturally focuses on the ability to steer the quantum state on a finite dimensional submanifold of the unit sphere in hilbert space and thus on analytic controllability a relatively straightforward strategy allows the extension of lie algebraic conditions for strong analytic controllability derived earlier for the simpler time independent system in which the d

lq optimal control of infinite dimensional systems by spectral factorization abstract we consider the standard lq optimal control of an exponentially stabilizable and detectable infinite dimensional semigroup state space system with bounded sensing and control it is reported that the reachable restriction of the lq optimal state feedback operator can be identified 1 by solving a spectral factorization problem delivering a bistable spectral factor with entries in the distributed proper stable transfer function algebra and 2 by obtaining any constant solution of an operator diophantine equation over the properties of the restricted solution feedback operator are discussed it is shown in particular that the lq optimal state feedback operator and its reachable restriction coincide whenever the unreachable state components are unobservable these theoretical results are applied to a simple model of heat diffusion with collocated sensor and actuator leading to an approximation procedure converging exponentially fast to the lq optimal state feedback operator this procedure is based on approximate spectral factorization by symmetric extraction and on simple residue calculus

robust stabilizability of normalized coprime factors the infinite dimensional case the problem of robustly stabilizing a linear system subject to h bounded perturbations in the numerator and the denominator of its normalized left coprime factorization is considered for a class of infinite dimensional systems this class has possible unbounded finite rank input and output operators which include many delay and distributed systems the optimal stability margin is expressed in terms of the solutions of the control and filter algebraic riccati equations

optimal linear quadratic control of coupled parabolic hyperbolic pdes abstractthis paper focuses on the optimal control design for a system of coupled parabolic hypebolic partial differential equations by using the infinite dimensional state space description and the corresponding operator riccati equation some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear quadratic lq optimal control problem a state lq feedback operator is computed by solving the operator riccati equation which is converted into a set of algebraic and differential riccati equations thanks to the eigenvalues and the eigenvectors of the parabolic operator the results are applied to a non isothermal packed bed catalytic reactor the lq optimal controller designed in the early portion of the paper is implemented for the original nonlinear model numerical simulations are performed to show the controller performances

optimal lq feedback regulation of a nonisothermal plug flow reactor model by spectral factorization the linear quadratic lq optimal temperature and reactant concentration regulation problem is studied for a partial differential equation model of a nonisothermal plug flow tubular reactor by using a nonlinear infinite dimensional hilbert state space description first the dynamical properties of the linearized model around a constant temperature equilibrium profile along the reactor are studied it is shown that it is exponentially stable and approximately reachable next the general concept of lq feedback is introduced it turns out that any lq feedback is optimal from the input output viewpoint and stabilizing for the plug flow reactor linearized model a state lq feedback operator is computed via the solution of a matrix riccati differential equation mrde in the space variable thanks to the reachability property the computed lq feedback is actually the optimal one then the latter is applied to the nonlinear model and the resulting closed loop system dynamical performances are analyzed a criterion is given which guarantees that the constant temperature equilibrium profile is an asymptotically stable equilibrium of the closed loop system moreover under the same criterion it is shown that the control law designed previously is optimal along the nonlinear closed loop model with respect to some cost criterion the results are illustrated by some numerical simulations

continuity of the spectral factorization on a vertical strip the continuity of the mapping which associates a spectral factor to a spectral density is investigated this mapping can be defined on several classes of spectral densities and spectral factors for the usual largest class of spectral densities i e essential bounded functions on the imaginary axis that are bounded away from zero it is known that this mapping is not continuous it is shown here that for slightly smaller but still generic class the mapping becomes continuous

light logics and optimal reduction completeness and complexity typing of lambda terms in elementary and light affine logic eal and lal respectively has been studied for two different reasons on the one hand the evaluation of typed terms using lal eal respectively proof nets admits a guaranteed polynomial elementary respectively bound on the other hand these terms can also be evaluated by optimal reduction using the abstract version of lamping s algorithm the first reduction is global while the second one is local and asynchronous we prove that for lal eal respectively typed terms lamping s abstract algorithm also admits a polynomial elementary respectively bound we also give a proof of its soundness and completeness for eal and lal with type fixpoints by using a simple geometry of interaction model context semantics

a formal framework for specifying sequent calculus proof systems intuitionistic logic and intuitionistic type systems are commonly used as frameworks for the specification of natural deduction proof systems in this paper we show how to use classical linear logic as a logical framework to specify sequent calculus proof systems and to establish some simple consequences of the specified sequent calculus proof systems in particular derivability of an inference rule from a set of inference rules can be decided by bounded linear logic programming search on the specified rules we also present two simple and decidable conditions that guarantee that the cut rule and non atomic initial rules can be eliminated

brief paper lq control design of a class of hyperbolic pde systems application to fixed bed reactor a general linear controller design method for a class of hyperbolic linear partial differential equation pdes systems is presented this is achieved by using an infinite dimensional hilbert state space description with infinite dimensional distributed input and output a state lq feedback operator is computed via the solution of a matrix riccati differential equation in the space variable the proposed method is applied to a fixed bed chemical reactor control problem where one elementary reaction takes place an optimal controller is designed for linearized fixed bed reactor model it is applied to the original nonlinear model and the resulting closed loop stability is analyzed numerical simulations are performed to show the performance of the designed controller

additives of linear logic and normalization part i a restricted church rosser property we define a generalized cut elimination procedure for proof nets of fall linear logic without constants for which we prove a restricted church rosser property

distributed system transfer functions of exponential order o is a real number we construct a transfer function algebra of fractions viz f o for modelling possibly unstable distributed systems such that i fcirc in f o is holomorphic in re s o i e is o stable iff fcirc is o exponentially stable and ii we allow delay in the direct input output transmission of the system this algebra is a a restriction of the algebra b o developed by callier and desoer 1978 1980 a b an extension of the algebra of proper rational functions such that the exponential order properties of the latter transfer functions of lumped systems are maintained the algebra f o can be used for modelling and feedback system design it is shown that standard semigroup systems are better modelled by a transfer function in f o rather than b o

an abstract approach to stratification in linear logic we study the notion of stratification as used in subsystems of linear logic with low complexity bounds on the cut elimination procedure the so called light subsystems from an abstract point of view introducing a logical system in which stratification is handled by a separate modality this modality which is a generalization of the paragraph modality of girard s light linear logic arises from a general categorical construction applicable to all models of linear logic we thus learn that stratification may be formulated independently of exponential modalities when it is forced to be connected to exponential modalities it yields interesting complexity properties in particular from our analysis stem three alternative reformulations of baillot and mazza s linear logic by levels one geometric one interactive and one semantic

model checking higher order programs we propose a novel verification method for higher order functional programs based on higher order model checking or more precisely model checking of higher order recursion schemes recursion schemes for short the most distinguishing feature of our verification method for higher order programs is that it is sound complete and automatic for the simply typed calculus with recursion and finite base types and for various program verification problems such as reachability flow analysis and resource usage verification we first show that a variety of program verification problems can be reduced to model checking problems for recursion schemes by transforming a program into a recursion scheme that generates a tree representing all the interesting possible event sequences of the program we then develop a new type based model checking algorithm for recursion schemes and implement a prototype recursion scheme model checker to our knowledge this is the first implementation of a recursion scheme model checker experiments show that our model checker is reasonably fast despite the worst case time complexity of recursion scheme model checking being hyperexponential in general altogether the results provide a new promising approach to verification of higher order functional programs

soft linear logic and polynomial time we present a subsystem of second order linear logic with restricted rules for exponentials so that proofs correspond to polynomial time algorithms and vice versa

a type assignment for λ calculus complete both for fptime and strong normalization one of the aims of implicit computational complexity is the design of programming languages with bounded computational complexity one of the most promising approaches to this aim is based on the use of lambda calculus as paradigmatic programming language and the design of type assignment systems for lambda terms where types guarantee both the functional correctness and the complexity bound along this line we propose a system of stratified types inspired by intersection types where intersection is a non associative operator this system is correct and complete for polynomial time when a uniform coding scheme is considered moreover all the strongly normalizing terms are typed in it thus increasing the typing power with respect to the previous proposals based on light logics

bounded combinatory logic and lower complexity we introduce a stratified version of combinatory logic1 in which there are two classes of terms called player and opponent such that the class of player terms is strictly contained in the class of opponent terms we show that the system characterizes polynomial time in a similar way to soft linear logic with the addition of explicit lazy products to the player terms and various notions of distributivity we obtain a characterization of polynomial space this paper is an expanded version of the abstract presented at dice 2013

principal type schemes for an extended type theory we consider the extension of curry s basic functionality theory presented by barendregt et al to appear and we define for any term x a principal type scheme p t s we prove that all and the only type schemes deducible for x can be obtained from the p t s of x by suitable operations

on the expressivity of elementary linear logic elementary linear logic is a simple variant of linear logic due to girard and which characterizes in the proofs as programs approach the class of elementary functions that is to say functions computable in time bounded by a tower of exponentials of fixed height other systems like light and soft linear logics have then been defined to characterize in a similar way the more interesting complexity class of polynomial time functions but at the price of either a more complicated syntax or of more sophisticated encodings these logical systems can serve as the basis of type systems for calculus ensuring polynomial time complexity bounds on well typed terms this paper aims at reviving interest in elementary linear logic by showing that despite its simplicity it can capture smaller complexity classes than that of elementary functions for that we carry a detailed analysis of its normalization procedure and study the complexity of functions represented by a given type we then show that by considering a slight variant of this system with type fixpoints and free weakening elementary affine logic with fixpoints we can characterize the complexity of functions of type w k 2 b where w and b are respectively types for binary words and booleans the key point is a sharper study of the normalization bounds we characterize in this way the class p of polynomial time predicates and more generally the hierarchy of classes k exp for k 0 where k exp is the union of dtime 2 k n i for i 1

phase semantics and decidability of elementary affine logic light elementary and soft linear logics are formal systems derived from linear logic enjoying remarkable normalization properties in this paper we prove decidability of elementary affine logic eal the result is obtained by semantical means first defining a class of phase models for eal and then proving soundness and strong completeness following okada s technique phase models for light affine logic and soft linear logic are also defined and shown complete

principality and type inference for intersection types using expansion variables principality of typings is the property that for each typable term there is a typing from which all other typings are obtained via some set of operations type inference is the problem of finding a typing for a given term if possible we define an intersection type system which has principal typings and types exactly the strongly normalizable terms more interestingly every finite rank restriction of this system using leivant s first notion of rank has principal typings and also has decidable type inference this is in contrast to system f where the finite rank restriction for every finite rank at 3 and above has neither principal typings nor decidable type inference furthermore the notion of principal typings for our system involves only one operation substitution rather than several operations not all substitution based as in earlier presentations of principality for intersection types without rank restrictions in our system the earlier notion of expansion is integrated in the form of expansion variables which are subject to substitution as are ordinary variables a unification based type inference algorithm is presented using a new form of unification unification

spurious reflection of elastic waves due to gradually changing finite element size summary when a homogeneous elastic continuum is modelled by a non uniform finite element grid the differences in the size of adjacent finite elements can cause a spurious wave reflection which does not exist in the continuum extending previous studies in which the spurious wave reflection was investigated for the case of two uniform grids with a sudden element size change from one grid to the other the present study deals with the case when the two uniform grids of different element sizes are separated by a transition zone through which the element size varies gradually either by a geometric progression or by an arithmetic progression the solution is carried out in complex variables and numerical plots of the results are given when the ratio of wavelength to the largest element size is as low as 4 1 the spurious wave reflection is very significant while for the ratios over 10 1 it is insignificant inserting a transition zone with gradually varying element size between the two uniform parts of the grid somewhat mitigates the phenomenon of spurious reflection but this is significant only when the ratio of element sizes in the uniform grids is small less than about 1 5 1 varying the element size throughout the transition zone in an arithmetic progression seems slightly better than in a geometric progression the spurious wave reflection is less pronounced for higher order elements in particular for linear strain elements as compared to constant strain elements the spurious reflection is also less severe for consistent mass than for lumped mass

spectral factorization by symmetric extraction for distributed parameter systems the spectral factorization problem of a scalar coercive spectral density is considered in the framework of the callier desoer algebra of distributed parameter system transfer functions criteria are given for the infinite product representation of a meromorphic coercive spectral density of finite order and for the convergence of infinite product representations of spectral factors i e for the convergence of the symmetric extraction method for solving the spectral factorization problem of such spectral density these convergence criteria are applied to the solution of the linear quadratic optimal control problem by spectral factorization for a specific class of semigroup hilbert state space systems with a riesz spectral generator the speed of convergence of the symmetric extraction method is also considered as an example a damped vibrating string model is handled

lq boundary control of a diffusion convection reaction system in this work the boundary control of a distributed parameter system modelled by linear parabolic partial differential equations pdes with spatially varying coefficients is studied an infinite dimensional state space setting is considered and an exact transformation of the boundary actuation is realised to obtain an evolutionary model the evolutionary model which incorporates the spatially varying coefficients of the underlying set of the pdes is used for subsequent linear quadratic regulator synthesis the formulated linear quadratic state feedback controller is applied to a nonlinear model of the reactor and its performance is studied

necessary and sufficient conditions for j spectral factorizations with a j lossless property for infinite dimensional systems in continuous and discrete time necessary and sufficient conditions for j spectral factorizations are given in terms of the existence of a self adjoint stabilizing solution of an appropriate riccati equation in infinite dimensions furthermore it is shown that a certain j lossless property holds if and only if the stabilizing solution to the riccati equation is nonnegative definite we prove these results first for the continuous time case and thereby derive analogous results for the discrete time case by means of a bilinear transformation of the complex plane

perpetual reductions in λ calculus this paper surveys a part of the theory ofs reduction in calculus which might aptly be calledperpetual reductions the theory is concerned withperpetual reduction strategies i e reduction strategies that compute infinite reduction paths from terms when possible and withperpetual redexes i e redexes whose contraction in terms preserves the possibility when present of infinite reduction paths the survey not only recasts classical theorems in a unified setting but also offers new results proofs and techniques as well as a number of applications to problems in calculus and type theory

quadratic optimal control of stable well posed linear systems we consider the infinite horizon quadratic cost minimization problem for a stable time invariant well posed linear system in the sense of salamon and weiss and show that it can be reduced to a spectral factorization problem in the control space more precisely we show that the optimal solution of the quadratic cost minimization problem is of static state feedback type if and only if a certain spectral factorization problem has a solution if both the system and the spectral factor are regular then the feedback operator can be expressed in terms of the riccati operator and the riccati operator is a positive self adjoint solution of an algebraic riccati equation this riccati equation is similar to the usual algebraic riccati equation but one of its coefficients varies depending on the subspace in which the equation is posed similar results are true for unstable systems as we have proved elsewhere

linear state space systems in infinite dimensional space the role and characterization of joint stabilizability detectability several fundamental results from the theory of linear state space systems in finite dimensional space are extended to encompass a class of linear state space systems in infinite dimensional space the results treated are those pertaining to the relationship between input output and internal stability the problem of dynamic output feedback stabilization and the concept of joint stabilizability detectability a complete structural characterization of jointly stabilizable detectable systems is obtained the generalized theory applies to a large class of linear state space systems assuming only that i the evolution of the state is governed by a strongly continuous semigroup of bounded linear operators ii the state space is hilbert space iii the input and output spaces are finite dimensional and iv the sensing and control operators are bounded general conclusions regarding the fundamental structure of control theoretic problems in infinite dimensional space can be drawn from these results

nehari problems and equalizing vectors for infinite dimensional systems for a class of infinite dimensional systems we obtain a simple frequency domain solution for the suboptimal nehari extension problem the approach is via j spectral factorization and it uses the concept of an equalizing vector moreover the connection between the equalizing vectors and the nehari extension problem is given

type inference for light affine logic via constraints on words light affine logic lal is a system due to girard and asperti capturing the complexity class p in a proof theoretical approach based on linear logic lal provides a typing for lambda calculus which guarantees that a well typed program is executable in polynomial time on any input we prove that the lal type inference problem for lambda calculus is decidable for propositional lal to establish this result we reformulate the type assignment system into an equivalent one which makes use of subtyping and is more flexible we then use a reduction to a satisfiability problem for a system of inequations on words over a binary alphabet for which we provide a decision procedure

on an interpretation of safe recursion in light affine logic we introduce a subalgebra bc of bellantoni and cook s safe recursion function algebra bc functions of the subalgebra have safe arguments that are non contractible i e non duplicable we propose a definition of safe and normal variables in light affine logic lal and show that bc is the largest subalgebra that is interpretable in lal relative to that definition though bc itself is not pf complete there are extensions of it by additional schemes for defining functions with safe arguments that are and are still interpretable in lal and so preserve pf closure we focus on one such which is bc augmented by a definition by cases construct and a restricted form of definition by recursion scheme over safe arguments as a corollary we obtain a new proof of the pf completeness of lal

a type assignment system for game semantics we present a type assignment system that provides a finitary interpretation of lambda terms in a game semantics model traditionally type assignment systems describe the semantic interpretation of terms in domain theoretic models quite surprisingly the type assignment system presented in this paper is very similar to the traditional ones the main difference being the omission of the subtyping rules

filter models with polymorphic types abstract using ideas and results from barendrecht 1983 and coppo 1984 on intersection types a comparable theory is developed for second order polymorphic types the set of filters constructed with polymorphic type forms with inclusion a continuous lattice which yields a model of what we call expansion i e the value of a term increases under reduction but not of conversion combining intersection with polymorphic types does give filter models but the two standard ways of interpreting terms do not coincide

godel s system t revisited the linear lambda calculus where variables are restricted to occur in terms exactly once has a very weak expressive power in particular all functions terminate in linear time in this paper we consider a simple extension with natural numbers and a restricted iterator only closed linear functions can be iterated we show properties of this linear version of godel s tusing a closed reduction strategy and study the class of functions that can be represented surprisingly this linear calculus offers a huge increase in expressive power over previous linear versions of t which are closed at construction rather than closed at reduction we show that a linear twith closed reduction is as powerful as t

introduction to clarithmetic ii the earlier paper introduction to clarithmetic i constructed an axiomatic system of arithmetic based on computability logic and proved its soundness and extensional completeness with respect to polynomial time computability the present paper elaborates three additional sound and complete systems in the same style and sense one for polynomial space computability one for elementary recursive time and or space computability and one for primitive recursive time and or space computability

analytic system problems and j lossless coprime factorization for infinite dimensional linear systems abstract this paper extends the coprime factorization approach to the synthesis of internally stabilizing controllers satisfying an h norm bound to a class of systems with irrational transfer matrices using the coprime factorization description the h control problem can be reduced to two stable analytic system problems such problems have solutions if and only if a certain j lossless factorization exists the full h synthesis problem is shown to be equivalent to the solution of two nested j lossless factorizations if the irrational transfer matrix has a state space realization then the known state space formulas for the h control problem may be recovered using the relationship between j lossless factorizations and solutions of riccati equations however the results derived here are valid for a larger class of infinite dimensional systems

reconciling nu gap metric and iqc based robust stability analysis this technical note elaborates on the flexibility of an approach that combines gap metric and integral quadratic constraint iqc based analysis in the study of uncertain feedback interconnections of distributed parameter transfer functions it is established that a standard gap ball robust stability result can be recovered within the blended iqc gap framework which only requires the existence of gap continuous paths within the uncertainty set of interest this is achieved in part by showing that sufficiently small gap balls are pathwise connected in the graph topology a linear fractional characterisation of the gap is a key ingredient this characterisation is underpinned by a certain j spectral factorisation also shown to exist herein

realizability models for bll like languages we give a realizability model of girard scedrov scott s bounded linear logic bll this gives a new proof that all numerical functions representable in that system are polytime our analysis naturally justifies the design of the bll syntax and suggests further extensions

quantum implicit computational complexity we introduce a quantum lambda calculus inspired by lafont s soft linear logic and capturing the polynomial quantum complexity classes eqp bqp and zqp the calculus is based on the classical control and quantum data paradigm this is the first example of a formal system capturing quantum complexity classes in the spirit of implicit computational complexity it is machine free and no explicit bound e g polynomials appears in its syntax

approximation and stabilization of distributed systems by lumped systems in this note we study two questions regarding linear time invariant distributed systems namely 1 when can the given system be approximated by a lumped system 2 when can the given system be stabilized by a lumped system in each case we obtain a complete answer to the question in terms of the behaviour of the purely atomic parts of the stable numerator and denominator of the plant

bounded quantification is undecidable f is a typed calculus with subtyping and bounded second order polymorphism first introduced by cardelli and wegner it has been widely studied as a core calculus for type systems with subtyping we use a reduction from the halting problem for two counter turing machines to show that the subtyping and typing relations of f are undecidable