an algebraic characterization of transition system equivalences abstract i castellani 1987 j comput system sci 34 210 235 has shown that observation equivalence of transition systems could be characterized by particular reductions systems are equivalent if and only if they can be reduced to the same form moreover every transition system has a minimal reduced form we extend these results to logical equivalence by an algebraic interpretation of temporal logics we characterize logical equivalence of transition systems by particular reductions saturating quasi homomorphisms or their power algebras of sets of states and paths and prove that every power algebra has a minimal reduced form we then offer alternative proofs for logical characterizations of observation equivalence in particular we apply our method to prove m hennessy and c stirling s 1984 lecture notes in comput sci vol 176 pp 301 311 springer verlag new york berlin result that future perfect logic characterizes observation equivalence of generalized transition systems i e systems whose infinite behaviours are restricted by arbitrary fairness constraints

on computing puiseux series for multiple imaginary characteristic roots of lti systems with commensurate delays obtaining the puiseux series of multiple imaginary characteristic roots mirs is a fundamental issue in the stability analysis of time delay systems however to the best of the authors knowledge this issue has not been fully investigated up to date this note focuses on the puiseux series expansion of mirs of linear time invariant systems including commensurate delays for an mir of any multiplicity we propose an algorithm for defining the structure of the puiseux series as well as the explicit computation of the corresponding coefficients by using the proposed method we can find all the puiseux series corresponding to all the root loci

an automata theoretic decision procedure for the propositional mu calculus the propositional mu calculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the propositional dynamic logic of fischer and ladner the infinite looping construct of streett and the game logic of parikh we give an elementary time decision procedure using a reduction to the emptiness problem for automata on infinite trees a small model theorem is obtained as a corollary

invariance properties for a class of quasipolynomials when a time delay system involves multiple imaginary roots mirs the stability analysis will become much more complicated than that in the case with only simple imaginary roots sirs an mir may exhibit different splitting behaviors and to the best of the authors knowledge their properties have not been fully investigated in this paper we focus on characterizing the invariance properties for mirs with any multiplicity furthermore the proposed methodology makes it possible to also cover some degenerate cases already encountered and discussed in the literature in addition we propose an easily implemented frequency sweeping method making it possible to derive the asymptotic behavior without invoking the puiseux series

entanglement and the complexity of directed graphs entanglement is a parameter for the complexity of finite directed graphs that measures to what extent the cycles of the graph are intertwined it is defined by way of a game similar in spirit to the cops and robber games used to describe treewidth directed treewidth and hypertree width nevertheless on many classes of graphs there are significant differences between entanglement and the various incarnations of treewidth entanglement is intimately related with the computational and descriptive complexity of the modal m calculus the number of fixed point variables needed to describe a finite graph up to bisimulation is captured by its entanglement this plays a crucial role in the proof that the variable hierarchy of the m calculus is strict we study complexity issues for entanglement and compare it to other structural parameters of directed graphs one of our main results is that parity games of bounded entanglement can be solved in polynomial time specifically we establish that the complexity of solving a parity game can be parametrised in terms of the minimal entanglement of subgames induced by a winning strategy furthermore we discuss the case of graphs of entanglement two while graphs of entanglement zero and one are very simple graphs of entanglement two allow arbitrary nesting of cycles and they form a sufficiently rich class for modelling relevant classes of structured systems we provide characterisations of this class and propose decomposition notions similar to the ones for treewidth dag width and kelly width

logical vs behavioural specifications abstract there are two fundamentally different approaches for specifying and verifying properties of systems the logical approach makes use of specifications given as formulae of temporal or modal logics and relies on efficient model checking algorithms the behavioural approach exploits various equivalence or refinement checking methods provided the specifications are given in the same formalism as implementations in this paper we provide translations between the logical formalism of calculus and the behavioural formalism of disjunctive modal transition systems the translations preserve structural properties of the input specification and allow us to perform logical operations on the behavioural specifications as well as behavioural compositions on logical formulae the unification of both approaches provides additional methods for component based stepwise design

enhancing unsatisfiable cores for ltl with information on temporal relevance ltl is frequently used to express specifications in many domains such as embedded systems or business processes witnesses can help to understand why an ltl specification is satisfiable and a number of approaches exist to make understanding a witness easier in the case of unsatisfiable specifications unsatisfiable cores ucs i e parts of an unsatisfiable formula that are themselves unsatisfiable are a well established means for debugging however little work has been done to help understanding a uc of an unsatisfiable ltl formula in this paper we suggest to enhance a uc of an unsatisfiable ltl formula with information about the time points at which the subformulas of the uc are relevant for unsatisfiability in previous work we showed how to obtain a uc in ltl by translating the ltl formula into a clausal normal form applying temporal resolution extracting a clausal uc from the resolution proof and mapping the clausal uc back to a uc in ltl in this paper we extend that method by extracting information at which time points the clauses of a clausal uc are relevant for unsatisfiability from a resolution proof and by transferring that information to a uc in ltl we implement our method in trp and we experimentally evaluate it

on the convergence of he s variational iteration method in this work we will consider he s variational iteration method for solving second order initial value problems we will discuss the use of this approach for solving several important partial differential equations this method is based on the use of lagrange multipliers for identification of optimal value of a parameter in a functional this procedure is a powerful tool for solving the large amount of problems using the variational iteration method it is possible to find the exact solution or an approximate solution of the problem this technique provides a sequence of functions which converges to the exact solution of the problem our emphasis will be on the convergence of the variational iteration method in the current paper this scheme will be investigated in details and efficiency of the approach will be shown by applying the procedure on several interesting and important models

games for the m calculus abstract given a formula of the propositional calculus we construct a tableau of the formula and define an infinite game of two players of which one wants to show that the formula is satisfiable and the other seeks the opposite the strategy for the first player can be further transformed into a model of the formula while the strategy for the second forms what we call a refutation of the formula using martin s determinacy theorem we prove that any formula has either a model or a refutation this completeness result is a starting point for the completeness theorem for the calculus to be presented elsewhere however we argue that refutations have some advantages of their own they are generated by a natural system of sound logical rules and can be presented as regular trees of the size exponential in the size of a refuted formula this last aspect completes the small model theorem for the calculus established by emerson and jutla 1988 thus on a more practical side refutations can be used as small objects testifying incorrectness of a program specification expressed by a formula we illustrate this point by an example

a piecewise variational iteration method for treating a nonlinear oscillator of a mass attached to a stretched elastic wire abstract in this paper we introduce a piecewise variational iteration method for treating a nonlinear oscillator of a mass attached to a stretched elastic wire for the nonlinear oscillator the present method can produce a good approximation to the exact solution in a very large region while the standard variational iteration method vim gives a good approximation only in a small region the numerical results obtained show that the present method does not share the drawback of the standard vim and can provide very accurate analytical approximate solutions for both small and large values of the oscillation amplitude and parameter

the finite graph problem for two way alternating automata two way alternating automata on infinite trees were introduced by vardi reasoning about the part with two way automata lecture notes in computer science vol 11 springer berlin 1998 pp 628 641 here we consider alternating two way automata on graphs and show the decidability of the following problem does a given automaton with the buchi condition accept any finite graph using this result we demonstrate the decidability of the finite model problem for a certain fragment of the modal calculus with backward modalities

a new method for computing delay margins for stability of linear delay systems this note is concerned with stability properties of linear time invariant delay systems we consider delay systems of retarded type modeled both as a high order scalar differential difference equation and as a set of first order differential difference equations expressed in state space form we provide a computational method that can be used to compute a delay interval such that the system under consideration is stable for all delay values that lie in the computed interval this method requires computing only the eigenvalues and generalized eigenvalues of certain constant matrices and it can be implemented efficiently based on this method we further state a simple necessary and sufficient condition concerning stability independent of delay for each of the two types of the models

an initial semantics for the m calculus on trees and rabin s complementation lemma in this paper we show that the function associated with any closed or nonclosed term of the calculus on trees can be represented by a recognizable set of trees whose nodes are labeled by letters and by sets of variables rabin s complementation lemma is an immediate consequence of this result

compositionality of hennessy milner logic by structural operational semantics this paper presents a method for the decomposition of hml formulas it can be used to decide whether a process algebra term satisfies a hml formula by checking whether subterms satisfy certain formulas obtained by decomposing the original formula the method uses the structural operational semantics of the process algebra the main contribution of this paper is the extension of an earlier decomposition method for the de simone format from the ph d thesis of larsen in 1986 to more general formats

reversals in stability of linear time delay systems a finer characterization abstract in most of the numerical examples of time delay systems proposed in the literature the number of unstable characteristic roots remains positive before and after a multiple critical imaginary root cir appears as the delay seen as a parameter increases this fact may lead to some misunderstandings i a multiple cir may at most affect the instability degree ii it cannot cause any stability reversals stability transitions from instability to stability as far as we know whether the appearance of a multiple cir can induce stability is still unclear in fact when a cir generates a stability reversal has not been specifically investigated in this paper we provide a finer analysis of stability reversals and some new insights into the classification the link between the multiplicity of a cir and the asymptotic behavior with the stabilizing effect based on these results we present an example illustrating that a multiple cir s asymptotic behavior is able to cause a stability reversal to the best of the authors knowledge such an example is a novelty in the literature on time delay systems

results on the propositional μ calculus abstract in this paper we define and study a propositional calculus l which consists essentially of propositional modal logic with a least fixpoint operator l is syntactically simpler yet strictly more expressive than propositional dynamic logic pdl for a restricted version we give an exponential time decision procedure small model property and complete deductive system theory subsuming the corresponding results for pdl

completeness of kozen s axiomatisation of the propositional m calculus propositional calculus is an extension of the propositional modal logic with the least fixpoint operator in the paper introducing the logic kozen posed a question about completeness of the axiomatisation which is a small extension of the axiomatisation of the model system k it is shown that this axiomatisation is complete

on the complexity of checking semantic equivalences between pushdown processes and finite state processes simulation preorder equivalence and bisimulation equivalence are the most commonly used equivalences in concurrency theory their standard definitions are often called strong simulation bisimulation while weak simulation bisimulation abstracts from internal t actions we study the computational complexity of checking these strong and weak semantic preorders equivalences between pushdown processes and finite state processes we present a complete picture of the computational complexity of these problems and also study fixed parameter tractability in two important input parameters x the size of the finite control of the pushdown process and y the size of the finite state process all simulation problems are generally exptime complete and only become polynomial if both parameters x and y are fixed weak bisimulation equivalence is pspace complete but becomes polynomial if and only if parameter x is fixed strong bisimulation equivalence is pspace complete but becomes polynomial if either parameter x or y is fixed

application of the harmonic balance method to a nonlinear oscillator typified by a mass attached to a stretched wire abstract the first order harmonic balance method via the first fourier coefficient is used to construct two approximate frequency amplitude relations for a conservative nonlinear oscillatory system in which the restoring force has an irrational form this system corresponds to the motion of a mass attached to a stretched wire two procedures are used to approximately solve the nonlinear differential equation in the first the differential equation is rewritten in a form that does not contain the square root expression while in the second the differential equation is solved directly the approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that in the second procedure application of the harmonic balance method produces an infinite set of harmonics while in the first procedure only two harmonics are produced both approximate frequencies are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed the discrepancy between the second approximate frequency and the exact one never exceeds 2 2

forgetting in multi agent modal logics abstract in the past decades forgetting has been investigated for many logics and has found many applications in knowledge representation and reasoning in this paper we study forgetting in multi agent modal logics we adopt the semantic definition of existential bisimulation quantifiers as that of forgetting we resort to canonical formulas of modal logics introduced by moss an arbitrary modal formula is equivalent to the disjunction of a unique set of satisfiable canonical formulas we show that for the logics of k n d n t n k 45 n kd 45 n and s 5 n the result of forgetting an atom from a satisfiable canonical formula can be computed by simply substituting the literals of the atom with thus we show that these logics are closed under forgetting and hence have uniform interpolation finally we generalize the above results to include common knowledge of propositional formulas

characterization definability and separation via saturated models abstract three important results about the expressivity of a modal logic l are the characterization theorem that identifies a modal logic l as a fragment of a better known logic the definability theorem that provides conditions under which a class of l models can be defined by a formula or a set of formulas of l and the separation theorem that provides conditions under which two disjoint classes of l models can be separated by a class definable in l we provide general conditions under which these results can be established for a given choice of model class and modal language whose expressivity is below first order logic besides some basic constraints that most modal logics easily satisfy the fundamental condition that we require is that the class of saturated models in question has the hennessy milner property with respect to the notion of observational equivalence under consideration given that the characterization definability and separation theorems are among the cornerstones in the model theory of l this property can be seen as a test that identifies the adequate notion of observational equivalence for a particular modal logic

simulation preorder over simple process algebras we consider the problem of simulation preorder equivalence between infinite state process and finite state ones first we describe a general method how to utilize the decidability of bisimulation problems to solve certain instances of the corresponding simulation problems for certain process classes the method allows us to design effective reductions of simulation problems to their bisimulation counterparts and some new decidability border for the problem of simulation preorder equivalence are decidable in exptime between pushdown and finite state ones on the other hand simulation preorder is undecidable between pa and finite state process in both directions these results also hold for those pa and finite state process which are deterministic and normed and trace equivalence is also shown to be undecidable for pa finally we prove that simulation preorder in both directions and simulation equivalence are interact able between all classes of infinite state systems in the hierarchy of process rewrite systems and finite state ones this result is obtained by showing that the problem whether a bpa or bpp process simulation a finite state one is pspace hard and the other direction is co np hard consequently simulation equivalence between bpa or bpp and finite state processes is also co np hard

infinite games on finitely coloured graphs with applications to automata on infinite trees we examine a class of infinite two person games on finitely coloured graphs the main aim is to construct finite memory winning strategies for both players this problem is motivated by applications to finite automata on infinite trees a special attention is given to the exact amount of memory needed by the players for their winning strategies based on a previous work of gurevich and harrington and on subsequent improvements of mcnaughton we propose a unique framework that allows to reestablish and to improve various results concerning memoryless strategies due to emerson and jutla mostowski klarlund

a piecewise variational iteration method for riccati differential equations in this paper we introduce a piecewise variational iteration method for riccati differential equations which is a modified variational iteration method mvim the solutions of riccati differential equations obtained using the traditional variational iteration method vim give good approximations only in the neighborhood of the initial position however the solutions obtained using the mvim give good approximations for a larger interval rather than a local vicinity of the initial position some numerical examples are selected to illustrate the effectiveness and simplicity of the method numerical results show that the method does not share the drawback of the conventional vim and is a satisfactory method for riccati differential equations

variational iteration method new development and applications variational iteration method has been favourably applied to various kinds of nonlinear problems the main property of the method is in its flexibility and ability to solve nonlinear equations accurately and conveniently in this paper recent trends and developments in the use of the method are reviewed major applications to nonlinear wave equation nonlinear fractional differential equations nonlinear oscillations and nonlinear problems arising in various engineering applications are surveyed the confluence of modern mathematics and symbol computation has posed a challenge to developing technologies capable of handling strongly nonlinear equations which cannot be successfully dealt with by classical methods variational iteration method is uniquely qualified to address this challenge the flexibility and adaptation provided by the method have made the method a strong candidate for approximate analytical solutions this paper outlines the basic conceptual framework of variational iteration technique with application to nonlinear problems both achievements and limitations are discussed with direct reference to approximate solutions for nonlinear equations a new iteration formulation is suggested to overcome the shortcoming a very useful formulation for determining approximately the period of a nonlinear oscillator is suggested examples are given to illustrate the solution procedure

three logics for branching bisimulation three temporal logics are introduced that induce on labeled transition systems the same identifications as branching bisimulation a behavioral equivalence that aims at ignoring invisible transitions while preserving the branching structure of systems the first logic is an extension of hennessy milner logic with an until operator the second one is another extension of hennessy milner logic which exploits the power of backward modalities the third logic is ctl without the next time operator a relevant side effect of the last characterization is that it sets a bridge between the state and action based approaches to the semantics of concurrent systems

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

numerical solutions of nonlinear evolution equations using variational iteration method the variational iteration method is used to solve three kinds of nonlinear partial differential equations coupled nonlinear reaction diffusion equations hirota satsuma coupled kdv system and drinefel d sokolov wilson equations numerical solutions obtained by the variational iteration method are compared with the exact solutions revealing that the obtained solutions are of high accuracy he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomial in adomian method the method is straightforward and concise and it can also be applied to other nonlinear evolution equations in mathematical physics

digraph decompositions and monotonicity in digraph searching graph decompositions such as tree decompositions and associated width measures have been the focus of much attention in structural and algorithmic graph theory in particular it has been found that many otherwise intractable problems become tractable on graph classes of bounded tree width more recently proposals have been made to define a similar notion to tree width for directed graphs several proposals have appeared so far supported by algorithmic applications in this paper we explore the limits of algorithmic applicability of digraph decompositions and show that various natural candidates for problems which potentially could benefit from digraphs having small directed width remain np complete even on almost acyclic graphs closely related to graph and digraph decompositions are graph searching games an important property of graph searching games is monotonicity and a large number of papers addresses the question whether particular variants of these games are monotone however so far for two natural types of graph searching games underlying dag and kelly decompositions the question whether they are monotone was still open we settle this issue by showing that both variants the visible and the inert invisible graph searching games on directed graphs are non monotone

an automata theoretic approach to branching time model checking translating linear temporal logic formulas to automata has proven to be an effective approach for implementing linear time model checking and for obtaining many extensions and improvements to this verification method on the other hand for branching temporal logic automata theoretic techniques have long been thought to introduce an exponential penalty making them essentially useless for model checking recently bernholtz and grumberg 1993 have shown that this exponential penalty can be avoided though they did not match the linear complexity of non automata theoretic algorithms in this paper we show that alternating tree automata are the key to a comprehensive automata theoretic framework for branching temporal logics not only can they be used to obtain optimal decision procedures as was shown by muller et al but as we show here they also make it possible to derive optimal model checking algorithms moreover the simple combinatorial structure that emerges from the automata theoretic approach opens up new possibilities for the implementation of branching time model checking and has enabled us to derive improved space complexity bounds for this long standing problem

complete stability robustness of third order lti multiple time delay systems a unique procedure is presented in this paper for a complete stability robustness of the third order lti multiple time delay systems lti mtds the uniqueness of the treatment is simply due to the fact that there is no comparable methodology presently in the literature the end result of this procedure is an exhaustive and precise determination of the stable regions in the domain of time delays the backbone of the method is a novel framework called the cluster treatment of characteristic roots ctcr ctcr is constructed over two fundamental propositions the first proposition claims the existence of a bounded number of so called kernel curves where the only imaginary characteristic roots occur the second proposition is on an interesting directional invariance property of the crossing tendencies of these imaginary roots for simplicity of conveyance and without loss of generality the number of time delays is taken as two in this document the new methodology is expandable to higher order dynamics with more time delays than two as the authors intend to demonstrate in future publications publications

a frequency sweeping framework for stability analysis of time delay systems for time delay systems the asymptotic behavior analysis of the critical imaginary roots w r t the infinitely many critical delays is an open problem in order to find a general solution we will exploit the link between the asymptotic behavior of critical imaginary roots and the asymptotic behavior of frequency sweeping curves from a new analytic curve perspective as a consequence we will establish a frequency sweeping framework with three main results 1 a finer regularity singularity classification for time delay systems will be obtained 2 the general invariance property will be proved and hence the asymptotic behavior of the critical imaginary roots w r t the infinitely many critical delays can be adequately studied 3 the complete stability problem can be fully solved moreover the frequency sweeping framework is extended to cover a broader class of time delay systems finally the geometric insights of frequency sweeping curves are investigated consequently some deeper properties on the asymptotic behavior of time delay systems and the link to frequency sweeping curves are found

logical definability of fixed points note abstract we define a class of monotonic functions whose least fixed points are weakly definable in the sense of rabin we use this property to give a new proof that v definable sets of trees are recognized by rabin s special automata

application of the variational iteration method to inverse heat source problems this paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions the numerical solution is developed by using the variational iteration method this method is based on the use of lagrange multipliers for the identification of optimal values of parameters in a functional using this method a rapid convergent sequence can be obtained which tends to the exact solution of the problem furthermore the variational iteration method does not require the discretization of the problem thus the variational iteration method is suitable for finding the approximation of the solution without discretization of the problem two numerical examples are presented to illustrate the strength of the method

tracking the algebraic multiplicity of crossing imaginary roots for generic quasipolynomials a vandermonde based approach a standard approach in analyzing dynamical systems consists in identifying and understanding the eigenvalues bifurcations when crossing the imaginary axis efficient methods for crossing imaginary roots identification exist however to the best of the author s knowledge the multiplicity of such roots was not deeply investigated in recent papers by the authors 1 2 it is emphasized that the multiplicity of the zero spectral value can exceed the number of the coupled scalar delay differential equations and a constructive approach vandermonde based allowing to an adaptive bound for such a multiplicity is provided namely it is shown that the zero spectral value multiplicity depends on the system structure number of delays and number of non zero coefficients of the associated quasipolynomial rather than the degree of the associated quasipolynomial 3 this technical note extends the constructive approach in investigating the multiplicity of crossing imaginary roots j omega where omega neq 0 and establishes a link with a new class of functional confluent vandermonde matrices a symbolic algorithm for computing the lu factorization for such matrices is provided as a byproduct of the proposed approach a bound sharper than the polya szego generic bound arising from the principle argument is established

the alternation hierarchy in fixpoint logic with chop is strict too fixpoint logic with chop extends the modal calculus with a sequential composition operator which results in an increase in expressive power we develop a game theoretic characterisation of its model checking problem and use these games to show that the alternation hierarchy in this logic is strict the structure of this result follows the lines of arnold s proof showing that the alternation hierarchy in the modal calculus is strict over the class of binary trees

maximal traces and path based coalgebraic temporal logics this paper gives a general coalgebraic account of temporal logics whose semantics involves a notion of computation path examples of such logics include the logic ctl for transition systems and the logic pctl for probabilistic transition systems our path based temporal logics are interpreted over coalgebras of endofunctors obtained as the composition of a computation type e g non deterministic or stochastic with a general transition type the semantics of such logics relies on the existence of execution maps similar to the trace maps introduced by jacobs and co authors as part of the coalgebraic theory of finite traces hasuo et al 2007 1 we consider finite execution maps derived from the theory of finite traces and a new notion of maximal execution map that accounts for maximal possibly infinite executions the latter is needed to recover the logics ctl and pctl as specific path based logics

colored stability crossing sets for siso delay systems this paper considers the stability of a single input single output siso system with an input output i o delay called siso delay system hereafter we first derive an algebraic criterion to solve the complete stability w r t the delay tau next the stability analysis is extended to the case with additional free plant and or controller parameters denoted by a vector x by adopting a mathematical tool for polynomial algebra the discrimination system the complete classification of the critical imaginary roots cirs in the whole x tau parameter space may be obtained furthermore with the above results we present the stability crossing sets scss in a new form called the colored scss for each point on the scs the asymptotic behavior information of the corresponding cir can be coded by a certain color red green or yellow hence the stability in the x tau space can be analyzed easily and intuitively moreover the geometry of the scss can be investigated from a new perspective which will help not only to better understand the stability of the siso delay system but also to considerably simplify the procedure for generating the colored scss

stability of linear time invariant fractional delay systems of retarded type in the space of delay parameters this paper presents a new method for assessing the bounded input bounded output stability of a class of fractional delay systems with commensurate orders and multiple commensurate delays of retarded type in the proposed method first by mapping the principal sheet of the riemann surface and a pseudo delay transformation an auxiliary polynomial is generated then this auxiliary polynomial is employed to find roots of the characteristic equation on the imaginary axis the properties of the root path close to these roots are used to identify intervals of delay values in which the system is stable the obtained results are illustrated via some numerical examples

approximate von neumann entropy for directed graphs in this paper we develop an entropy measure for assessing the structural complexity of directed graphs although there are many existing alternative measures for quantifying the structural properties of undirected graphs there are relatively few corresponding measures for directed graphs to fill this gap in the literature we explore an alternative technique that is applicable to directed graphs we commence by using chung s generalization of the laplacian of a directed graph to extend the computation of von neumann entropy from undirected to directed graphs we provide a simplified form of the entropy which can be expressed in terms of simple node in degree and out degree statistics moreover we find approximate forms of the von neumann entropy that apply to both weakly and strongly directed graphs and that can be used to characterize network structure we illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real world data sets including structures from protein databases and high energy physics theory citation networks

measure properties of regular sets of trees abstract we investigate measure theoretic properties of regular sets of infinite trees as a first result we prove that every regular set is universally measurable and that every borel measure on the polish space of trees is continuous with respect to a natural transfinite stratification of regular sets into 1 ranks we also expose a connection between regular sets and the algebra of r sets introduced by a kolmogorov in 1928 as a foundation for measure theory we show that the game tree languages w i k are wadge complete for the finite levels of the hierarchy of r sets we apply these results to answer positively an open problem regarding the game interpretation of the probabilistic calculus

brief paper extraction of 3d stability switching hypersurfaces of a time delay system with multiple fixed delays stability switching hypersurfaces ssh of a general class of linear time invariant lti multiple time delay systems mtds are extracted the number of delays and system order n 0 in this problem are given but they are arbitrarily large hence the extraction of ssh becomes non trivial a novel and efficient procedure reveals the 3d projections of dimensional ssh without the need for finding the ssh in achieving this computation times required remain in the same order of magnitude independently of and n 0 case studies demonstrate the effectiveness of the approach

an axiomatization of bisimulation quantifiers via the µ calculus this paper deals with bisimulation quantifiers logic bql that is the extension of propositional dynamic logic pdl with the so called bisimulation quantifiers this logic is expressively equivalent to the calculus an extension of modal logic with extremal fixpoints albeit its formulas are easier to understand in this work we provide a complete axiomatization of bql based on certain normal form results for the calculus obtained by janin and walukiewicz

the discrete strategy improvement algorithm for parity games and complexity measures for directed graphs abstract the problem whether winning regions and wining strategies for parity games can be computed in polynomial time is a major open problem in the field of infinite games which is relevant for many applications in logic and formal verification for some time the discrete strategy improvement algorithm due to jurdzinski and voge had been considered to be a candidate for solving parity games in polynomial time however it has recently been proved by oliver friedmann that this algorithm requires super polynomially many iteration steps for all popular local improvements rules including switch all also with fearnley s snare memorisation switch best random facet random edge switch half least recently considered and zadeh s pivoting rule we analyse the examples provided by friedmann in terms of complexity measures for directed graphs such as treewidth dag width kelly width entanglement directed pathwidth and cliquewidth it is known that for every class of parity games on which one of these parameters is bounded the winning regions can be efficiently computed it turns out that with respect to almost all of these measures the complexity of friedmann s counterexamples is bounded and indeed in most cases by very small numbers this analysis strengthens in some sense friedmann s results and shows that the discrete strategy improvement algorithm is even more limited than one might have thought not only does it require super polynomial running time in the general case where the problem of polynomial time solvability is open it even has super polynomial time lower bounds on natural classes of parity games on which efficient algorithms are known

the μ calculus alternation depth hierarchy is infinite over finite planar graphs abstract we prove that the alternation hierarchy of the modal calculus is infinite over finite planar graphs

an algebraic and algorithmic method for analysing transition systems to describe significant properties of concurrent processes a formal algebra is defined whose terms are interpreted in transition systems as effectively computable functions of power algebras of sets of states and transitions we study the expressive power of this formal system and compare it with temporal logics

modular construction of complete coalgebraic logics we present a modular approach to defining logics for a wide variety of state based systems the systems are modelled as coalgebras and we use modal logics to specify their observable properties we show that the syntax semantics and proof systems associated with such logics can all be derived in a modular fashion moreover we show that the logics thus obtained inherit soundness completeness and expressiveness properties from their building blocks we apply these techniques to derive sound complete and expressive logics for a wide variety of probabilistic systems for which no complete axiomatisation has been obtained so far

on the formalization of the modal µ calculus in the calculus of inductive constructions we present a natural deduction proof system for the propositional modal calculus and its formalization in the calculus of inductive constructions we address several problematic issues such as the use of higher order abstract syntax in inductive sets in the presence of recursive constructors and the formalization of modal sequent style rules and of context sensitive grammars the formalization can be used in the system coq providing an experimental computer aided proof environment for the interactive development of error free proofs in the modal calculus the techniques we adopt can be readily ported to other languages and proof systems featuring similar problematic issues

applicability of fair simulation in this paper we compare four notions of fair simulation direct 9 delay 12 game 19 and exists 16 our comparison refers to three main aspects the time complexity of constructing the fair simulation the ability to use it for minimization and the relationship between the fair simulations and universal branching time logics we developed a practical application that is based on this comparison the application is a new implementation for the assume guarantee modular framework presented by grumberg at al in acm transactions on programming languages and systems toplas 16 1994 843 the new implementation significantly improves the complexity of the framework

technical communique invariance properties in the root sensitivity of time delay systems with double imaginary roots if i w ir is an eigenvalue of a time delay system for the delay t 0 then i w is also an eigenvalue for the delays t k t 0 k2 p w for any k z we investigate the sensitivity periodicity and invariance properties of the root i w for the case that i w is a double eigenvalue for some t k it turns out that under natural conditions the condition that the root exhibits the completely regular splitting property if the delay is perturbed the presence of a double imaginary root i w for some delay t 0 implies that i w is a simple root for the other delays t k k 0 moreover we show how to characterize the root locus around i w the entire local root locus picture can be completely determined from the square root splitting of the double root we separate the general picture into two cases depending on the sign of a single scalar constant the imaginary part of the first coefficient in the square root expansion of the double eigenvalue

control of infinite behavior of finite automata a problem in the control of automata on infinite strings is defined and analyzed the key to the investigation is the development of a fixpoint characterization of the controllability subset of a deterministic rabin automaton the set of states from which the automaton can be controlled to the satisfaction of its own acceptance condition the fixpoint representation allows straightforward computation of the controllability subset and the construction of a suitable state feedback control for the automaton the results have applications to control synthesis automaton synthesis and decision procedures for logical satisfiability in particular they represent a direct efficient and natural solution to church s problem the construction of winning strategies for two player zero sum omega regular games of perfect information and the emptiness problem for automata on infinite trees

local model checking for infinite state spaces bradtield j and c stirling local model checking for infinite spaces theoretical computer science 96 1992 157 174 we present a sound and complete tableau proof system for establishing whether a set of elements of an arbitrary transition system model has a property expressed in a slight extension of the modal mu calculus the proof system we believe offers a very general verification method applicable to a wide range of computational systems in the last twenty years many approaches to program verification have been developed hoare s partial correctness logic for simple while programs gave an early sound and relatively complete proof system this approach was subsequently extended to total correctness and to richer classes of programs dynamic logics offered a more abstract view of hoare logics especially in their propositional versions pnueli pioneered the use of propositional temporal logics as more general program logics capable of describing crucial properties of perpetual concurrent systems a variety of temporal logics have been studied particularly branching and linear time many useful decidability and expressiveness results relating logics and automata have been obtained as well as sound and complete axiomatizations of validity a slightly earlier tradition in the study of correctness was given by the work on program schemes where second order logics were advocated especially in the form of the mu calculus due to de bakker de roever and park an elegant generalization of propositional dynamic and temporal logics drawing on this tradition is the propositional modal mu calculus due to pratt and kozen the modal mu calculus has been shown to include propositional

proving properties of dynamic process networks we present the first compositional proof system for checking processes against formulas in the modal calculus which is capable of handling dynamic process networks the proof system is obtained in a systematic way from the operational semantics of the underlying process algebra a non trivial proof example is given and the proof system is shown to be sound in general and complete for finite state processes

an elementary proof of the completeness of pdl abstract we give an elementary proof of the completeness of the segerberg axions for propositional dynamic logic

alternating time temporal logic temporal logic comes in two varieties linear time temporal logic assumes implicit universal quantification over all paths that are generated by the execution of a system branching time temporal logic allows explicit existential and universal quantification over all paths we introduce a third more general variety of temporal logic alternating time temporal logic offers selective quantification over those paths that are possible outcomes of games such as the game in which the system and the environment alternate moves while linear time and branching time logics are natural specification languages for closed systems alternating time logics are natural specification languages for open systems for example by preceding the temporal operator eventually with a selective path quantifier we can specify that in the game between the system and the environment the system has a strategy to reach a certain state the problems of receptiveness realizability and controllability can be formulated as model checking problems for alternating time formulas depending on whether or not we admit arbitrary nesting of selective path quantifiers and temporal operators we obtain the two alternating time temporal logics atl and atl atl and atl are interpreted over concurrent game structures every state transition of a concurrent game structure results from a choice of moves one for each player the players represent individual components and the environment of an open system concurrent game structures can capture various forms of synchronous composition for open systems and if augmented with fairness constraints also asynchronous composition over structures without fairness constraints the model checking complexity of atl is linear in the size of the game structure and length of the formula and the symbolic model checking algorithm for ctl extends with few modifications to atl over structures with weak fairness constraints atl model checking requires the solution of 1 pair rabin games and can be done in polynomial time over structures with strong fairness constraints atl model checking requires the solution of games with boolean combinations of buchi conditions and can be done in pspace in the case of atl the model checking problem is closely related to the synthesis problem for linear time formulas and requires doubly exponential time

when not losing is better than winning abstraction and refinement for the full μ calculus this work presents a novel game based approach to abstraction refinement for the full m calculus interpreted over 3 valued semantics a novel notion of non losing strategy is introduced and exploited for refinement previous works on refinement in the context of 3 valued semantics require a direct algorithm for solving a 3 valued model checking game this was necessary in order to have the information needed for refinement available on one game board in contrast while still considering a 3 valued model checking game here we reduce the problem of solving the game to solving two 2 valued model checking parity games in case the result is indefinite don t know the corresponding non losing strategies when combined hold all the information needed for refinement this approach is beneficial since it can use any solver for 2 valued parity games thus it can take advantage of newly developed such algorithms with improved complexity

concurrent program schemes and their logics abstract we define and investigate several classes of concurrent program schemes including goto schemes and two versions of structured schemes based on extensions of the regular expressions to trees the schemes are studied on the first order boolean variable and propositional levels we also define and study the dynamic logics based on these classes of schemes including issues of decidability and axiomatization

variational iteration method some recent results and new interpretations this paper is an elementary introduction to the concepts of variational iteration method first the main concepts in variational iteration method such as general lagrange multiplier restricted variation correction functional are explained heuristically subsequently the solution procedure is systematically addressed in particular for nonlinear oscillators particular attention is paid throughout the paper to give an intuitive grasp for the method the main motivation is to put things together in a convenient form for later reference and systematic use

on the μ calculus over transitive and finite transitive frames we prove that the modal m calculus collapses to first order logic over the class of finite transitive frames the proof is obtained by using some byproducts of a new proof of the collapse of the m calculus to the alternation free fragment over the class of transitive frames moreover we prove that the modal m calculus is buchi and co buchi definable over the class of all models where in a strongly connected component vertexes are distinguishable by means of the propositions they satisfy

digraph measures kelly decompositions games and orderings we consider various well known equivalent complexity measures for graphs such as elimination orderings k trees and cops and robber games and study their natural translations to digraphs we show that on digraphs the translations of these measures are also equivalent and induce a natural connectivity measure we introduce a decomposition for digraphs and an associated width kelly width which is equivalent to the aforementioned measure we demonstrate its usefulness by exhibiting potential applications including polynomial time algorithms for np complete problems on graphs of bounded kelly width and complexity analysis of asymmetric matrix factorization finally we compare the new width to other known decompositions of digraphs

tarskian set constraints we investigate set constraints over set expressions with tarskian functional and relational operations unlike the herbrand constructor symbols used in recent set constraint formalisms the meaning of a tarskian function symbol is interpreted in an arbitrary first order structure we show that satisfiability of tarskian set constraints is decidable in nondeterministic doubly exponential time we also give complexity results and open problems for various extensions and restrictions of the language

a partial k arboretum of graphs with bounded treewidth the notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies this survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class also some mutual relations between such classes are discussed

an improved algorithm for the evaluation of fixpoint expressions many automated finite state verification procedures can be viewed as fixpoint computations over a finite lattice typically the powerset of the set of system states hence fixpoint calculi such as the propositional calculus have proven useful both as ways to describe verification algorithms and as specification formalisms in their own right we consider the problem of evaluating expressions in a fixpoint calculus over a given model a naive algorithm for this task may require time n q where n is the maximum length of a chain in the lattice and q is the depth of fixpoint nesting in 1986 emerson and lei presented a method requiring about n d steps where d is the number of alternations between least and greatest fixpoints more recent algorithms have reduced the exponent by one or two but the complexity has remained at about nd in this paper we present a new algorithm that makes extensive use of monotonicity considerations to solve the problem in about nd 2 steps thus the time required by our method is only about the square root of the time required by the earlier algorithms

stability of linear neutral time delay systems exact conditions via matrix pencil solutions in this note we study the stability properties of linear neutral delay systems we consider systems described by both neutral differential difference and state space equations and we seek to determine the delay margin of such systems that is the largest range of delay values for which a neutral delay system may preserve its stability in both cases we show that the delay margin can be found by computing the eigenvalues and generalized eigenvalues of certain constant matrices which can be executed efficiently and with high precision the results extend previously known work on retarded systems and demonstrate that similar stability tests exist for neutral systems in particular the tests require essentially the same amount of computation required for retarded systems

convergence factors of newton methods for nonlinear eigenvalue problems abstract consider a complex sequence k k 0 convergent to c with order p n the convergence factor is typically defined as the fraction c k k 1 k p in the limit k in this paper we prove formulas characterizing c k in the limit k for two different newton type methods for nonlinear eigenvalue problems the formulas are expressed in terms of the left and right eigenvectors the two treated methods are called the method of successive linear problems mslp and augmented newton and are widely used in the literature we prove several explicit formulas for c k for both methods formulas for both methods are found for simple as well as double eigenvalues in some cases we observe in examples that the limit c k as k does not exist for cases where this limit does not appear to exist we prove other limiting expressions such that a characterization of c k in the limit is still possible

on model checking for the m calculus and its fragments in this paper we consider the model checking problem for the calculus and show that it is succinctly equivalent to the non emptiness problem of finite state automata on infinite binary trees with the parity acceptance condition we also present efficient model checking algorithms for two rich subclasses of the calculus formulas and relate their expressive power to well known extensions of branching time temporal logics

incompleteness of states w r t traces in model checking cousot and cousot introduced and studied a general past future time specification language called calculus featuring a natural time symmetric trace based semantics the standard state based semantics of the calculus is an abstract interpretation of its trace based semantics which turns out to be incomplete that is trace incomplete even for finite systems as a consequence standard state based model checking of the calculus is incomplete w r t trace based model checking this paper shows that any refinement or abstraction of the domain of sets of states induces a corresponding semantics which is still trace incomplete for any propositional fragment of the calculus this derives from a number of results one for each incomplete logical temporal connective of the calculus that characterize the structure of models i e transition systems whose corresponding state based semantics of the calculus is trace complete lete

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

advanced clustering with frequency sweeping methodology for the stability analysis of multiple time delay systems a new methodology advanced clustering with frequency sweeping acfs is introduced for the stability analysis of the most general class of linear time invariant time delay systems with multiple delays acfs is a cross fertilization of algebraic geometry frequency sweeping technique and the root clustering paradigm and it can directly extract the 2 d cross sections of the stability views in any two delay domain in this domain acfs can also test the delay independent stability based on necessary and sufficient conditions and can compute for the delay dependent case the precise lower and upper bounds of the only parameter the frequency that acfs sweeps case studies that are prohibitive to analyze with the existing analytical methods are presented to demonstrate the strengths of the method

polynomial two parameter eigenvalue problems and matrix pencil methods for stability of delay differential equations several recent methods used to analyze asymptotic stability of delay differential equations ddes involve determining the eigenvalues of a matrix a matrix pencil or a matrix polynomial constructed by kronecker products despite some similarities between the different types of these so called matrix pencil methods the general ideas used as well as the proofs differ considerably moreover the available theory hardly reveals the relations between the different methods in this work a different derivation of various matrix pencil methods is presented using a unifying framework of a new type of eigenvalue problem the polynomial two parameter eigenvalue problem of which the quadratic two parameter eigenvalue problem is a special case this framework makes it possible to establish relations between various seemingly different methods and provides further insight in the theory of matrix pencil methods we also recognize a few new matrix pencil variants to determine dde stability finally the recognition of the new types of eigenvalue problem opens a door to efficient computation of dde stability

an analytic stability test for a class of time delay systems stability properties of linear dynamic systems with characteristic equations of the form sigma min i 0 max n p i s e shi 0 where all the polynomials p i are of order leq r in s can be determined from a polynomial equation in s of order leq 2n r

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

proof systems for satisfiability in hennessy milner logic with recursion abstract an extension of hennessy milner logic with recursion is presented a recursively specified formula will have two standard interpretations a minimal one and a maximal one minimal interpretations of formulas are useful for expressing liveness properties of processes whereas maximal interpretations are useful for expressing safety properties we present sound and complete proof systems for both interpretations for when a process satisfies a possibly recursive formula the rules of the proof systems consist of an introduction rule for each possible structure of a formula and are intended to extend the work of stirling and winskel moreover the proof systems may be presented directly in prolog to yield a decision procedure for verifying when a finite state process satisfies a specification given as a possibly recursive formula