system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

topology recognition with advice in topology recognition each node of an anonymous network has to deterministically produce an isomorphic copy of the underlying graph with all ports correctly marked this task is usually unfeasible without any a priori information such information can be provided to nodes as advice an oracle knowing the network can give a possibly different string of bits to each node and all nodes must reconstruct the network using this advice after a given number of rounds of communication during each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations the time of completing topology recognition is the number of rounds it takes and the size of advice is the maximum length of a string given to nodes we investigate tradeoffs between the time in which topology recognition is accomplished and the minimum size of advice that has to be given to nodes we provide upper and lower bounds on the minimum size of advice that is sufficient to perform topology recognition in a given time in the class of all graphs of size n and diameter d n for any constant 1 in most cases our bounds are asymptotically tight

renaming in an asynchronous environment this paper is concerned with the solvability of the problem of processor renaming in unreliable completely asynchronous distributed systems fischer et al prove in 8 that nontrivial consensus cannot be attained in such systems even when only a single benign processor failure is possible in contrast this paper shows that problems of processor renaming can be solved even in the presence of up to t n 2 faulty processors contradicting the widely held belief that no nontrivial problem can be solved in such a system the problems deal with renaming processors so as to reduce the size of the initial name space when only uniqueness of the new names is required we present a lower bound of n 1 on the size of the new name space and a renaming algorithm that establishes an upper bound on n t if the new names are required also to preserve the original order a tight bound of 2 n t 1 1 is obtained

well posedness of feedback systems insights into exact robustness analysis and approximate computations this paper establishes a framework for robust stability analysis of linear time invariant uncertain systems the uncertainty is assumed to belong to an arbitrary subset of complex matrices the concept used here is well posedness of feedback systems leading to necessary and sufficient conditions for robust stability based on this concept some insights into exact robust stability conditions are given in particular frequency domain and state space conditions for well posedness are provided in terms of hermitian form inequalities it is shown that these inequalities can be interpreted as small gain conditions with a generalized class of scalings given by linear fractional transformations lft using the lft scaled small gain condition in the state space setting the duality is established between the h sub spl infin norm condition with frequency dependent scalings and the parameter dependent lyapunov condition connections to the existing results including the structured singular value and the integral quadratic constraints are also discussed finally we show that our well posedness conditions can be used to give a less conservative yet computable bound on the real structured singular value this result is illustrated by numerical examples

tree exploration with advice we study the amount of knowledge about the network that is required in order to efficiently solve a task concerning this network the impact of available information on the efficiency of solving network problems such as communication or exploration has been investigated before but assumptions concerned availability of particular items of information about the network such as the size the diameter or a map of the network in contrast our approach is quantitative we investigate the minimum number of bits of information bits of advice that has to be given to an algorithm in order to perform a task with given efficiency we illustrate this quantitative approach to available knowledge by the task of tree exploration a mobile entity robot has to traverse all edges of an unknown tree using as few edge traversals as possible the quality of an exploration algorithm a is measured by its competitive ratio i e by comparing its cost number of edge traversals to the length of the shortest path containing all edges of the tree depth first search has competitive ratio 2 and in the absence of any information about the tree no algorithm can beat this value we determine the minimum number of bits of advice that has to be given to an exploration algorithm in order to achieve competitive ratio strictly smaller than 2 our main result establishes an exact threshold number of bits of advice that turns out to be roughly loglogd where d is the diameter of the tree more precisely for any constant c we construct an exploration algorithm with competitive ratio smaller than 2 using at most loglogd c bits of advice and we show that every algorithm using loglogd g d bits of advice for any function g unbounded from above has competitive ratio at least 2

topological abstraction of higher dimensional automata higher dimensional automata constitute a very expressive model for concurrent systems in this paper we discuss topological abstraction of higher dimensional automata i e the replacement of hdas by smaller ones that can be considered equivalent from the point of view of both computer science and topology by definition topological abstraction preserves the homotopy type the trace category and the homology graph of an hda we establish conditions under which cube collapses yield topological abstractions of hdas

the real structured singular value is hardly approximable this paper investigates the problem of approximating the real structured singular value real spl mu a negative result is provided which shows that the problem of checking if spl mu 0 is np hard this result is much more negative than the known np hard result for the problem of checking if spl mu 0 even exponential functions of n unless np p a similar statement holds for the lower bound of spl mu our result strengthens a recent result by toker which demonstrates that obtaining a sublinear approximation for spl mu is np hard

integration of brownian vector fields summary using the wiener chaos decomposition we show that strong solutions of non lipschitzian s d e s are given by random markovian kernels the example of sobolev flows is studied in some detail exhibiting interesting phase transitions

topology recognition and leader election in colored networks topology recognition and leader election are fundamental tasks in distributed computing in networks the first of them requires each node to find a labeled isomorphic copy of the network while the result of the second one consists in a single node adopting the label 1 leader with all other nodes adopting the label 0 and learning a path to the leader we consider both these problems in networks whose nodes are equipped with not necessarily distinct labels called colors and ports at each node of degree d are arbitrarily numbered 0 1 d 1 colored networks are generalizations both of labeled networks in which nodes have distinct labels and of anonymous networks in which nodes do not have labels all nodes have the same color in colored networks topology recognition and leader election are not always feasible hence we study two more general problems consider a colored network and an input i given to its nodes the aim of the problem top for this colored network and for i is to solve topology recognition in this network if this is possible under input i and to have all nodes answer unsolvable otherwise likewise the aim of the problem le is to solve leader election in this network if this is possible under input i and to have all nodes answer unsolvable otherwise we show that nodes of a network can solve problems top and le if they are given as input i an upper bound k on the number of nodes of a given color called the size of this color on the other hand we show that if the nodes are given an input that does not bound the size of any color then the answer to top and le must be unsolvable even for the class of rings under the assumption that nodes are given an upper bound k on the size of a given color we study the time of solving problems top and le in the local model in which during each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations we give an algorithm to solve each of these problems in arbitrary networks in time o k d d log n d where d is the diameter of the network and n is its size we also show that this time is optimal by exhibiting classes of networks in which every algorithm solving problems top or le must use time k d d log n d

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

a multiloop generalization of the circle criterion for stability margin analysis in order to provide a theoretical tool well suited for use in characterizing the stability margins e g gain and phase margins of multiloop feedback systems multiloop input output stability results generalizing the circle stability criterion are considered generalized conic sectors with centers and radii determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency dependent convex set of modeling errors including nonlinearities gain variations and phase variations which the system must be able to tolerate in each feedback loop without instability the resulting stability criterion gives sufficient conditions for closed loop stability in the presence of such frequency dependent modeling errors even when the modeling errors occur simultaneously in all loops so for example stability is assured as loop gains and phases vary throughout a set of nonzero measure whose boundaries are frequency dependent the stability conditions yield an easily interpreted scalar measure of the amount by which a muitiloop system exceeds or falls short of its stability margin specifications

improved upper bounds for the mixed structured singular value in this paper we take a new look at the mixed structured singular value problem a problem of finding important applications in robust stability analysis several new upper bounds are proposed using a very simple approach which we call the multiplier approach these new bounds are convex and computable by using linear matrix inequality lmi techniques we show most importantly that these upper bounds are actually lower bounds of a well known upper bound which involves the so called d scaling for complex perturbations and g scaling for real perturbations

on modelling mobility we present a model of distributed computation which is based on a fragment of the calculus relying on asynchronous point to point communication we enrich the model with the following features the explicit distribution of processes to locations the routing of messages the mobility of processes and the failure of locations and their detection our contributions are two folds at the specification level we give a synthetic and flexible formalization of the features mentioned above at the verification level we provide original methods to reason about the bisimilarity of processes

ordinal subdivision and special pasting in quasicategories abstract quasicategories are simplicial sets with properties generalising those of the nerve of a category they model weak 1 categories using a combinatorially defined ordinal subdivision we examine composition rules for certain special pasting diagrams in quasicategories the subdivision is of combinatorial interest in its own right and is linked with various combinatorial constructions

electing a leader in a synchronous ring the problem of electing a leader in a synchronous ring of n processors is considered both positive and negative results are obtained on the one hand if processor ids are chosen from some countable set then there is an algorithm that uses only o n messages in the worst case on the other hand any algorithm that is restricted to use only comparisons of ids requires o n log n messages in the worst case alternatively if the number of rounds is required to be bounded by some t in the worst case and ids are chosen from any set having at least n t elements for a certain very fast growing function then any algorithm requires o n log n messages in the worst case

a dual formulation of mixed spl mu and on the losslessness of d g scaling this paper studies the mixed structured singular value spl mu and the well known d g scaling upper bound spl nu a dual characterization of spl mu and spl nu is derived which intimately links the two values using the duals it is shown that spl nu is guaranteed to be lossless i e equal to spl mu if and only if 2 m sub r m sub e m sub c spl les 3 where m sub r m sub c and m sub c are the numbers of repeated real scalar blocks repeated complex scalar blocks and full complex blocks respectively the losslessness result further leads to a variation of the well known kalman yakubovich popov lemma and lyapunov inequalities

new combinatorial topology bounds for renaming the upper bound in the renaming task n 1 processes start with unique input names from a large space and must choose unique output names taken from a smaller name space 0 1 k to rule out trivial solutions a protocol must be anonymous the value chosen by a process can depend on its input name and on the execution but not on the specific process id attiya et al 1990 showed that renaming has a wait free solution when k 2n several algebraic topology proofs of a lower bound stating that no such protocol exists when k

modulus of continuity of the canonic brownian motion on the group of diffeomorphisms of the circle abstract an explicit modulus of holder continuity is given for the flow associated to the canonic brownian motion on the diffeomorphism group of the circle

on the kalman yakubovich popov lemma the purpose of this note is to present a new elementary proof for the multivariable k y p lemma a minimum of linear algebra and finite dimensional convexity theory is used

a finiteness condition for rewriting systems abstract we present a purely combinatorial approach to the question of whether or not a finitely presented monoid has a finite canonical presentation our approach is based on the notion of finite derivation type which is a combinatorial condition satisfied by certain rewriting systems our main result states that if a monoid m has a finite canonical presentation then all finite presentations of m have finite derivation type by proving that a certain monoid s1 does not have finite derivation type we show in addition that the homological finiteness condition fp is not sufficient to guarantee that a finitely presented monoid with a decidable word problem has a finite canonical presentation

a non topological proof for the impossibility of k set agreement in the k set agreement task each process proposes a value and each correct process has to decide a value which was proposed so that at most k distinct values are decided using topological arguments it has been proved that k set agreement is unsolvable in the asynchronous wait free read write shared memory model when k

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

passivity analysis and passification for uncertain signal processing systems the problem of passivity analysis finds important applications in many signal processing systems such as digital quantizers decision feedback equalizers and digital and analog filters equally important is the problem of passification where a compensator needs to be designed for a given system to become passive this paper considers these two problems for a large class of systems that involve uncertain parameters time delays quantization errors and unmodeled high order dynamics by characterizing these and many other types of uncertainty using a general tool called integral quadratic constraints iqcs we present solutions to the problems of robust passivity analysis and robust passification more specifically for the analysis problem we determine if a given uncertain system is passive for all admissible uncertainty satisfying the iqcs similarly for the problem of robust passification we are concerned with finding a loop transformation such that a particular part of the uncertain signal processing system becomes passive for all admissible uncertainty the solutions are given in terms of the feasibility of one or more linear matrix inequalities lmis which can be solved efficiently

stability analysis with dissipation inequalities and integral quadratic constraints this technical note considers the stability of a feedback connection of a known linear time invariant system and a perturbation the input output behavior of the perturbation is described by an integral quadratic constraint iqc iqc stability theorems can be formulated in the frequency domain or with a time domain dissipation inequality the two approaches are connected by a non unique factorization of the frequency domain iqc multiplier the factorization must satisfy two properties for the dissipation inequality to be valid first the factorization must ensure the time domain iqc holds for all finite times second the factorization must ensure that a related matrix inequality when feasible has a positive semidefinite solution this technical note shows that a class of frequency domain iqc multipliers has a factorization satisfying these two properties thus the dissipation inequality test with an appropriate factorization can be used with no additional conservatism

some properties of an upper bound for spl mu a convex upper bound of the mixed structured singular value spl mu is analyzed the upper bound is based on a multiplier method it is simple it can exploit low rank properties and it is shown to be less conservative than the well known d g scaling a direct relationship with d g scaling is given the upper bound can be modified to one that is continuous with an explicit lipschitz constant

brief paper factorization of multipliers in passivity and iqc analysis multipliers are often used to find conditions for the absolute stability of lur e systems they can be used either in conjunction with passivity theory or within the more recent framework of integral quadratic constraints iqcs we compare the use of multipliers in both approaches passivity theory requires that the multipliers have a canonical factorization and it has been suggested in the literature that this represents an advantage of the iqc theory we consider sufficient conditions on the nonlinearity class for the associated multipliers to have a canonical factorization

continuous time analysis eigenstructure assignment and h sub 2 synthesis with enhanced linear matrix inequalities lmi characterizations this note describes a new framework for the analysis and synthesis of control systems which constitutes a genuine continuous time extension of results that are only available in discrete time in contrast to earlier results the proposed methods involve a specific transformation on the lyapunov variables and a reciprocal variant of the projection lemma in addition to the classical linearizing transformations on the controller data for a wide range of problems including robust analysis and synthesis multichannel h sub 2 stateand output feedback syntheses the approach leads to potentially less conservative linear matrix inequality lmi characterizations this comes from the fact that the technical restriction of using a single lyapunov function is to some extent ruled out in this new approach moreover the approach offers new potentials for problems that cannot be handled using earlier techniques an important instance is the eigenstructure assignment problem blended with lyapunov type constraints which is given a simple and tractable formulation

a domain of spacetime intervals in general relativity we prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology from this one can show that from only a countable dense set of events and the causality relation it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner the ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special category of domains called interval domains we obtain a mathematical setting in which one can study causality independently of geometry and differentiable structure and which also suggests that spacetime emerges from something discrete

canonical brownian motion on the diffeomorphism group of the circle for infinitesimal data given on the group of diffeomorphism of the circle with respect to the metric h3 2 the associated brownian motion has been constructed by malliavin c r acad sci parist 329 1999 325 329 in this work we shall give another approach and prove the invariance of heat measures under the adjoint action of s1

algebraic topology and concurrency we show in this article that some concepts from homotopy theory in algebraic topology are relevant for studying concurrent programs we exhibit a natural semantics of semaphore programs based on partially ordered topological spaces which are studied up to elastic deformation or homotopy giving information about important properties of the program such as deadlocks unreachables serializability essential schedules etc in fact it is not quite ordinary homotopy that has to be used but rather a directed homotopy that does not reverse the flow of time we show some of the essential differences between ordinary and directed homotopy through examples we also relate the topological view to a combinatorial view of concurrent programs closer to transition systems through the notion of a cubical set finally we apply some of these concepts to the proof of the safeness of a two phase protocol well known and used in concurrent database theory we end up with a list of problems from both a mathematical and a computer scientific point of view

algorithms for the certified write all problem in this paper we prove new upper bounds on the complexity of the certified write all problem with respect to an adaptive adversary our strongest result is that for any epsilon 0 there exists an o p 1 epsilon work algorithm for the p processor p memory cell write all we also give a randomized o p 2 log p work algorithm for a p processor p 2 memory cell write all

basic observables for a calculus for global computing we develop the semantic theory of a foundational language for modelling applications over global computers whose interconnection structure can be explicitly manipulated together with process distribution process mobility and remote asynchronous communication through distributed data repositories the language has primitives for explicitly modelling inter node connections and for dynamically activating and deactivating them for the proposed language we define natural notions of extensional observations and study their closure under operational reductions and or language contexts to obtain barbed congruence and may testing equivalence we then focus on barbed congruence and provide an alternative characterisation in terms of a labelled bisimulation to test practical usability of the semantic theory we model a system of communicating mobile devices and use the introduced proof techniques to verify one of its key properties

on continuity discontinuity in robustness indicators continuity discontinuity of robustness indicators is reviewed for the case of real or mixed uncertainty a regularization of a conservative bound to the robustness margin is proposed and its properties are discussed in the case of polynomial families with affine dependency on the uncertainty a regularization of the robustness margin results

computational complexity of real structured singular value in l sub p setting this paper studies a generalized real structured singular value spl mu problem where uncertain parameters are bounded by an l sub p norm two results are presented the first one shows that this generalized spl mu problem is np hard for any given rational number p spl isin 1 spl infin the np hardness holds as long as le the size of the largest repeated block exceeds one this result generalizes the known np hardness result for the conventional spl mu problem with p spl infin the second result which strengthens the first one considers the approximability problem of the generalized spl mu we show that the problem of obtaining an estimate for the generalized spl mu with some guaranteed bounds on the relative error remains to be np hard regardless how large this bound is

modified nevanlinna pick interpolation and feedback stabilization of linear plants with uncertainty in the gain factor abstract this paper is a sequel to an earlier work in which we applied classical novnnlinna pick interpolation to the stabilization of a single input output plant with uncertainly in the gain factor by means of an asymptotically stable control and feedback sensor in this present work we show that for the proper design we need a modification of the classical interpolation procedure a point not clearly brought out in our previous paper

tight bounds for asynchronous renaming this article presents the first tight bounds on the time complexity of shared memory renaming a fundamental problem in distributed computing in which a set of processes need to pick distinct identifiers from a small namespace we first prove an individual lower bound of k process steps for deterministic renaming into any namespace of size subexponential in k where k is the number of participants the bound is tight it draws an exponential separation between deterministic and randomized solutions and implies new tight bounds for deterministic concurrent fetch and increment counters queues and stacks the proof is based on a new reduction from renaming to another fundamental problem in distributed computing mutual exclusion we complement this individual bound with a global lower bound of k log k c on the total step complexity of renaming into a namespace of size ck for any c 1 this result applies to randomized algorithms against a strong adversary and helps derive new global lower bounds for randomized approximate counter implementations that are tight within logarithmic factors on the algorithmic side we give a protocol that transforms any sorting network into a randomized strong adaptive renaming algorithm with expected cost equal to the depth of the sorting network this gives a tight adaptive renaming algorithm with expected step complexity o log k where k is the contention in the current execution this algorithm is the first to achieve sublinear time and it is time optimal as per our randomized lower bound finally we use this renaming protocol to build monotone consistent counters with logarithmic step complexity and linearizable fetch and increment registers with polylogarithmic cost

reaching approximate agreement in the presence of faults this paper considers a variant of the byzantine generals problem in which processes start with arbitrary real values rather than boolean values or values from some bounded range and in which approximate rather than exact agreement is the desired goal algorithms are presented to reach approximate agreement in asynchronous as well as synchronous systems the asynchronous agreement algorithm is an interesting contrast to a result of fischer et al who show that exact agreement with guaranteed termination is not attainable in an asynchronous system with as few as one faulty process the algorithms work by successive approximation with a provable convergence rate that depends on the ratio between the number of faulty processes and the total number of processes lower bounds on the convergence rate for algorithms of this form are proved and the algorithms presented are shown to be optimal

more choices allow more faults set consensus problems in totally asynchronous systems abstract we define the k set consensus problem as an extension of the consensus problem where each processor decides on a single value such that the set of decided values in any run is of size at most k we require the agreement condition that all values decided upon are initial values of some processor we show that the problem has a simple k 1 resilient protocol in a totally asynchronous system in an attempt to come up with a matching lower bound on the number of failures we study the uncertainty condition which requires that there must be some initial configuration from which all possible input values can be decided we prove using a combinatorial argument that any k resilient protocol for the k set agreement problem would satisfy the uncertainty condition while this is not true for any k 1 resilient protocol this result seems to strengthen the conjecture that there is no k resilient protocol for this problem we prove this result for a restricted class of protocols our motivation for studying this problem is to test whether the number of choices allowed to the processors is related to the number of faults we hope that this will provide intuition towards achieving better bounds for more practical problems that arise in distributed computing e g the renaming problem the larger goal is to characterize the boundary between possibility and impossibility in asynchronous systems given multiple faults

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

random conformal weldings we construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle the homeomorphism is constructed using the exponential of x where x is the restriction of the 2 dimensional free field on the circle and the parameter is in the high temperature regime beta sqrt 2 the welding problem is solved by studying a non uniformly elliptic beltrami equation with a random complex dilatation for the existence a method of lehto is used this requires sharp probabilistic estimates to control conformal moduli of annuli and they are proven by decomposing the free field as a sum of independent fixed scale fields and controlling the correlations of the complex dilatation restricted to dyadic cells of various scales for the uniqueness we invoke a result by jones and smirnov on conformal removability of holder curves our curves are closely related to sle for 4

the combinatorial structure of wait free solvable tasks this paper presents a self contained study of wait free solvable tasks a new necessary condition for wait free solvability based on a restricted set of executions is proved this set of executions induces a very simple to understand structure which is used to prove tight bounds for k set consensus and renaming the framework is based on topology but uses only elementary combinatorics and in contrast to previous works does not rely on algebraic or geometric arguments

are wait free algorithms fast the time complexity of wait free algorithms in normal executions where no failures occur and processes operate at approximately the same speed is considered a lower bound of log n on the time complexity of any wait free algorithm that achieves approximate agreement among n processes is proved in contrast there exists a non wait free algorithm that solves this problem in constant time this implies an o log n time separation between the wait free and non wait free computation models on the positive side we present an o log n time wait free approximate agreement algorithm the complexity of this algorithm is within a small constant of the lower bound

computational complexity of spl mu calculation the structured singular value spl mu measures the robustness of uncertain systems numerous researchers over the last decade have worked on developing efficient methods for computing spl mu this paper considers the complexity of calculating spl mu with general mixed real complex uncertainty in the framework of combinatorial complexity theory in particular it is proved that the spl mu recognition problem with either pure real or mixed real complex uncertainty is np hard this strongly suggests that it is futile to pursue exact methods for calculating spl mu of general systems with pure real or mixed uncertainty for other than small problems

labeling schemes for flow and connectivity this paper studies labeling schemes for flow and connectivity functions a flow labeling scheme using o log n cdot log hat omega log 2 n bit labels is presented for general n vertex graphs with maximum integral capacity hat omega this is shown to be asymptotically optimal for edge connectivity this yields a tight bound of theta log 2 n bits a k vertex connectivity labeling scheme is then given for general n vertex graphs using at most 3 log n bits for k 2 5 log n bits for k 3 and 2k log n bits for k 3 finally a lower bound of omega k log n is established for k vertex connectivity on n vertex graphs where k is polylogarithmic in n

the rank one mixed m problem and kharitonov type analysis the general mixed problem has been shown to be np hard so that the exact solution of the general problem is computationally intractable except for small problems in this paper we consider not the general problem but a particular special case of this problem the rank one mixed problem we show that for this case the mixed problem is equivalent to its upper bound which is convex and it can in fact be computed easily and exactly this special case is shown to be equivalent to the so called affine parameter variation problem for a polynomial with perturbed coefficients which has been examined in detail in the literature and for which several celebrated kharitonov type results have been proven

a cutting plane algorithm for robustness analysis of periodically time varying systems an algorithm for robustness analysis of periodic systems is derived the system under consideration consists of a linear periodically time varying plant in feedback interconnection with a structured uncertainty conditions for robust stability and robust performance can be formulated in terms of periodic integral quadratic constraints iqcs in this way the robustness analysis becomes a problem of optimizing the parameters of the iqc a cutting plane algorithm is suggested for solving this infinite dimensional optimization problem

global analysis of piecewise linear systems using impact maps and surface lyapunov functions this paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems pls this methodology infers global properties of pls solely by studying the behavior at switching surfaces associated with pls the main idea is to analyze impact maps i e maps from one switching surface to the next switching surface such maps are known to be unfriendly maps in the sense that they are highly nonlinear multivalued and not continuous we found however that an impact map induced by an linear time invariant flow between two switching surfaces can be represented as a linear transformation analytically parametrized by a scalar function of the state this representation of impact maps allows the search for surface lyapunov functions sulf to be done by simply solving a semidefinite program allowing global asymptotic stability robustness and performance of limit cycles and equilibrium points of pls to be efficiently checked this new analysis methodology has been applied to relay feedback on off and saturation systems where it has shown to be very successful in globally analyzing a large number of examples in fact it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology examples analyzed include systems of relative degree larger than one and of high dimension for which no other analysis methodology could be applied this success in globally analyzing certain classes of pls has shown the power of this new methodology and suggests its potential toward the analysis of larger and more complex pls

online computation with advice we consider a model for online computation in which the online algorithm receives together with each request some information regarding the future referred to as advice the advice is a function defined by the online algorithm of the whole request sequence the advice provided to the online algorithm may allow an improvement in its performance compared to the classical model of complete lack of information regarding the future we are interested in the impact of such advice on the competitive ratio and in particular in the relation between the size b of the advice measured in terms of bits of information per request and the improved competitive ratio since b 0 corresponds to the classical online model and b log a where a is the algorithm s action space corresponds to the optimal offline one our model spans a spectrum of settings ranging from classical online algorithms to offline ones in this paper we propose the above model and illustrate its applicability by considering two of the most extensively studied online problems namely metrical task systems mts and the k server problem for mts we establish tight up to constant factors upper and lower bounds on the competitive ratio of deterministic and randomized online algorithms with advice for any choice of 1 b q logn where n is the number of states in the system we prove that any randomized online algorithm for mts has competitive ratio w log n b and we present a deterministic online algorithm for mts with competitive ratio o log n b for the k server problem we construct a deterministic online algorithm for general metric spaces with competitive ratio k o 1 b for any choice of q 1 b logk

a survey of extreme point results for robustness of control systems abstract this paper surveys a subset of the body of research which was sparked by kharitonov s theorem the focal point is extreme point results for robust stability and robust performance that is we give conditions under which satisfaction of a performance specification is ascertained for a family of systems by only checking a finite subset of the extreme members of this family the results which are surveyed apply mainly to systems with structured real parametric uncertainty in addition a number of counterexamples are given to illustrate cases for which an extreme point result does not hold for such cases a solution via the so called edge theorem is often possible

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

frequency domain criteria of robust stability for slowly time varying systems the problem of stability of feedback systems with structured slowly time varying uncertain gains is considered for the case when the pair uncertain gain derivative belongs to a given convex set a sufficient frequency domain condition of stability is obtained this condition is an mimo generalization of the siso results derived in the 60s in the context of the positivity theory

a topological treatment of early deciding set agreement the k set agreement problem consists for a set of n processes to agree on less than k among n possibly different values each initially known to only one process the problem is at the heart of distributed computing and generalizes the celebrated consensus problem this paper considers the k set agreement problem in a synchronous message passing distributed system where up to t processes can fail by crashing we determine the number of communication rounds needed for all correct processes to reach a decision in a given run as a function of the degree of coordination k and the number of processes that actually fail in the run email protected t we prove that for any integer email protected k

integral quadratic constraint approach vs multiplier approach integral quadratic constraints iqc arise in many optimal and or robust control problems the iqc approach can be viewed as a generalization of the classical multiplier approach in the absolute stability theory in this paper we study the relationship between the two approaches for robust stability analysis using a slightly modified multiplier approach we show that the existence of an iqc is equivalent to the existence of a multiplier in most known cases it is hoped that this result provides some new insight into both approaches and makes them more useful in robust control applications

quasi invariance of brownian measures on the group of circle homeomorphisms and infinite dimensional riemannian geometry abstract a cameron martin type theorem is proved for the canonical brownian motion on the group of homeomorphisms of the circle

computing with infinitely many processes we explore four classic problems in concurrent computing election mutual exclusion consensus and naming when the number of processes which may participate is unbounded partial information about the number of processes actually participating and the concurrency level is shown to affect the computability and complexity of solving these problems when using only atomic registers we survey and generalize work carried out in models with known bounds on the number of processes and prove several new results these include improved bounds for election when participation is required and a new adaptive starvation free mutual exclusion algorithm for unbounded concurrency we also survey results in models with shared objects stronger than atomic registers such as test set bits semaphores or read modify write registers and update them for the unbounded case

deadlocks and dihomotopy in mutual exclusion models higher dimensional automata hda represent a promising tool for modelling true concurrency in a both combinatorial and topological framework within these models fast algorithms investigating deadlocks and unreachable regions have been devised previously on a background of easily understandable directed geometric ideas in this article we modify notions and methods from homotopy theory to define and investigate essentially different schedules in a hda and to detect whether two given runs are essentially different using an algorithm again based on directed geometry

numerical methods of lyapunov function construction and their application to the absolute stability problem the minimax approach is used to study numerical selection of a lyapunov function from a multiparameter class of functions a numerical method is suggested for plotting an absolute stability region in the space of system gains for a control system with several nonstationary nonlinearities

heat kernel analysis on infinite dimensional heisenberg groups abstract we introduce a class of non commutative heisenberg like infinite dimensional lie groups based on an abstract wiener space the ricci curvature tensor for these groups is computed and shown to be bounded brownian motion and the corresponding heat kernel measures t t 0 are also studied we show that these heat kernel measures admit 1 gaussian like upper bounds 2 cameron martin type quasi invariance results 3 good l p bounds on the corresponding radon nikodym derivatives 4 integration by parts formulas and 5 logarithmic sobolev inequalities the last three results heavily rely on the boundedness of the ricci tensor

weak morphisms of higher dimensional automata abstract we introduce weak morphisms of higher dimensional automata and use them to define preorder relations for hdas among which are homeomorphic abstraction and trace equivalent abstraction it is shown that homeomorphic abstraction is essentially always stronger than trace equivalent abstraction we also define the trace language of an hda and show that for a large class of hdas it is invariant under trace equivalent abstraction

distinguishing views in symmetric networks the view of a node in a port labeled network is an infinite tree encoding all walks in the network originating from this node we prove that for any integers n d 1 there exists a port labeled network with at most n nodes and diameter at most d which contains a pair of nodes whose infinite views are different but whose views truncated to depth d log n d are identical

computer aided stability analysis renders popov criterion obsolete a class of multipliers that can be used for producing alternative stability tests for systems having a single incrementally conic nonlinearity f x has been nearly parameterized by zames and falb 1 the present note demonstrates how linear programming can be used to compute optimal multipliers leading to a frequency domain stability criterion that is less conservative than the standard graphical criteria

on the gap between the complex structured singular value and its convex upper bound the gap between the complex structured singular value of a complex matrix m and its convex upper bound is considered new necessary and sufficient conditions for the existence of the gap are derived it is shown that determining whether there exists such a gap is as difficult as evaluating a structured singular value of a reduced rank matrix whose rank is equal to the multiplicity of the largest singular value of m furthermore if an upper bound on this reduced rank problem can be obtained it is shown that this provides an upper bound on the original problem that is lower than the convex relaxation upper bound an example that illustrates our procedure is given we also give the solution of several structured approximation problems of independent interest

solving the at most once problem with nearly optimal effectiveness we present and analyze a wait free deterministic algorithm for solving the at most once problem how m shared memory fail prone processes perform asynchronously n jobs at most once our algorithmic strategy provides for the first time nearly optimal effectiveness which is a measure that expresses the total number of jobs completed in the worst case the effectiveness of our algorithm equals n 2m 2 this is up to an additive factor of m close to the known effectiveness upper bound n m 1 over all possible algorithms and improves on the previously best known deterministic solutions that have effectiveness only n logm o n we also present an iterative version of our algorithm that for any m o n logn3 is both effectiveness optimal and work optimal for any constant 0 we then employ this algorithm to provide a new algorithmic solution for the write all problem which is work optimal for any m o n logn3

on execution spaces of pv programs semaphores were introduced by dijkstra as a tool for modeling concurrency in computer programs in this paper we provide a formal definition of pv programs i e programs using semaphores their state spaces and execution spaces the main goal of this paper is to prove that every finite homotopy type may appear as a connected component of the execution space of a pv program

wait free k set agreement is impossible the topology of public knowledge in the classical consensus problem each of n processors receives a private input value and produces a decision value which is one of the original input values with the requirement that all processors decide the same value a central result in distributed computing is that in several standard models including the asynchronous shared memory model this problem has no deterministic solution the k set agreement problem is a generalization of the classical consensus proposed by chaudhuri inform and comput 105 1993 pp 132 158 where the agreement condition is weakened so that the decision values produced may be different as long as the number of distinct values is at most k for n k geq 2 it was not known whether this problem is solvable deterministically in the asynchronous shared memory model in this paper we resolve this question by showing that for any k n there is no deterministic wait free protocol for n processors that solves the k set agreement problem the proof technique is new it is based on the development of a topological structure on the set of possible processor schedules of a protocol this topological structure has a natural interpretation in terms of the knowledge of the processors of the state of the system this structure reveals a close analogy between the impossibility of wait free k set agreement and the brouwer fixed point theorem for the k dimensional ball

homology for higher rank graphs and twisted c algebras abstract we introduce a homology theory for k graphs and explore its fundamental properties we establish connections with algebraic topology by showing that the homology of a k graph coincides with the homology of its topological realisation as described by kaliszewski et al we exhibit combinatorial versions of a number of standard topological constructions and show that they are compatible from a homological point of view with their topological counterparts we show how to twist the c algebra of a k graph by a t valued 2 cocycle and demonstrate that examples include all noncommutative tori in the appendices we construct a cubical set q from a k graph and demonstrate that the homology and topological realisation of coincide with those of q as defined by grandis

brownian measures on jordan virasoro curves associated to the weil petersson metric abstract in this paper existence of the brownian measure on jordan curves with respect to the weil petersson metric is established the step from brownian motion on the diffeomorphism group of the circle to brownian motion on jordan curves in c requires probabilistic arguments well beyond the classical theory of conformal welding due to the lacking quasi symmetry of canonical brownian motion on diff s 1 a new key step in our construction is the systematic use of a kahlerian diffusion on the space of jordan curves for which the welding functional gives rise to conformal martingales together with a douady earle type conformal extension of vector fields on the circle to the disk

approximate distance oracles let g v e be an undirected weighted graph with vvv n and vev m let k 1 be an integer we show that g v e can be preprocessed in o kmn1 k expected time constructing a data structure of size o kn1p1 k such that any subsequent distance query can be answered approximately in o k time the approximate distance returned is of stretch at most 2k 1 that is the quotient obtained by dividing the estimated distance by the actual distance lies between 1 and 2k 1 a 1963 girth conjecture of erdos implies that n1p1 k space is needed in the worst case for any real stretch strictly smaller than 2kp1 the space requirement of our algorithm is therefore essentially optimal the most impressive feature of our data structure is its constant query time hence the name oracle previously data structures that used only o n1p1 k space had a query time of n1 k our algorithms are extremely simple and easy to implement efficiently they also provide faster constructions of sparse spanners of weighted graphs and improved tree covers and distance labelings of weighted or unweighted graphs

a layered analysis of consensus this paper introduces a simple notion of layering as a tool for analyzing well behaved runs of a given model of distributed computation using layering a model independent analysis of the consensus problem is performed and then applied to proving lower bounds and impossibility results for consensus in a number of familiar and less familiar models the proofs are simpler and more direct than existing ones and they expose a unified structure to the difficulty of reaching consensus in particular the proofs for the classical synchronous and asynchronous models now follow the same outline a new notion of connectivity among states in runs of a consensus protocol called potence connectivity is introduced this notion is more general than previous notions of connectivity used for this purpose and plays a key role in the uniform analysis of consensus

computing boolean functions on anonymous networks abstract we study the bit complexity of computing boolean functions on anonymous networks let n be the number of nodes the diameter and d the maximal node degree of the network for arbitrary anonymous networks we give a general algorithm of polynomial bit complexity o n 3 d 2 log n for computing any boolean function which is computable on the network this improves upon the previous best known algorithm which was of exponential bit complexity o d n 2 for symmetric functions on arbitrary networks we give an algorithm with bit complexity o n 3 d 2 log 2 n this same algorithm is shown to have even lower bit complexity for a number of specific networks for example tori hypercubes and random regular graphs we also consider the class of distance regular unlabeled networks and show that on such networks symmetric functions can be computed efficiently in o n d log n bits