generating equilateral random polygons in confinement in this paper we continue an earlier study diao et al 2011 j phys a math theor 44 405202 on the generation algorithms of random equilateral polygons confined in a sphere here the equilateral random polygons are rooted at the center of the confining sphere and the confining sphere behaves like an absorbing boundary one way to generate such a random polygon is the accept reject method in which an unconditioned equilateral random polygon rooted at origin is generated the polygon is accepted if it is within the confining sphere otherwise it is rejected and the process is repeated the algorithm proposed in this paper offers an alternative to the accept reject method yielding a faster generation process when the confining sphere is small in order to use this algorithm effectively a large reusable data set needs to be pre computed only once we derive the theoretical distribution of the given random polygon model and demonstrate with strong numerical evidence that our implementation of the algorithm follows this distribution a run time analysis and a numerical error estimate are given at the end of the paper

graded modalities in strategy logic abstract strategy logic sl is a logical formalism for strategic reasoning in multi agent systems its main feature is that it has variables for strategies that are associated to specific agents using a binding operator in this paper we introduce graded strategy logic graded sl an extension of sl by graded quantifiers over tuples of strategy variables i e there exist at least g different tuples x 1 x n of strategies where g is a cardinal from the set n 0 1 2 0 we prove that the model checking problem of graded sl is decidable we then turn to the complexity of fragments of graded sl when the g s are restricted to finite cardinals written graded n sl the complexity of model checking is no harder than for sl i e it is non elementary in the quantifier block rank we illustrate our formalism by showing how to count the number of different strategy profiles that are nash equilibria ne by analysing the structure of the specific formulas involved we conclude that the important problem of checking for the existence of a unique ne can be solved in 2 exptime which is not harder than merely checking for the existence of such an equilibrium

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

model checking graded computation tree logic with finite path semantics abstract this paper introduces graded computation tree logic with finite path semantics gctl f for short a variant of computation tree logic ctl in which path quantifiers are interpreted over finite paths and can count the number of such paths state formulas of gctl f are interpreted over kripke structures the syntax of gctl f has path quantifiers of the form e g which express that there are at least g many distinct finite paths that satisfy after defining and justifying the logic gctl f we solve its model checking problem and establish that its computational complexity is pspace complete moreover we investigate gctl f under the imperfect information setting precisely we introduce gctlk f an epistemic extension of gctl f and prove that the model checking problem also in this case is pspace complete

modular strategies for recursive game graphs many problems in formal verification and program analysis can be formalized as computing winning strategies for two player games on graphs in this paper we focus on solving games in recursive game graphs which can model the control flow in sequential programs with recursive procedure calls while such games can be viewed as the pushdown games studied in the literature the natural notion of winning in our framework requires the strategies to be modular with only local memory that is resolution of choices within a module does not depend on the context in which the module is invoked but only on the history within the current invocation of the module while reachability in global pushdown games is known to be exptime complete we show reachability in modular games to be np complete we present a fixed point computation algorithm for solving modular games such that in the worst case the number of iterations is exponential in the total number of returned values from the modules if the strategy within a module does not depend on the global history but can remember the history of the past invocations of this module that is if memory is local but persistent we show that reachability becomes undecidable

network formation games with regular objectives classical network formation games are played on a directed graph players have reachability objectives each player has to select a path from his source to target vertices each edge has a cost shared evenly by the players using it we introduce and study network formation games with regular objectives in our setting the edges are labeled by alphabet letters and the objective of each player is a regular language over the alphabet of labels unlike the case of reachability objectives here the paths selected by the players need not be simple thus a player may traverse some edges several times edge costs are shared by the players with the share being proportional to the number of times the edge is traversed we study the existence of a pure nash equilibrium ne the inefficiency of a ne compared to a social optimum solution and computational complexity problems in this setting

alternating pushdown and stack automata the classes of languages accepted by alternating pushdown automata alternating stack automata and alternating nonerasing stack automata both with and without an auxiliary space bounded worktape are characterized in terms of complexity classes defined by time bounded deterministic turing machines it is also shown that alternating 2 way finite state machines accept only regular languages

refining strategic ability in alternating time temporal logic we propose extending alternating time temporal logic atl by a unary operator i about distributing the powers of some given agent i to a given set of sub agents i means that i s powers can be distributed in a way which satisfies the atl condition on the strategic ability of the coalitions the members of may form possibly together with others agents we prove the decidability of model checking of formulas whose subformulas have the form i11imm with no further occurrences of in we also give some axioms and proof rules about the new operator

stochastic cellular automata with gibbsian invariant measures a geometric characterization is given of a class of stochastic cellular automata whose invariant probability measures are gibbsian distributions i e markovian random fields this class whose members may be considered as the cartesian product of convex polytopes with a finite number of vertices contains all known automata of this type e g the metropolis gibbs sampler and heat bath algorithms and also a new family which is characterized by having nonreversible dynamic behavior the fact that there is a complete geometric structure instead of isolated points opens the possibility of using classical techniques such as convex programming for the design of optimal automata some examples of applications are given oriented towards the solution of image restoration problems

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

recurrent sampling models for the helmholtz machine many recent analysis by synthesis density estimation models of cortical learning and processing have made the crucial simplifying assumption that units within a single layer are mutually independent given the states of units in the layer below or the layer above in this article we suggest using either a markov random field or an alternative stochastic sampling architecture to capture explicitly particular forms of dependence within each layer we develop the architectures in the context of real and binary helmholtz machines recurrent sampling can be used to capture correlations within layers in the generative or the recognition models and we also show how these can be combined

improved model checking of hierarchical systems we present a unified game based approach for branching time model checking of hierarchical systems such systems are exponentially more succinct than standard state transition graphs as repeated sub systems are described only once early work on model checking of hierarchical systems shows that one can do better than a naive algorithm that flattens the system and removes the hierarchy given a hierarchical system s and a branching time specification j for it we reduce the model checking problem does s satisfy j to the problem of solving a hierarchical game obtained by taking the product of s with an alternating tree automaton a j for j our approach leads to clean uniform and improved model checking algorithms for a variety of branching time temporal logics in particular by improving the algorithm for solving hierarchical parity games we are able to solve the model checking problem for the m calculus in pspace and time complexity that is only polynomial in the depth of the hierarchy our approach also leads to an abstraction refinement paradigm for hierarchical systems the abstraction maintains the hierarchy and is obtained by merging both states and sub systems into abstract states

reasoning about graded strategy quantifiers abstract in this paper we introduce and study graded strategy logic gsl an extension of strategy logic sl with graded quantifiers sl is a powerful formalism that allows to describe useful game concepts in multi agent settings by explicitly quantifying over strategies treated as first order citizens in gsl by means of the existential construct x g one can enforce that there exist at least g strategies x satisfying dually via the universal construct x g one can ensure that all but less than g strategies x satisfy strategies in gsl are counted semantically this means that strategies inducing the same outcome even though looking different are counted as one while this interpretation is natural it requires a suitable machinery to allow for such a counting as we do precisely we introduce a non trivial equivalence relation over strategy profiles based on the strategic behavior they induce to give an evidence of gsl usability we investigate some basic questions about the vanilla gsl 1g fragment that is the vanilla restriction of the well studied one goal strategy logic fragment of sl augmented with graded strategy quantifiers we show that the model checking problem for this logic is ptime complete we also report on some positive results about the determinacy

the complexity of mean payoff pushdown games two player games on graphs are central in many problems in formal verification and program analysis such as synthesis and verification of open systems in this work we consider solving recursive game graphs or pushdown game graphs that model the control flow of sequential programs with recursion while pushdown games have been studied before with qualitative objectives such as reachability and regular objectives in this work we study for the first time such games with the most well studied quantitative objective the mean payoff objective in pushdown games two types of strategies are relevant 1 global strategies which depend on the entire global history and 2 modular strategies which have only local memory and thus do not depend on the context of invocation but rather only on the history of the current invocation of the module our main results are as follows 1 one player pushdown games with mean payoff objectives under global strategies are decidable in polynomial time 2 two player pushdown games with mean payoff objectives under global strategies are undecidable 3 one player pushdown games with mean payoff objectives under modular strategies are np hard 4 two player pushdown games with mean payoff objectives under modular strategies can be solved in np i e both one player and two player pushdown games with mean payoff objectives under modular strategies are np complete we also establish the optimal strategy complexity by showing that global strategies for mean payoff objectives require infinite memory even in one player pushdown games and memoryless modular strategies are sufficient in two player pushdown games finally we also show that all the problems have the same complexity if the stack boundedness condition is added where along with the mean payoff objective the player must also ensure that the stack height is bounded

augmenting atl with strategy contexts we study the extension of the alternating time temporal logic atl with strategy contexts contrary to the original semantics in this semantics the strategy quantifiers do not reset the previously selected strategies we show that our extension atl s c is very expressive but that its decision problems are quite hard model checking is k exptime complete when the formula has k nested strategy quantifiers satisfiability is undecidable but we prove that it is decidable when restricting to turn based games our algorithms are obtained through a very convenient translation to qctl the computation tree logic ctl extended with atomic quantification which we show also applies to strategy logic as well as when strategy quantification ranges over memoryless strategies

competition and multiple cause models if different causes can interact on any occasion to generate a set of patterns then systems modeling the generation have to model the interaction too we discuss a way of combining multiple causes that is based on the integrated segmentation and recognition architecture of keeler et al 1991 it is more cooperative than the scheme embodied in the mixture of experts architecture which insists that just one cause generate each output and more competitive than the noisy or combination function which was recently suggested by saund 1994a b simulations confirm its efficacy

simulating alternating tree automata by nondeterministic automata new results and new proofs of the theorems of rabin mcnaughton and safra abstract we give a proof that alternating tree automata can be simulated by nondeterministic tree automata which yields new complexity results and a unified proof of the theorems of rabin mcnaughton and safra we also give a simple axiomatic framework for uniformizing strategies

a logic for reasoning about counterfactual emotions the aim of this work is to propose a logical framework for the specification of cognitive emotions that are based on counterfactual reasoning about agents choices the prototypical counterfactual emotion is regret in order to meet this objective we exploit the well known stit logic belnap et al 2001 9 horty 2001 30 horty and belnap 1995 31 stit logic has been proposed in the domain of formal philosophy in the nineties and more recently it has been imported into the field of theoretical computer science where its formal relationships with other logics for multi agent systems such as atl and coalition logic cl have been studied stit is a very suitable formalism to reason about choices and capabilities of agents and groups of agents unfortunately the version of stit with agents and groups has been recently proved to be undecidable and not finitely axiomatizable in this work we study a decidable and finitely axiomatizable fragment of stit with agents and groups which is sufficiently expressive for our purpose of formalizing counterfactual emotions we call dfstit our stit fragment after having extended dfstit with knowledge modalities in the second part of article we exploit it in order to formalize four types of counterfactual emotions regret rejoicing disappointment and elation at the end of the article we present an application of our formalization of counterfactual emotions to a concrete example

pushdown module checking with imperfect information the model checking problem for finite state open systems module checking has been extensively studied in the literature both in the context of environments with perfect and imperfect information about the system recently the perfect information case has been extended to infinite state systems pushdown module checking in this paper we extend pushdown module checking to the imperfect information setting i e to the case where the environment has only a partial view of the email protected s control states and pushdown store content we study the complexity of this problem with respect to the branching time temporal logics ctl ctl and the propositional m calculus we show that pushdown module checking which is by itself harder than pushdown model checking becomes undecidable when the environment has imperfect information we also show that undecidability relies on hiding information about the pushdown store indeed we prove that with imperfect information about the control states but a visible pushdown store the problem is decidable and its complexity is 2exptime complete for ctl and the propositional m calculus and 3exptime complete for ctl

infinite games with finite knowledge gaps infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable unless the information is hierarchically ordered among the players we identify a class of games for which joint winning strategies can be constructed effectively without restricting the direction of information flow instead our condition requires that the players attain common knowledge about the actual state of the game over and over again along every play we show that it is decidable whether a given game satisfies the condition and prove tight complexity bounds for the strategy synthesis problem under regular winning conditions given by deterministic parity automata

the average crossing number of equilateral random polygons in this paper we study the average crossing number of equilateral random walks and polygons we show that the mean average crossing number acn of all equilateral random walks of length n is of the form a similar result holds for equilateral random polygons these results are confirmed by our numerical studies furthermore our numerical studies indicate that when random polygons of length n are divided into individual knot types the for each knot type can be described by a function of the form where a b and c are constants depending on and n0 is the minimal number of segments required to form the profiles diverge from each other with more complex knots showing higher than less complex knots moreover the profiles intersect with the acn profile of all closed walks these points of intersection define the equilibrium length of i e the chain length at which a statistical ensemble of configurations with given knot type upon cutting equilibration and reclosure to a new knot type does not show a tendency to increase or decrease this concept of equilibrium length seems to be universal and applies also to other length dependent observables for random knots such as the mean radius of gyration rg

a multiple cause mixture model for unsupervised learning this paper presents a formulation for unsupervised learning of clusters reflecting multiple causal structure in binary data unlike the hard k means clustering algorithm and the soft mixture model each of which assumes that a single hidden event generates each data point a multiple cause model accounts for observed data by combining assertions from many hidden causes each of which can pertain to varying degree to any subset of the observable dimensions we employ an objective function and iterative gradient descent learning algorithm resembling the conventional mixture model a crucial issue is the mixing function for combining beliefs from different cluster centers in order to generate data predictions whose errors are minimized both during recognition and learning the mixing function constitutes a prior assumption about underlying structural regularities of the data domain we demonstrate a weakness inherent to the popular weighted sum followed by sigmoid squashing and offer alternative forms of the nonlinearity for two types of data domain results are presented demonstrating the algorithm s ability successfully to discover coherent multiple causal representations in several experimental data sets

alternating finite automata on ω words abstract alternating finite automata on words are introduced as an extension of nondeterministic finite automata which process infinite sequences of symbols the classes of languages defined by alternating finite automata are investigated and characterized under four types of acceptance conditions it is shown that for one type of acceptance condition alternation increases the power in comparison with nondeterminism and for other three acceptance conditions nondeterministic finite automata on words have the same power as alternating ones

bounded model checking of strategy ability with perfect recall the paper works with a logic which has the expressiveness to quantify over strategies of bounded length the semantics of the logic is based on systems with multiple agents agents have incomplete information about the underlying system state and their strategies are based on perfect recall memory over observations and local actions the computational complexity of model checking is shown to be pspace complete we give two bdd based model checking algorithms the algorithms are implemented in a model checker and experimental results are reported to show their applications

doomsday equilibria for omega regular games abstract two player games on graphs provide the theoretical framework for many important problems such as reactive synthesis while the traditional study of two player zero sum games has been extended to multi player games with several notions of equilibria they are decidable only for perfect information games whereas several applications require imperfect information in this paper we propose a new notion of equilibria called doomsday equilibria which is a strategy profile where all players satisfy their own objective and if any coalition of players deviates and violates even one of the players objective then the objective of every player is violated we present algorithms and complexity results for deciding the existence of doomsday equilibria for various classes of regular objectives both for imperfect information games and for perfect information games we provide optimal complexity bounds for imperfect information games and in most cases for perfect information games

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

the complexity of one agent refinement modal logic we investigate the complexity of satisfiability for one agent refinement modal logic rml a known extension of basic modal logic ml obtained by adding refinement quantifiers on structures it is known that rml has the same expressiveness as ml but the translation of rml into ml is of non elementary complexity and rml is at least doubly exponentially more succinct than ml in this paper we show that rml satisfiability is only singly exponentially harder than ml satisfiability the latter being a well known pspace complete problem more precisely we establish that rml satisfiability is complete for the complexity class aexp pol i e the class of problems solvable by alternating turing machines running in single exponential time but only with a polynomial number of alternations note that nexptime aexp pol expspace 11this work is the revised and expanded version of 1

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

the growth of the mean average crossing number of equilateral polygons in confinement the physical and biological properties of collapsed long polymer chains as well as of highly condensed biopolymers such as dna in all organisms are known to be determined at least in part by their topological and geometrical properties with this purpose of characterizing the topological properties of such condensed systems equilateral random polygons restricted to confined volumes are often used however very few analytical results are known in this paper we investigate the effect of volume confinement on the mean average crossing number acn of equilateral random polygons the mean acn of knots and links under confinement provides a simple alternative measurement for the topological complexity of knots and links in the statistical sense for an equilateral random polygon of n segments without any volume confinement constrain it is known that its mean acn acn is of the order here we model the confining volume as a simple sphere of radius r we provide an analytical argument which shows that acn of an equilateral random polygon of n segments under extreme confinement meaning r n grows as o n2 we propose to model the growth of acn as a r n2 b r nln n under a less extreme confinement condition where a r and b r are functions of r with r being the radius of the confining sphere computer simulations performed show a fairly good fit using this model

uniform strategies rational relations and jumping automata a general concept of uniform strategies has recently been proposed as a relevant notion in game theory for computer science which subsumes various notions from the literature it relies on properties involving sets of plays in two player turn based arenas equipped with arbitrary binary relations between plays these properties are expressed in a language based on ctl with a quantifier over related plays there are two semantics for our quantifier a strict one and a full one that we study separately regarding the strict semantics the existence of a uniform strategy is undecidable for rational binary relations but introducing jumping tree automata and restricting attention to recognizable relations allows us to establish a 2 exptime complete complexity and still capture a class of two player imperfect information games with epistemic temporal objectives regarding the full semantics relying on information set automata we establish that the existence of a uniform strategy is decidable for rational relations and we provide a nonelementary synthesis procedure we also exhibit an essentially optimal subclass of rational relations for which the problem becomes 2 exptime complete considering rich classes of relations makes the theory of uniform strategies powerful it directly entails various results in logics of knowledge and time some of them already known and others new

a logic with revocable and refinable strategies in this article we present updatable strategy logic usl a multi agent temporal logic which subsumes the main propositions in this area such as atl atl atl sc and sl these logics allow to express the capabilities of agents to ensure the satisfaction of temporal properties usl mainly differs from sl in two ways semantically usl relies on multi strategies that is non deterministic strategies and the notion of strategy composition is extended to enable an agent to refine her strategy that is to update it without revoking it syntactically the logic features a binding operator enabling multi strategy refinements as well as an unbinding operator that allows an agent to explicitly revoke a multi strategy whereas revocation is implicit with the binding operator in sl we show that usl allows to express a notion of sustainable control for an agent i e a capability to always decide the satisfaction of a property that still holds even after the said capability has been employed furthermore usl allows the definition of a notion of equality between multi strategies that enables to consider quantification over deterministic strategies this makes usl strictly more expressive than sl finally we also show that the model checking problem for usl is decidable but non elementary as for sl

qualitative analysis of concurrent mean payoff games we consider concurrent games played by two players on a finite state graph where in every round the players simultaneously choose a move and the current state along with the joint moves determine the successor state we study the most fundamental objective for concurrent games namely mean payoff or limit average objective where a reward is associated to each transition and the goal of player 1 is to maximize the long run average of the rewards and the objective of player 2 is strictly the opposite i e the games are zero sum the path constraint for player 1 could be qualitative i e the mean payoff is the maximal reward or arbitrarily close to it or quantitative i e a given threshold between the minimal and maximal reward we consider the computation of the almost sure resp positive winning sets where player 1 can ensure that the path constraint is satisfied with probability 1 resp positive probability almost sure winning with qualitative constraint exactly corresponds to the question of whether there exists a strategy to ensure that the payoff is the maximal reward of the game our main results for qualitative path constraints are as follows 1 we establish qualitative determinacy results that show that for every state either player 1 has a strategy to ensure almost sure resp positive winning against all player 2 strategies or player 2 has a spoiling strategy to falsify almost sure resp positive winning against all player 1 strategies 2 we present optimal strategy complexity results that precisely characterize the classes of strategies required for almost sure and positive winning for both players and 3 we present quadratic time algorithms to compute the almost sure and the positive winning sets matching the best known bound of the algorithms for much simpler problems such as reachability objectives for quantitative constraints we show that a polynomial time solution for the almost sure or the positive winning set would imply a solution to a long standing open problem of solving the value problem of turn based deterministic mean payoff games that is not known to be solvable in polynomial time

on the mean and variance of the writhe of random polygons we here address two problems concerning the writhe of random polygons first we study the behavior of the mean writhe as a function length second we study the variance of the writhe suppose that we are dealing with a set of random polygons with the same length and knot type which could be the model of some circular dna with the same topological property in general a simple way of detecting chirality of this knot type is to compute the mean writhe of the polygons if the mean writhe is non zero then the knot is chiral how accurate is this method for example if for a specific knot type k the mean writhe decreased to zero as the length of the polygons increased then this method would be limited in the case of long polygons furthermore we conjecture that the sign of the mean writhe is a topological invariant of chiral knots this sign appears to be the same as that of an ideal conformation of the knot we provide numerical evidence to support these claims and we propose a new nomenclature of knots based on the sign of their expected writhes this nomenclature can be of particular interest to applied scientists the second part of our study focuses on the variance of the writhe a problem that has not received much attention in the past in this case we focused on the equilateral random polygons we give numerical as well as analytical evidence to show that the variance of the writhe of equilateral random polygons of length n behaves as a linear function of the length of the equilateral random polygon

natural gradient works efficiently in learning when a parameter space has a certain underlying structure the ordinary gradient of a function does not represent its steepest direction but the natural gradient does information geometry is used for calculating the natural gradients in the parameter space of perceptrons the space of matrices for blind source separation and the space of linear dynamical systems for blind source deconvolution the dynamical behavior of natural gradient online learning is analyzed and is proved to be fisher efficient implying that it has asymptotically the same performance as the optimal batch estimation of parameters this suggests that the plateau phenomenon which appears in the backpropagation learning algorithm of multilayer perceptrons might disappear or might not be so serious when the natural gradient is used an adaptive method of updating the learning rate is proposed and analyzed

characteristics of shape and knotting in ideal rings we present two descriptions of the local scaling and shape of ideal rings primarily featuring subsegments our focus will be the squared radius of gyration of subsegments and the squared internal end to end distance defined to be the average squared distance between vertices k edges apart we calculate the exact averages of these values over the space of all such ideal rings not just a calculation of the order of these averages and compare these to the equivalent values in open chains this comparison will show that the structure of ideal rings is similar to that of ideal chains for only exceedingly short lengths these results will be corroborated by numerical experiments they will be used to analyze the convergence of our generation method and the effect of knotting on these characteristics of shape

concurrent reachability games we consider concurrent two player games with reachability objectives in such games at each round player 1 and player 2 independently and simultaneously choose moves and the two choices determine the next state of the game the objective of player 1 is to reach a set of target states the objective of player 2 is to prevent this these are zero sum games and the reachability objective is one of the most basic objectives determining the set of states from which player 1 can win the game is a fundamental problem in control theory and system verification there are three types of winning states according to the degree of certainty with which player 1 can reach the target from type 1 states player 1 has a deterministic strategy to always reach the target from type 2 states player 1 has a randomized strategy to reach the target with probability 1 from type 3 states player 1 has for every real e 0 a randomized strategy to reach the target with probability greater than email protected we show that for finite state spaces all three sets of winning states can be computed in polynomial time type 1 states in linear time and type 2 and type 3 states in quadratic time the algorithms to compute the three sets of winning states also enable the construction of the winning and spoiling strategies

generating random walks and polygons with stiffness in confinement the purpose of this paper is to explore ways to generate random walks and polygons in confinement with a bias toward stiffness here the stiffness refers to the curvature angle between two consecutive edges along the random walk or polygon the stiffer the walk polygon the smaller this angle on average thus random walks and polygons with an elevated stiffness have lower than expected curvatures the authors introduced and studied several generation algorithms with a stiffness parameter that regulates the expected curvature angle at a given vertex in which the random walks and polygons are generated one edge at a time using conditional probability density functions our generating algorithms also allow the generation of unconfined random walks and polygons with any desired mean curvature angle in the case of random walks and polygons confined in a sphere of fixed radius we observe that as expected stiff random walks or polygons are more likely to be close to the confinement boundary the methods developed here require that the random walks and random polygons be rooted at the center of the confinement sphere

on composition of bounded recall plans abstract the article studies the ability of agents with bounded memory to execute consecutive composition of plans it gives an upper limit on the amount of memory required to execute the composed plans and shows that the limit cannot be improved furthermore the article shows that there are essentially no other universal properties of plans for bounded recall agents expressible through the relation there is a plan for an agent with a given memory size to navigate from one given set of states to another

alternating time temporal logic atl with finitely bounded semantics abstract we study a variant atl fb of the alternating time temporal logic atl with a non standard finitely bounded semantics fbs fbs was originally defined as a game theoretic semantics where players must commit to time limits when attempting to verify eventuality respectively to falsify safety formulae it turns out that fbs has a natural corresponding compositional semantics that essentially evaluates formulae only on finite initial segments of paths and imposes uniform bounds on all plays for the fulfilment of eventualities the resulting version atl fb differs in some essential features from the standard atl as it no longer has the finite model property though the two logics are equivalent on finite models we develop two tableau systems for atl fb the first one deals with infinite sets of formulae and may run in a transfinite sequence of steps whereas the second one deals only with finite sets of formulae in an extended language allowing explicit symbolic indication of time limits in formulae we prove soundness and completeness of the infinitary tableau system and prove that it is equivalent to the finitary one we also show that the finitary tableau system provides an exponential time decision procedure for the satisfiability problem of atl fb and thus establishes its exptime completeness furthermore we present an infinitary axiomatization for atl fb and prove its soundness and completeness

knots in self avoiding walks discusses the existence of knots in random self avoiding walks on a lattice using kesten s 1963 pattern theorem it is shown that almost all sufficiently long self avoiding walks on the three dimensional simple cubic lattice contain a knot

scaling behavior of random knots using numerical simulations we investigate how overall dimensions of random knots scale with their length we demonstrate that when closed non self avoiding random trajectories are divided into groups consisting of individual knot types then each such group shows the scaling exponent of 0 588 that is typical for self avoiding walks however when all generated knots are grouped together their scaling exponent becomes equal to 0 5 as in non self avoiding random walks we explain here this apparent paradox we introduce the notion of the equilibrium length of individual types of knots and show its correlation with the length of ideal geometric representations of knots we also demonstrate that overall dimensions of random knots with a given chain length follow the same order as dimensions of ideal geometric representations of knots

em algorithms for ml factor analysis the details of em algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models the algorithm is essentially the same for both cases and involves only simple least squares regression operations the largest matrix inversion required is for aq q symmetric matrix whereq is the matrix of factors the example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation

the complexity of tree automata and logics of programs the complexity of testing nonemptiness of finite state automata on infinite trees is investigated it is shown that for tree automata with the pairs or complemented pairs acceptance condition having m states and n pairs nonemptiness can be tested in deterministic time mn o n however it is shown that the problem is in general np complete or co np complete respectively the new nonemptiness algorithm yields exponentially improved essentially tight upper bounds for numerous important modal logics of programs interpreted with the usual semantics over structures generated by binary relations for example it follows that satisfiability for the full branching time logic ctl can be tested in deterministic double exponential time another consequence is that satisfiability for propositional dynamic logic pdl with a repetition construct pdl delta and for the propositional mu calculus l mu can be tested in deterministic single exponential time

randomness for free we consider two player zero sum games on finite state graphs these games can be classified on the basis of the information of the players and on the mode of interaction between them on the basis of information the classification is as follows a partial observation both players have partial view of the game b one sided complete observation one player has complete observation and c complete observation both players have complete view of the game on the basis of mode of interaction we have the following classification a concurrent players interact simultaneously and b turn based players interact in turn the two sources of randomness in these games are randomness in the transition function and randomness in the strategies in general randomized strategies are more powerful than deterministic strategies and probabilistic transitions give more general classes of games we present a complete characterization for the classes of games where randomness is not helpful in a the transition function probabilistic transitions can be simulated by deterministic transitions and b strategies pure strategies are as powerful as randomized strategies as a consequence of our characterization we obtain new undecidability results for these games

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

nash equilibria in symmetric graph games with partial observation we investigate a model for representing large multiplayer games which satisfy strong symmetry properties this model is made of multiple copies of an arena each player plays in his own arena and can partially observe what the other players do therefore this game has partial information and symmetry constraints which make the computation of nash equilibria difficult we show several undecidability results and for bounded memory strategies we precisely characterize the complexity of computing pure nash equilibria for qualitative objectives in this game model

a saturation method for the modal μ calculus over pushdown systems we present an algorithm for computing directly the denotation of a m calculus formula g over the configuration graph of a pushdown system our method gives the first extension of the saturation technique to the full m calculus finite word automata are used to represent sets of pushdown configurations starting from an initial automaton we perform a series of automaton manipulations which compute the denotation by recursion over the structure of the formula we introduce notions of under approximation soundness and over approximation completeness that apply to automaton transitions rather than runs our algorithm is relatively simple and direct and avoids an immediate exponential blow up finally we show experimentally that the direct algorithm is more efficient than via a reduction to parity games

efficient and dynamic algorithms for alternating buchi games and maximal end component decomposition the computation of the winning set for buchi objectives in alternating games on graphs is a central problem in computer aided verification with a large number of applications the long standing best known upper bound for solving the problem is o n m where n is the number of vertices and m is the number of edges in the graph we are the first to break the o n m boundary by presenting a new technique that reduces the running time to o n2 this bound also leads to o n2 time algorithms for computing the set of almost sure winning vertices for buchi objectives 1 in alternating games with probabilistic transitions improving an earlier bound of o n m 2 in concurrent graph games with constant actions improving an earlier bound of o n3 and 3 in markov decision processes improving for m n4 3 an earlier bound of o m m we then show how to maintain the winning set for buchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in o n amortized time per operation our algorithms are the first dynamic algorithms for this problem we then consider another core graph theoretic problem in verification of probabilistic systems namely computing the maximal end component decomposition of a graph we present two improved static algorithms for the maximal end component decomposition problem our first algorithm is an o m m time algorithm and our second algorithm is an o n2 time algorithm which is obtained using the same technique as for alternating buchi games thus we obtain an o min m m n2 time algorithm improving the long standing o n m time bound finally we show how to maintain the maximal end component decomposition of a graph under a sequence of edge insertions or a sequence of edge deletions in o n amortized time per edge deletion and o m worst case time per edge insertion again our algorithms are the first dynamic algorithms for this problem

profile trees for buchi word automata with application to determinization the determinization of buchi automata is a celebrated problem with applications in synthesis probabilistic verification and multi agent systems since the 1960s there has been a steady progress of constructions by mcnaughton safra piterman schewe and others despite the proliferation of solutions they are all essentially ad hoc constructions with little theory behind them other than proofs of correctness since safra all optimal constructions employ trees as states of the deterministic automaton and transitions between states are defined operationally over these trees the operational nature of these constructions complicates understanding implementing and reasoning about them and should be contrasted with complementation where a solid theory in terms of automata run dags underlies modern constructions in 2010 we described a profile based approach to buchi complementation where a profile is simply the history of visits to accepting states we developed a structural theory of profiles and used it to describe a complementation construction that is deterministic in the limit here we extend the theory of profiles to prove that every run dag contains a profile tree with at most a finite number of infinite branches we then show that this property provides a theoretical grounding for a new determinization construction where macrostates are doubly preordered sets of states in contrast to extant determinization constructions transitions in the new construction are described declaratively rather than operationally

curvature of random walks and random polygons in confinement the purpose of this paper is to study the curvature of equilateral random walks and polygons that are confined in a sphere curvature is one of several basic geometric properties that can be used to describe random walks and polygons we show that confinement affects curvature quite strongly and in the limit case where the confinement diameter equals the edge length the unconfined expected curvature value doubles from 2 to to study curvature a simple model of an equilateral random walk in spherical confinement in dimensions 2 and 3 is introduced for this simple model we derive explicit integral expressions for the expected value of the total curvature in both dimensions these expressions are functions that depend only on the radius r of the confinement sphere we then show that the values obtained by numeric integration of these expressions agrees with numerical average curvature estimates obtained from simulations of random walks finally we compare the confinement effect on curvature of random walks with random polygons

model checking open systems with alternating projection temporal logic abstract to specify properties of open systems with interval based temporal logics alternating projection temporal logic aptl is proposed by introducing concurrent game structures cgs to propositional projection temporal logic pptl further examples are given to show how properties of open systems can be specified by aptl formulas moreover to establish the automata based model theory for the new proposed logic generalized alternating buchi automata over concurrent game structures gbcgs are defined and a transformation from aptl formulas to gbcgs is presented in addition a decision procedure for checking the satisfiability of aptl formulas and a model checking approach for aptl with concurrent game structures cgss being models are presented

on the logic of cooperation and propositional control cooperation logics have recently begun to attract attention within the multi agent systems community using a cooperation logic it is possible to represent and reason about the strategic powers of agents and coalitions of agents in game like multi agent systems these powers are generally assumed to be implicitly defined within the structure of the environment and their origin is rarely discussed in this paper we study a cooperation logic in which agents are each assumed to control a set of propositional variables the powers of agents and coalitions then derive from the allocation of propositions to agents the basic modal constructs in this coalition logic of propositional control cl pc allow us to express the fact that a group of agents can cooperate to bring about a certain state of affairs after motivating and introducing cl pc we provide a complete axiom system for the logic investigate the issue of characterising control in cl pc with respect to the underlying power structures of the logic and formally investigate the relationship between cl pc and pauly s coalition logic we then show that the model checking and satisfiability problems for cl pc are both pspace complete and conclude by discussing our results and how cl pc sits in relation to other logics of cooperation

a fast ergodic algorithm for generating ensembles of equilateral random polygons knotted structures are commonly found in circular dna and along the backbone of certain proteins in order to properly estimate properties of these three dimensional structures it is often necessary to generate large ensembles of simulated closed chains i e polygons of equal edge lengths such polygons are called equilateral random polygons however finding efficient algorithms that properly sample the space of equilateral random polygons is a difficult problem currently there are no proven algorithms that generate equilateral random polygons with its theoretical distribution in this paper we propose a method that generates equilateral random polygons in a step wise uniform way we prove that this method is ergodic in the sense that any given equilateral random polygon can be generated by this method and we show that the time needed to generate an equilateral random polygon of length n is linear in terms of n these two properties make this algorithm a big improvement over the existing generating methods detailed numerical comparisons of our algorithm with other widely used algorithms are provided

a survey and comparison of discrete and continuous multi label optimization approaches for the potts model we present a survey and a comparison of a variety of algorithms that have been proposed over the years to minimize multi label optimization problems based on the potts model discrete approaches based on markov random fields as well as continuous optimization approaches based on partial differential equations can be applied to the task in contrast to the case of binary labeling the multi label problem is known to be np hard and thus one can only expect near optimal solutions in this paper we carry out a theoretical comparison and an experimental analysis of existing approaches with respect to accuracy optimality and runtime aimed at bringing out the advantages and short comings of the respective algorithms systematic quantitative comparison is done on the graz interactive image segmentation benchmark this paper thereby generalizes a previous experimental comparison klodt et al 2008 from the binary to the multi label case

alternating time temporal logics with linear past abstract we investigate the succinctness gap between two known equally expressive and different linear past extensions of standard atl we establish by formal non trivial arguments that the memoryful linear past extension the history leading to the current state is taken into account can be exponentially more succinct than the standard local linear past extension the history leading to the current state is forgotten as a second contribution we consider the atl like fragment denoted atl l p of the known memoryful linear past extension of atl we show that atl l p is strictly more expressive than atl and interestingly it can be exponentially more succinct than the more expressive logic atl moreover we prove that both satisfiability and model checking for the logic atl l p are exptime complete

reasoning about coalitional games we develop investigate and compare two logic based knowledge representation formalisms for reasoning about coalitional games the main constructs of coalitional game logic cgl are expressions for representing the ability of coalitions which may be combined with expressions for representing the preferences that agents have over outcomes modal coalitional game logic mcgl is a normal modal logic in which the main construct is a modality for expressing the preferences of groups of agents for both frameworks we give complete axiomatisations and show how they can be used to characterise solution concepts for coalitional games we show that while cgl is more expressive than mcgl the former can only be used to reason about coalitional games with finitely many outcomes while mcgl can be used to reason also about games with infinitely many outcomes and is in addition more succinct we characterise the computational complexity of satisfiability for cgl and give a tableaux based decision procedure

fair simulation relations parity games and state space reduction for buchi automata we give efficient algorithms improving optimal known bounds for computing a variety of simulation relations on the state space of a buchi automaton our algorithms are derived via a unified and simple parity game framework this framework incorporates previously studied notions like fair and direct simulation but also a new natural notion of simulation called delayed simulation which we introduce for the purpose of state space reduction we show that delayed simulation unlike fair simulation preserves the automaton language upon quotienting and allows substantially better state space reduction than direct simulation using our parity game approach which relies on an algorithm by jurdzinski we give efficient algorithms for computing all of the above simulations in particular we obtain an o mn3 time and o mn space algorithm for computing both the delayed and the fair simulation relations the best prior algorithm for fair simulation requires time and space o n6 our framework also allows one to compute bisimulations we compute the fair bisimulation relation in o mn3 time and o mn space whereas the best prior algorithm for fair bisimulation requires time and space o n10

complete axiomatization and decidability of alternating time temporal logic alternating time temporal logic atl introduced by alur henzinger and kupferman is a logical formalism for the specification and verification of open systems involving multiple autonomous players agents components in particular this logic allows for the explicit expression of coalition abilities in such systems modelled as infinite transition games between the coalition and its complement formally atl is a non normal multi modal extension of ctl regarded as a one player fragment of atl with temporal operators indexed by coalitions of players and thus expressing selective quantification over those paths which can be effected as outcomes of infinite transition games between the coalition and its complement we present a sound and complete axiomatization of the logic atl based on pauly s axiomatization of his coalition logic augmented with axioms and rules for fixed point formulae characterizing the temporal operators the completeness proof is by construction of a bounded branching tree model for each atl consistent formula these models can be folded into finite models thus rendering the finite model property for atl we also describe an automata based decision procedure for atl by translating the satisfiability problem to the nonemptiness problem for alternating automata on infinite trees when considering formulae over a fixed finite set of players the decidability problem is shown to be exptime complete