quantum integrability in systems with finite number of levels we consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners we argue that if the matrices depend on a real parameter one can define quantum integrability from this feature alone leading to specific results such as exact solvability poissonian energy level statistics and to level crossings

reasoning about action i a possible worlds approach abstract reasoning about change is an important aspect of commonsense reasoning and planning in this paper we describe an approach to reasoning about change for rich domains where it is not possible to anticipate all situations that might occur the approach provides a solution to the frame problem and to the related problem that it is not always reasonable to explicitly specify all of the consequences of actions the approach involves keeping a single model of the world that is updated when actions are performed the update procedure involves constructing the nearest world to the current one in which the consequences of the actions under consideration hold the way we find the nearest world is to construct proofs of the negation of the explicit consequences of the expected action and to remove a premise in each proof from the current world computationally this construction procedure appears to be tractable for worlds like our own where few things tend to change with each action or where change is regular

optimal nonblocking directed control of discrete event systems for the control of discrete event systems the notion of directed control refines that of supervisory control a directed controller is one that selects at most one controllable event to be enabled at any state without disabling any uncontrollable event which is in fact how a discrete event control is implemented in contrast a supervisory controller computes a maximal allowable set of controllable events at each state leaving undecided exactly which controllable event should be enabled in previous works we developed a framework for the computation of optimal directed controllers and a polynomial synthesis algorithm for acyclic plants in this paper we present a novel synthesis approach for general plants i e plants with or without cycles thus providing a complete solution to the optimal directed control problem the complexity of the approach remains polynomial in the size of plant

impediments to universal preference based default theories research on nonmonotonic and default reasoning has identified several important criteria for preferring alternative default inferences the theories of reasoning based on each of these criteria may uniformly be viewed as theories of rational inference in which the reasoner selects maximally preferred states of belief though researchers have noted some cases of apparent conflict between the preferences supported by different theories it has been hoped that these special theories of reasoning may be combined into a universal logic of nonmonotonic reasoning we show that the different categories of preferences conflict more than has been realized and adapt formal results from social choice theory to prove that every universal theory of default reasoning will violate at least one reasonable principle of rational reasoning our results can be interpreted as demonstrating that within the preferential framework we cannot expect much improvement on the rigid lexicographic priority mechanisms that have been proposed for conflict resolution

second order necessary conditions in constrained semismooth optimization first and second order conditions are given which must necessarily be satisfied by local minimizers for certain finite dimensional nonsmooth nonlinear programming problems the problems considered are of standard form having a finite number of equality and inequality constraints the principal result does not require a constraint qualification but does require that the functions be semismooth at the minimizer the necessary conditions are stated in terms of the generalized gradients of nonsmooth analysis and certain second order directional derivatives

exact solution of generalized tavis cummings models in quantum optics quantum inverse methods are developed for the exact solution of models which describe n two level atoms interacting with one mode of the quantized electromagnetic field containing an arbitrary number of excitations m either a kerr type nonlinearity or a stark shift term can be included in the model and it is shown that these two cases can be mapped from one to the other the method of solution provides a general framework within which many related problems can similarly be solved explicit formulae are given for the rabi splitting of the models for some n and m on and off resonance it is also shown that the solution of the pure tavis cummings model can be reduced to solving a homogeneous ordinary differential equation of second order generalization of the method to the case of several cavity modes is indicated

a class of parameter dependent commuting matrices we present a novel class of real symmetric matrices in arbitrary dimension d linearly dependent on a parameter x the matrix elements satisfy a set of nontrivial constraints that arise from asking for commutation of pairs of such matrices for all x and an intuitive sufficiency condition for the solvability of certain linear equations that arise therefrom this class of matrices generically violates the wigner von neumann non crossing rule and is argued to be intimately connected with finite dimensional hamiltonians of quantum integrable systems

minimizing conflicts a heuristic repair method for constraint satisfaction and scheduling problems abstract the paper describes a simple heuristic approach to solving large scale constraint satisfaction and scheduling problems in this approach one starts with an inconsistent assignment for a set of variables and searches through the space of possible repairs the search can be guided by a value ordering heuristic the min conflicts heuristic that attempts to minimize the number of constraint violations after each step the heuristic can be used with a variety of different search strategies we demonstrate empirically that on the n queens problem a technique based on this approach performs orders of magnitude better than traditional backtracking techniques we also describe a scheduling application where the approach has been used successfully a theoretical analysis is presented both to explain why this method works well on certain types of problems and to predict when it is likely to be most effective

the size of bdds and other data structures in temporal logics model checking temporal logic model checking is a verification method in which we describe a system the model and then we verify whether important properties expressed in a temporal logic formula hold in the system many model checking tools employ bdds or some other data structure to represent sets of states it has been empirically observed that the bdds used in these algorithms may grow exponentially as the model and formula increase in size we formally prove that no kind of data structure of polynomial size can represent the set of valid initial states for all models and all formulae this result holds for all data structures where a state can be checked in polynomial time therefore it holds not only for all types of bdds regardless of variable ordering but also for more powerful data structures such as rbcs mtbdds adds and sdds thus the size explosion of bdds is not a limit of these specific data representation structures but is unavoidable every formalism used in the same way would lead to an exponential size blow up

robust kernel isomap isomap is one of widely used low dimensional embedding methods where geodesic distances on a weighted graph are incorporated with the classical scaling metric multidimensional scaling in this paper we pay our attention to two critical issues that were not considered in isomap such as 1 generalization property projection property 2 topological stability then we present a robust kernel isomap method armed with such two properties we present a method which relates the isomap to mercer kernel machines so that the generalization property naturally emerges through kernel principal component analysis for topological stability we investigate the network flow in a graph providing a method for eliminating critical outliers the useful behavior of the robust kernel isomap is confirmed through numerical experiments with several data sets

integrability and level crossing manifolds in a quantum hamiltonian system we consider a two spin model represented classically by a nonlinear autonomous hamiltonian system with two degrees of freedom and a nontrivial integrability condition and quantum mechanically by a real symmetric hamiltonian matrix with invariant blocks of dimensionalities k frac 1 2 l l 1 l 1 2 dots in the six dimensional parameter space of this model classical integrability is satisfied on a five dimensional hypersurface and level crossings occur on four dimensional manifolds that are completely embedded in the integrability hypersurface except for some lower dimensional submanifolds under mild assumptions the classical integrability condition can be reconstructed from a purely quantum mechanical study of level degeneracies in finite dimensional invariant blocks of the hamiltonian matrix our conclusions are based on rigorous results for k 3 and on numerical results for k 6 10

a new representation and associated algorithms for generalized planning constructing plans that can handle multiple problem instances is a longstanding open problem in ai we present a framework for generalized planning that captures the notion of algorithm like plans and unifies various approaches developed for addressing this problem using this framework and building on the tvla system for static analysis of programs we develop a novel approach for computing generalizations of classical plans by identifying sequences of actions that will make measurable progress when placed in a loop in a wide class of problems that we characterize formally in the paper these methods allow us to find generalized plans with loops for solving problem instances of unbounded sizes and also to determine the correctness and applicability of the computed generalized plans we demonstrate the scope and scalability of the proposed approach on a wide range of planning problems

constrained best euclidean distance embedding on a sphere a matrix optimization approach the problem of data representation on a sphere of unknown radius arises from various disciplines such as statistics spatial data representation psychology constrained multidimensional scaling and computer science machine learning and pattern recognition the best representation often needs to minimize a distance function of the data on a sphere as well as to satisfy some euclidean distance constraints it is those spherical and euclidean distance constraints that present an enormous challenge to the existing algorithms in this paper we reformulate the problem as an euclidean distance matrix optimization problem with a low rank constraint we then propose an iterative algorithm that uses a quadratically convergent newton cg method at each step we study fundamental issues including constraint nondegeneracy and the nonsingularity of generalized jacobian that ensure the quadratic convergence of the newton method we use some classic examples from the spherical multidimensional scaling to demonstrat

karush kuhn tucker systems regularity conditions error bounds and a class of newton type methods we consider optimality systems of karush kuhn tucker kkt type which arise for example as primal dual conditions characterizing solutions of optimization problems or variational inequalities in particular we discuss error bounds and newton type methods for such systems an exhaustive comparison of various regularity conditions which arise in this context is given we obtain a new error bound under an assumption which we show to be strictly weaker than assumptions previously used for kkt systems such as quasi regularity or semistability equivalently the r0 property error bounds are useful among oth er things for identifying active constraints and developing efficient local algorithms we propose a family of local newton type algorithms this family contains some known active set newton methods as well as some new methods regularity conditions required for local superlinear convergence compare favorably with convergence conditions of nonsmooth newton methods and sequential quadratic programming methods

second order necessary conditions in semismooth optimization first and second order conditions are given which are necessary for a functionf to have a local minimal value atx inrn it is assumed thatf is locally lipschitzian nearx and semismooth atx the necessary conditions are expressed in terms of the generalized gradients of nonsmooth analysis and certain second order directional derivatives the method of proof bears no resemblance to standard methods three special cases are discussed here but applications to constrained problems are made elsewhere

expressive equivalence of planning formalisms abstract a concept of expressive equivalence for planning formalisms based on polynomial transformations is defined it is argued that this definition is reasonable and useful both from a theoretical and from a practical perspective if two languages are equivalent then theoretical results carry over and more practically we can model an application problem in one language and then easily use a planner for the other language in order to cope with the problem of exponentially sized solutions for planning problems an even stronger concept of expressive equivalence is introduced using the novel esp reduction four different formalisms for propositional planning are then analyzed namely two variants of strips ground tweak and the sas formalism although these may seem to exhibit different degrees of expressive power it is proven that they are in fact expressively equivalent under esp reduction this means that neither negative goals partial initial states nor multi valued state variables increase the expressiveness of standard propositional strips

the relaxed nonlinear phss like iteration method for absolute value equations finding the solution of the absolute value equation ave a x x b has attracted much attention in recent years in this paper we propose a relaxed nonlinear phss like iterative method which is more efficient than the picard hss iterative method for the ave and is a generalization of the nonlinear hss like iteration method for the ave by using the theory of nonsmooth analysis we prove the convergence of the relaxed nonlinear phss like iterative method for the ave numerical experiments are given to demonstrate the feasibility robustness and effectiveness of the relaxed nonlinear hss like method

state space search nogood learning online refinement of critical path dead end detectors in planning abstract conflict directed learning is ubiquitous in constraint satisfaction problems like sat but has been elusive for state space search on reachability problems like classical planning almost all existing approaches learn nogoods relative to a fixed solution length bound in which case planning reachability reduces to a constraint satisfaction problem here we introduce an approach to learning more powerful nogoods that are sound regardless of solution length i e that identify dead end states for which no solution exists the key technique we build on are critical path heuristics h c relative to a set c of conjunctions these recognize a dead end state s returning h c s if s has no solution even when allowing to break up conjunctive subgoals into the elements of c our key idea is to learn c during search whenever forward search has identified an unrecognized dead end s where h c s we analyze the situation at s and add new conjunctions into c in a way guaranteeing to obtain h c s thus we learn to recognize s as well as similar dead ends search may encounter in the future we furthermore learn clauses where s implies h c s to avoid the overhead of computing h c on every search state arranging these techniques in a depth first search we obtain an algorithm approaching the elegance of nogood learning in constraint satisfaction learning to refute search subtrees we run comprehensive experiments on solvable and unsolvable planning benchmarks in cases where forward search can identify dead ends and where h c dead end detection is effective our techniques reduce the depth first search space size by several orders of magnitude and often result in state of the art performance

task decomposition on abstract states for planning under nondeterminism although several approaches have been developed for planning in nondeterministic domains solving large planning problems is still quite difficult in this work we present a new planning algorithm called yoyo for solving planning problems in fully observable nondeterministic domains yoyo combines an htn based mechanism for constraining its search and a binary decision diagram bdd representation for reasoning about sets of states and state transitions we provide correctness theorems for yoyo and an experimental comparison of it with mbp and nd shop2 the two previously best algorithms for planning in nondeterministic domains in our experiments yoyo could easily deal with problem sizes that neither mbp nor nd shop2 could scale up to and could solve problems about 100 to 1000 times faster than mbp and nd shop2

classification of parameter dependent quantum integrable models their parameterization exact solution and other properties we study general quantum integrable hamiltonians linear in a coupling constant and represented by finite n n real symmetric matrices the restriction on the coupling dependence leads to a natural notion of nontrivial integrals of motion and classification of integrable families into types according to the number of such integrals a type m family in our definition is formed by n m nontrivial mutually commuting operators linear in the coupling working from this definition alone we parameterize type m operators i e resolve the commutation relations and obtain an exact solution for their eigenvalues and eigenvectors we show that our parameterization covers all type 1 2 and 3 integrable models and discuss the extent to which it is complete for other types we also present robust numerical observation on the number of energy level crossings in type m integrable systems and analyze the taxonomy of types in the 1d hubbard model

a convex matrix optimization for the additive constant problem in multidimensional scaling with application to locally linear embedding the additive constant problem has a long history in multidimensional scaling and it has recently been used to resolve the issue of indefiniteness of the geodesic distance matrix in isomap but it would lead to a large positive constant being added to all eigenvalues of the centered geodesic distance matrix often causing significant distortion of the original distances in this paper we reformulate the problem as a convex optimization of almost negative semidefinite matrix so as to achieve minimal variation of the original distances we then develop a newton cg method and further prove its quadratic convergence finally we include a novel application to the famous lle locally linear embedding in nonlinear dimensionality reduction addressing the issue when the input of lle has missing values we justify the use of the developed method to tackle this issue by establishing that the local gram matrix used in lle can be obtained through a local euclidean distance matrix the effectiveness of our method is

a newton cg augmented lagrangian method for semidefinite programming we consider a newton cg augmented lagrangian method for solving semidefinite programming sdp problems from the perspective of approximate semismooth newton methods in order to analyze the rate of convergence of our proposed method we characterize the lipschitz continuity of the corresponding solution mapping at the origin for the inner problems we show that the positive definiteness of the generalized hessian of the objective function in these inner problems a key property for ensuring the efficiency of using an inexact semismooth newton cg method to solve the inner problems is equivalent to the constraint nondegeneracy of the corresponding dual problems numerical experiments on a variety of large scale sdp problems with the matrix dimension n up to 4 110 and the number of equality constraints m up to 2 156 544 show that the proposed method is very efficient we are also able to solve the sdp problem fap36 with n 4 110 and m 1 154 467 in the seventh dimacs implementation challenge much more accurately than in previous attempts

strong planning under partial observability rarely planning domains are fully observable for this reason the ability to deal with partial observability is one of the most important challenges in planning in this paper we tackle the problem of strong planning under partial observability in nondeterministic domains find a conditional plan that will result in a successful state regardless of multiple initial states nondeterministic action effects and partial observability we make the following contributions first we formally define the problem of strong planning within a general framework for modeling partially observable planning domains second we propose an effective planning algorithm based on and or search in the space of beliefs we prove that our algorithm always terminates and is correct and complete in order to achieve additional effectiveness we leverage on a symbolic bdd based representation for the domain and propose several search strategies we provide a thorough experimental evaluation of our approach based on a wide selection of benchmarks we compare the performance of the proposed search strategies and identify a uniform winner that combines heuristic distance measures with mechanisms that reduce runtime uncertainty then we compare our planner mbp with other state of the art systems mbp is able to outperform its competitor systems often by orders of magnitude

da 2 merging operators a new framework for propositional merging is presented da2 merging operators parameterized by a distance between interpretations and two aggregation functions are introduced many distances and aggregation functions can be used and many merging operators already defined in the literature including both model based ones and syntax based ones can be encoded as specific da2 operators both logical and complexity properties of those operators are studied an important result is that under very weak assumptions query entailment from merged bases is only at the first level of the polynomial hierarchy when any of the da2 operators is used as a by product complexity results for several existing merging operators are derived as well

integrable time dependent quantum hamiltonians we formulate a set of conditions under which the nonstationary schr odinger equation with a time dependent hamiltonian is exactly solvable analytically the main requirement is the existence of a non abelian gauge field with zero curvature in the space of system parameters known solvable multistate landau zener models satisfy these conditions our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability we also validate some prior conjectures including the solution of the driven generalized tavis cummings model

state variable planning under structural restrictions algorithms and complexity abstract computationally tractable planning problems reported in the literature so far have almost exclusively been defined by syntactical restrictions to better exploit the inherent structure in problems it is probably necessary to study also structural restrictions on the underlying state transition graph the exponential size of this graph though makes such restrictions costly to test hence we propose an intermediate approach using a state variable model for planning and defining restrictions on the separate state transition graphs for each state variable we identify such restrictions which can tractably be tested and we present a planning algorithm which is correct and runs in polynomial time under these restrictions the algorithm has been implemented and it outperforms graphplan on a number of test instances in addition we present an exhaustive map of the complexity results for planning under all combinations of four previously studied syntactical restrictions and our five new structural restrictions this complexity map considers both the optimal and non optimal plan generation problem

on the complexity of planning for agent teams and its implications for single agent planning if the complexity of planning for a single agent is described by some function f of the input how much more difficult is it to plan for a team of n cooperating agents if these agents are completely independent we can simply solve n single agent problems scaling linearly with the number of agents but if all the agents interact tightly we really need to solve a single problem that is n times larger which could be exponentially in n harder to solve is a more general characterization possible to formulate this question precisely we minimally extend the standard strips model to describe multi agent planning problems then we identify two problem parameters that help us answer our question the first parameter is independent of the precise task the multi agent system should plan for and it captures the structure of the possible direct interactions between the agents via the tree width of a graph induced by the team the second parameter is task dependent and it captures the minimal number of interactions by the most interacting agent in the team that is needed to solve the problem we show that multi agent planning problems can be solved in time exponential only in these parameters thus when these parameters are bounded the complexity scales only polynomially in the size of the agent team these results also have direct implications for the single agent case by casting single agent planning tasks as multi agent planning tasks we can devise novel methods for decomposition based planning for single agents we analyze one such method and use the techniques developed to provide some of the strongest tractability results for classical single agent planning to date

red black planning to date delete relaxation underlies some of the most effective heuristics for deterministic planning despite its success however delete relaxation has significant pitfalls in many important classes of planning domains and it has been a challenge from the outset to devise heuristics that take some deletes into account we herein devise an elegant and simple method for doing just that in the context of finite domain state variables we define red variables to take the relaxed semantics in which they accumulate their values rather than switching between them as opposed to black variables that take the regular semantics red black planning then interpolates between relaxed planning and regular planning simply by allowing a subset of variables to be painted red we investigate the tractability region of red black planning extending chen and gimenez characterization theorems for regular planning to the more general red black setting in particular we identify significant islands of tractable red black planning use them to design practical heuristic functions and experiment with a range of painting strategies for automatically choosing the red variables our experiments show that these new heuristic functions can improve significantly on the state of the art in satisficing planning 1

a generalized newton method for absolute value equations associated with second order cones in this paper we introduce the absolute value equations associated with second order cones socave in short which is a generalization of the absolute value equations discussed recently in the literature it is proved that the socave is equivalent to a class of second order cone linear complementarity problems soclcp in short in particular we propose a generalized newton method for solving the socave and show that the proposed method is globally linearly and locally quadratically convergent under suitable assumptions we also report some preliminary numerical results of the proposed method for solving the socave and the soclcp which show the efficiency of the proposed method

discovering hidden structure in factored mdps markov decision processes mdps describe a wide variety of planning scenarios ranging from military operations planning to controlling a mars rover however email protected s solution techniques scale poorly limiting email protected practical applicability in this work we propose algorithms that automatically discover and exploit the hidden structure of factored mdps doing so helps solve mdps faster and with less memory than state of the art techniques our algorithms discover two complementary state abstractions basis functions and nogoods a basis function is a conjunction of literals if the conjunction holds true in a state this guarantees the existence of at least one trajectory to the goal conversely a nogood is a conjunction whose presence implies the non existence of any such trajectory meaning the state is a dead end we compute basis functions by regressing goal descriptions through a determinized version of the mdp nogoods are constructed with a novel machine learning algorithm that uses basis functions as training data our state abstractions can be leveraged in several ways we describe three diverse approaches goth a heuristic function for use in heuristic search algorithms such as rtdp retrase an mdp solver that performs modified bellman backups on basis functions instead of states and sixthsense a method to quickly detect dead end states in essence our work integrates ideas from deterministic planning and basis function based approximation leading to methods that outperform existing approaches by a wide margin

semismoothness and decomposition of maximal normal operators abstract a function is semismooth if and only if its subdifferential is semicontinuous all the semicontinuous operators form a big linear subspace of the maximal normal operator space by big we mean that this subspace includes all the continuous operators and all the maximal monotone operators all the decomposable maximal normal operators form another big subspace

finite termination of a newton type algorithm for a class of affine variational inequality problems abstract many optimization problems can be reformulated as a system of equations one may use the generalized newton method or the smoothing newton method to solve the reformulated equations so that a solution of the original problem can be found such methods have been powerful tools to solve many optimization problems in the literature in this paper we propose a newton type algorithm for solving a class of monotone affine variational inequality problems avips for short in the proposed algorithm the techniques based on both the generalized newton method and the smoothing newton method are used in particular we show that the algorithm can find an exact solution of the avip in a finite number of iterations under an assumption that the solution set of the avip is nonempty preliminary numerical results are reported

planning for conjunctive goals abstract the problem of achieving conjunctive goals has been central to domain independent planning research the nonlinear constraint posting approach has been most successful previous planners of this type have been complicated heuristic and ill defined i have combined and distilled the state of the art into a simple precise implemented algorithm tweak which i have proved correct and complete i analyze previous work on domain independent conjunctive planning in retrospect it becomes clear that all conjunctive planners linear and nonlinear work the same way the efficiency and correctness of these planners depends on the traditional add delete list representation for actions which drastically limits their usefulness i present theorems that suggest that efficient general purpose planning with more expressive action representations is impossible and suggest ways to avoid this problem

the link between integrability level crossings and exact solution in quantum models we investigate the connection between energy level crossings in integrable systems and their integrability i e the existence of a set of non trivial integrals of motion in particular we consider a general quantum hamiltonian linear in the coupling u h u t uv and require that it has the maximum possible number of nontrivial commuting partners also linear in u we demonstrate how this commutation requirement alone leads to 1 an exact solution for the energy spectrum and 2 level crossings which are always present in these hamiltonians in violation of the wigner von neumann non crossing rule moreover we construct these hamiltonians explicitly by resolving the above commutation requirement and show their equivalence to a sector of gaudin magnets central spin hamiltonians in contrast fewer than the maximum number of conservation laws does not guarantee level crossings

complexity of finite horizon markov decision process problems controlled stochastic systems occur in science engineering manufacturing social sciences and many other cntexts if the systems is modeled as a markov decision process mdp and will run ad infinitum the optimal control policy can be computed in polynomial time using linear programming the problems considered here assume that the time that the process will run is finite and based on the size of the input there are mny factors that compound the complexity of computing the optimal policy for instance there are many factors that compound the complexity of this computation for instance if the controller does not have complete information about the state of the system or if the system is represented in some very succint manner the optimal policy is provably not computable in time polynomial in the size of the input we analyze the computational complexity of evaluating policies and of determining whether a sufficiently good policy exists for a mdp based on a number of confounding factors including the observability of the system state the succinctness of the representation the type of policy even the number of actions relative to the number of states in almost every case we show that the decision problem is complete for some known complexity class some of these results are familiar from work by papadimitriou and tsitsiklis and others but some such as our pl completeness proofs are surprising we include proofs of completeness for natural problems in the as yet little studied classes np pp

affine scaling interior levenberg marquardt method for bound constrained semismooth equations under local error bound conditions we develop and analyze a new affine scaling levenberg marquardt method with nonmonotonic interior backtracking line search technique for solving bound constrained semismooth equations under local error bound conditions the affine scaling levenberg marquardt equation is based on a minimization of the squared euclidean norm of linear model adding a quadratic affine scaling matrix to find a solution that belongs to the bounded constraints on variable the global convergence results are developed in a very general setting of computing trial directions by a semismooth levenberg marquardt method where a backtracking line search technique projects trial steps onto the feasible interior set we establish that close to the solution set the affine scaling interior levenberg marquardt algorithm is shown to converge locally q superlinearly depending on the quality of the semismooth and levenberg marquardt parameter under an error bound assumption that is much weaker than the standard nonsingularity condition that is bd regular condition under nonsmooth case a nonmonotonic criterion should bring about speed up the convergence progress in the contours of objective function with large curvature

contingent planning under uncertainty via stochastic satisfiability we describe a new planning technique that efficiently solves probabilistic propositional contingent planning problems by converting them into instances of stochastic satisfiability ssat and solving these problems instead we make fundamental contributions in two areas the solution of ssat problems and the solution of stochastic planning problems this is the first work extending the planning as satisfiability paradigm to stochastic domains our planner zander can solve arbitrary goal oriented finite horizon partially observable markov decision processes pomdps an empirical study comparing zander to seven other leading planners shows that its performance is competitive on a range of problems

on the convergence of modified newton methods for solving equations containing a non differentiable term we provide a semilocal convergence analysis for certain modified newton methods for solving equations containing a non differentiable term the sufficient convergence conditions of the corresponding newton methods are often taken as the sufficient conditions for the modified newton methods that is why the latter methods are not usually treated separately from the former however here we show that weaker conditions as well as a finer error analysis than before can be obtained for the convergence of modified newton methods numerical examples are also provided

semismooth matrix valued functions matrix valued functions play an important role in the development of algorithms for semidefinite programming problems this paper studies generalized differential properties of such functions related to nonsmooth smoothing newton methods the first part of this paper discusses basic properties such as the generalized derivative rademacher s theorem b derivative directional derivative and semismoothness the second part shows that the matrix absolute value function the matrix semidefinite projection function and the matrix projective residual function are strongly semismooth

the quest for solvable multistate landau zener models recently integrability conditions ics in mutistate landau zener mlz theory were proposed 1 they describe common properties of all known solved systems with linearly time dependent hamiltonians here we show that ics enable efficient computer assisted search for new solvable mlz models that span complexity range from several interacting states to mesoscopic systems with many body dynamics and combinatorially large phase space this diversity suggests that nontrivial solvable mlz models are numerous in addition we refine the formulation of ics and extend the class of solvable systems to models with points of multiple diabatic level crossing

computing the nearest euclidean distance matrix with low embedding dimensions euclidean distance embedding appears in many high profile applications including wireless sensor network localization where not all pairwise distances among sensors are known or accurate the classical multi dimensional scaling cmds generally works well when the partial or contaminated euclidean distance matrix edm is close to the true edm but otherwise performs poorly a natural step preceding cmds would be to calculate the nearest edm to the known matrix a crucial condition on the desired nearest edm is for it to have a low embedding dimension and this makes the problem nonconvex there exists a large body of publications that deal with this problem some try to solve the problem directly and some are the type of convex relaxations of it in this paper we propose a numerical method that aims to solve this problem directly our method is strongly motivated by the majorized penalty method of gao and sun for low rank positive semi definite matrix optimization problems the basic geometric object in our study is the set of edms having a low embedding dimension we establish a zero duality gap result between the problem and its lagrangian dual problem which also motivates the majorization approach adopted numerical results show that the method works well for the euclidean embedding of network coordinate systems and for a class of problems in large scale sensor network localization and molecular conformation

towards efficient universal planning a randomized approach one of the most widespread approaches to reactive planning is schoppers universal plans we propose a stricter definition of universal plans which guarantees a weak notion of soundness not present in the original definition and isolate three different types of completeness that capture different behaviors exhibited by universal plans we show that universal plans which run in polynomial time and are of polynomial size cannot satisfy even the weakest type of completeness unless the polynomial hierarchy collapses by relaxing either the polynomial time or the polynomial space requirement the construction of universal plans satisfying the strongest type of completeness becomes trivial as an alternative approach we study randomized universal planning by considering a randomized version of completeness and a restricted but nontrivial class of problems we show that there exists randomized universal plans running in polynomial time and using polynomial space which are sound and complete for the restricted class of problems we also report experimental results on this approach to planning showing that the performance of a randomized planner is not easily compared to that of a deterministic planner

analysis of nonsmooth symmetric matrix valued functions with applications to semidefinite complementarity problems for any function f from mathbb r to mathbb r one can define a corresponding function on the space of n n block diagonal real symmetric matrices by applying f to the eigenvalues of the spectral decomposition we show that this matrix valued function inherits from f the properties of continuity local lipschitz continuity directional differentiability frechet differentiability continuous differentiability as well as rho order semismoothness our analysis uses results from nonsmooth analysis as well as perturbation theory for the spectral decomposition of symmetric matrices we also apply our results to the semidefinite complementarity problem addressing some basic issues in the analysis of smoothing semismooth newton methods for solving this problem

weak strong and strong cyclic planning via symbolic model checking planning in nondeterministic domains yields both conceptual and practical difficulties from the conceptual point of view different notions of planning problems can be devised for instance a plan might either guarantee goal achievement or just have some chances of success from the practical point of view the problem is to devise algorithms that can effectively deal with large state spaces in this paper we tackle planning in nondeterministic domains by addressing conceptual and practical problems we formally characterize different planning problems where solutions have a chance of success weak planning are guaranteed to achieve the goal strong planning or achieve the goal with iterative trial and error strategies strong cyclic planning in strong cyclic planning all the executions associated with the solution plan always have a possibility of terminating and when they do they are guaranteed to achieve the goal we present planning algorithms for these problem classes and prove that they are correct and complete we implement the algorithms in the mbp planner by using symbolic model checking techniques we show that our approach is practical with an extensive experimental evaluation mbp compares positively with state of the art planners both in terms of expressiveness and in terms of performance

constraint nondegeneracy strong regularity and nonsingularity in semidefinite programming it is known that the karush kuhn tucker kkt conditions of semidefinite programming can be reformulated as a nonsmooth system via the metric projector over the cone of symmetric and positive semidefinite matrices we show in this paper that the primal and dual constraint nondegeneracies the strong regularity the nonsingularity of the b subdifferential of this nonsmooth system and the nonsingularity of the corresponding clarke s generalized jacobian at a kkt point are all equivalent moreover we prove the equivalence between each of these conditions and the nonsingularity of clarke s generalized jacobian of the smoothed counterpart of this nonsmooth system used in several globally convergent smoothing newton methods in particular we establish the quadratic convergence of these methods under the primal and dual constraint nondegeneracies but without the strict complementarity

the computational complexity of propositional strips planning abstract i present several computational complexity results for propositional strips planning i e strips planning restricted to ground formulas different planning problems can be defined by restricting the type of formulas placing limits on the number of pre and postconditions by restricting negation in pre and postconditions and by requiring optimal plans for these types of restrictions i show when planning is tractable polynomial and intractable np hard in general it is pspace complete to determine if a given planning instance has any solutions extremely severe restrictions on both the operators and the formulas are required to guarantee polynomial time or even np completeness for example when only ground literals are permitted determining plan existence is pspace complete even if operators are limited to two preconditions and two postconditions when definite horn ground formulas are permitted determining plan existence is pspace complete even if operators are limited to zero preconditions and one postcondition one of the interesting tractable problems is if each operator is restricted to positive preconditions and one postcondition only ground literals the blocks world problem slightly modified is a subproblem of this restricted planning problem these results in combination with previous analyses are not encouraging for domain independent planning

on the computational complexity of temporal projection planning and plan validation abstract one kind of temporal reasoning is temporal projection the computation of the consequences of a set of events this problem is related to a number of other temporal reasoning tasks such as plan validation and planning we show that one particular simple case of temporal projection on partially ordered events turns out to be harder than previously conjectured while planning is easy under the same restrictions additionally we show that plan validation is tractable for an even larger class of plans the unconditional plans for which temporal projection is np hard thus indicating that temporal projection may not be a necessary ingredient in planning and plan validation analyzing the partial decision procedure for the temporal projection problem that has been proposed by other authors we notice that it fails to be complete for unconditional plans a case where we have shown plan validation tractable

weak directional closedness and generalized subdifferentials abstract spingarn introduced the notion of a submonotone operator and showed that the clarke subdifferential is submonotone if and only if it is semismooth in the sense of mifflin and regular in the sense of clarke in this article a property of operators referred to as weak directional closedness wdc is introduced the wdc property is used to extend spingarn s result to a broad class of generalized subdifferentials for locally lipschitz functions two members of this class of subdifferentials are the clarke subdifferential which is always wdc and the michel penot subdifferential which may or may not be wdc a subdifferential that is wdc and is contained in the clarke subdifferential is constructed it is shown that this subdifferential coincides with the michel penot subdifferential whenever the michel penot subdifferential is wdc and submonotone

the influence of k dependence on the complexity of planning a planning problem is k dependent if each action has at most k pre conditions on variables unaffected by the action this concept is of interest because k is a constant for all but a few of the current benchmark domains in planning and is known to have implications for tractability in this paper we present an algorithm for solving planning problems in p k the class of k dependent planning problems with binary variables and polytree causal graphs we prove that our algorithm runs in polynomial time when k is a fixed constant if in addition the causal graph has bounded depth we show that plan generation is linear in the size of the input although these contributions are theoretical due to the limited scope of the class p k suitable reductions from more complex planning problems to p k could potentially give rise to fast domain independent heuristics

conformant planning via symbolic model checking and heuristic search in this paper we tackle the problem of conformant planning find a sequence of actions that guarantees goal achievement regardless of an uncertain initial condition and of nondeterministic action effects our approach set in the framework of search in the belief space is based on two main intuitions first symbolic model checking techniques binary decision diagrams in particular can be used to represent and expand the search space and to provide an efficient computational platform second driving the search solely with reachability information is not effective and the notion of knowledge has to be taken explicitly into account we make the following contributions first we thoroughly analyze reachability heuristics we formally prove their admissibility we show how they can be implemented by means of symbolic techniques and experimentally evaluate them second we analyze the limitations of reachability heuristics and propose more informed yet admissible heuristics based on a formal notion of knowledge third we present a practical conformant planning algorithm where the search is explicitly based on the notion of target knowledge i e the amount of information that has to be available in order to reach the goal the search alternates between the acquire knowledge mode where actions have the precise purpose of gathering necessary information and the reach goal mode where actions are directed towards the goal finally we provide a thorough experimental comparison between several conformant planners our approach is sometimes able to outperform the competitor systems by orders of magnitude

kernel functions for case based planning case based planning can take advantage of former problem solving experiences by storing in a plan library previously generated plans that can be reused to solve similar planning problems in the future although comparative worst case complexity analyses of plan generation and reuse techniques reveal that it is not possible to achieve provable efficiency gain of reuse over generation we show that the case based planning approach can be an effective alternative to plan generation when similar reuse candidates can be chosen in this paper we describe an innovative case based planning system called oakplan which can efficiently retrieve planning cases from plan libraries containing more than ten thousand cases choose heuristically a suitable candidate and adapt it to provide a good quality solution plan which is similar to the one retrieved from the case library given a planning problem we encode it as a compact graph structure that we call planning encoding graph which gives us a detailed description of the topology of the planning problem by using this graph representation we examine an approximate retrieval procedure based on kernel functions that effectively match planning instances achieving extremely good performance in standard benchmark domains the experimental results point out the effect of the case base size and the importance of accurate matching functions for global system performance overall we show that oakplan is competitive with state of the art plan generation systems in terms of number of problems solved cpu time plan difference values and plan quality when cases similar to the current planning problem are available in the plan library

a regularization semismooth newton method based on the generalized fischer burmeister function for p0 ncps we consider a regularization method for nonlinear complementarity problems with f being a p 0 function which replaces the original problem with a sequence of the regularized complementarity problems in this paper this sequence of regularized complementarity problems are solved approximately by applying the generalized newton method for an equivalent augmented system of equations constructed by the generalized fischer burmeister fb ncp functions f p with p 1 we test the performance of the regularization semismooth newton method based on the family of ncp functions through solving all test problems from mcplib numerical experiments indicate that the method associated with a smaller p for example email protected 1 1 2 usually has better numerical performance and the generalized fb functions f p with email protected 1 1 2 can be used as the substitutions for the fb function f 2

conformant planning via heuristic forward search a new approach conformant planning is the task of generating plans given uncertainty about the initial state and action effects and without any sensing capabilities during plan execution the plan should be successful regardless of which particular initial world we start from it is well known that conformant planning can be transformed into a search problem in belief space the space whose elements are sets of possible worlds we introduce a new representation of that search space replacing the need to store sets of possible worlds with a need to reason about the effects of action sequences the reasoning is done by implication tests on propositional formulas in conjunctive normal form cnf that capture the action sequence semantics based on this approach we extend the classical heuristic forward search planning system ff to the conformant setting the key to this extension is an appropriate extension of the relaxation that underlies ff s heuristic function and of ff s machinery for solving relaxed planning problems the extended machinery includes a stronger form of the cnf implication tests that we use to reason about the effects of action sequences our experimental evaluation shows the resulting planning system to be superior to the state of the art conformant planners mbp kacmbp and gpt in a variety of benchmark domains

quantum integrability in the multistate landau zener problem we analyze hamiltonians linear in the time variable for which the multistate landau zener lz problem is known to have an exact solution we show that they either belong to families of mutually commuting hamiltonians polynomial in time or reduce to the lz problem which is considered trivially integrable the former category includes the equal slope bow tie and generalized bow tie models for each of these models we explicitly construct the corresponding families of commuting matrices the equal slope model is a member of an integrable family that consists of the maximum possible number for a given matrix size of commuting matrices linear in time the bow tie model belongs to a previously unknown similarly maximal family of quadratic commuting matrices we thus conjecture that quantum integrability understood as the existence of nontrivial parameter dependent commuting partners is a necessary condition for the lz solvability descendants of the lz hamiltonian are e g general su 2 and hamiltonians time dependent linear chain linear nonlinear and double oscillators we explicitly obtain solutions to all these lz problems from the case

the analytical solution of the additive constant problem ifd is a measure of dissimilarity on a finite set withn elements the smallest positive constantc such thatd c has an euclidean representation for allc c is shown to be the largest eigen value of a matrix of size 2n

representing action indeterminacy and ramifications abstract we define and study a high level language for describing actions more expressive than the action language a introduced by gelfond and lifschitz the new language ar allows us to describe actions with indirect effects ramifications nondeterministic actions and actions that may be impossible to execute it has symbols for nonpropositional fluents and for the fluents that are exempt from the commonsense law of inertia temporal projection problems specified using the language ar can be represented as nested abnormality theories based on the situation calculus

optimal admissible composition of abstraction heuristics additive ensembles of admissible heuristics constitute the most general form of exploiting the individual strengths of numerous admissible heuristics in optimal planning however the same set of heuristics can be additively composed in infinitely many ways and the quality of the resulting heuristic estimate depends directly on the choice of the composition focusing on abstraction heuristics we describe a procedure that takes a deterministic planning problem a forward search state and a set of abstraction based admissible heuristics and derives an optimal additive composition of these heuristics with respect to the given state most importantly we show that this procedure is polynomial time for arbitrary sets of all abstraction heuristics with which we are acquainted including explicit abstractions such as pattern databases regular or constrained and merge and shrink and implicit abstractions such as fork decomposition and abstractions based on tractable constraint optimization over tree shaped constraint networks

computational complexity of planning and approximate planning in the presence of incompleteness abstract in the last several years there have been several studies about the computational complexity of classical planning assuming that the planner has complete knowledge about the initial situation recently there have been proposals to use sensing actions to plan in the presence of incompleteness in this paper we study the complexity of planning in such cases in our study we use the action description language a proposed in 1991 by gelfond and lifschitz and its extensions it is known that if we consider only plans of tractable polynomial duration planning in a with complete information about the initial situation is np complete even checking whether a given objective is attainable from a given initial state is np complete in this paper we show that the planning problem in the presence of incompleteness is indeed harder it belongs to the next level of the complexity hierarchy in precise terms it is 2 p complete to overcome the complexity of this problem baral and son have proposed several approximations we show that under certain conditions one of these approximations 0 approximation makes the problem np complete thus indeed reducing its complexity

solution dependence on initial conditions in differential variational inequalities in the first part of this paper we establish several sensitivity results of the solution x t to the ordinary differential equation ode initial value problem ivp dx dt f x x 0 as a function of the initial value for a nondifferentiable f x specifically we show that for xi t equiv x t xi 0 0 leq t leq t a if f is b differentiable on xi t then so is the solution operator x t at 0 b if f is semismooth on xi t then so is x t at 0 c if f has a linear newton approximation on xi t then so does x t at 0 moreover the linear newton approximation of the solution operator can be obtained from the solution of a linear differential inclusion in the second part of the paper we apply these ode sensitivity results to a differential variational inequality dvi and discuss a the existence uniqueness and lipschitz dependence of solutions to subclasses of the dvi subject to boundary conditions via an implicit function theorem for semismooth equations and b the convergence of a nonsmooth shooting method for numerically computing such boundary value solutions

conformant plans and beyond principles and complexity conformant planning is used to refer to planning for unobservable problems whose solutions like classical planning are linear sequences of operators called linear plans the term conformant is automatically associated with both the unobservable planning model and with linear plans mainly because the only possible solutions for unobservable problems are linear plans in this paper we show that linear plans are not only meaningful for unobservable problems but also for partially observable problems in such case the execution of a linear plan generates observations from the environment which must be collected by the agent during the execution of the plan and used at the end in order to determine whether the goal had been achieved or not this is the typical case in problems of diagnosis in which all the actions are knowledge gathering actions thus there are substantial differences about linear plans for the case of unobservable or fully observable problems and for the case of partially observable problems while linear plans for the former model must conform with properties in state space linear plans for partially observable problems must conform with properties in belief space this differences surface when the problems are allowed to express epistemic goals and conditions using modal logic and place the plan existence decision problem in different complexity classes linear plans is one extreme point in a discrete spectrum of solution forms for planning problems the other extreme point is contingent plans in which there is a branch point for every possible observation at each time step and thus the number of branch points is not bounded a priori in the middle of the spectrum there are plans with a bounded number of branch points thus linear plans are plans with zero branch points and contingent plans are plans with unbounded number of branch points in this work we lay down foundations and principles for the general treatment of linear plans and plans of bounded branching and provide exact complexity results for novel decision problems we also show that linear plans for partially observable problems are not only of theoretical interest since some challenging real life problems can be dealt with them

quasi newton trust region algorithm for non smooth least squares problems1this work was supported by cnpq of brazil and the national natural science foundation of china 1 in this paper we present a quasi newton trust region algorithm for non smooth least squares problems which possess the smooth plus non smooth decomposition this method uses a smooth subproblem with second order information to approximate the locally lipschitzian function which is important to increase the convergence rate of the algorithm and deal with the large residual non smooth least squares problems the global and superlinear convergence of this algorithm are established

applicability conditions for plans with loops computability results and algorithms the utility of including loops in plans has been long recognized by the planning community loops in a plan help increase both its applicability and the compactness of its representation however progress in finding such plans has been limited largely due to lack of methods for reasoning about the correctness and safety properties of loops of actions we present novel algorithms for determining the applicability and progress made by a general class of loops of actions these methods can be used for directing the search for plans with loops towards greater applicability while guaranteeing termination as well as in post processing of computed plans to precisely characterize their applicability experimental results demonstrate the efficiency of these algorithms we also discuss the factors which can make the problem of determining applicability conditions for plans with loops incomputable

heuristics for planning with penalties and rewards formulated in logic and computed through circuits the automatic derivation of heuristic functions for guiding the search for plans is a fundamental technique in planning the type of heuristics that have been considered so far however deal only with simple planning models where costs are associated with actions but not with states in this work we address this limitation by formulating a more expressive planning model and a corresponding heuristic where preferences in the form of penalties and rewards are associated with fluents as well the heuristic that is a generalization of the well known delete relaxation heuristic is admissible informative but intractable exploiting a correspondence between heuristics and preferred models and a property of formulas compiled in d dnnf we show however that if a suitable relaxation of the domain expressed as the strong completion of a logic program with no time indices or horizon is compiled into d dnnf the heuristic can be computed for any search state in time that is linear in the size of the compiled representation this representation defines an evaluation network or circuit that maps states into heuristic values in linear time while this circuit may have exponential size in the worst case as for obdds this is not necessarily so we report empirical results discuss the application of the framework in settings where there are no goals but just preferences and illustrate the versatility of the account by developing a new heuristic that overcomes limitations of delete based relaxations through the use of valid but implicit plan constraints in particular for the traveling salesman problem the new heuristic captures the exact cost while the delete relaxation heuristic which is also exponential in the worst case captures only the minimum spanning tree lower bound

the complexity of achievement and maintenance problems in agent based systems we completely classify the computational complexity of the basic achievement and maintenance agent design problems in bounded environments when these problems are parameterized by the number of environment states and the number of agent actions the different problems are p complete np complete co np complete or pspace complete when they are not trivial we also consider alternative achievement and maintenance agent design problems by allowing longer runs in environments that is our environments are bounded but the bounds are more liberal than was the case previously again we obtain a complete classification but so that the different problems are dexptime complete nexptime complete co nexptime complete or nexpspace complete when they are not trivial

off shell bethe ansatz equations and n point correlators in the su 2 wznw theory we prove that the wavevectors of the off shell bethe ansatz equation for the inhomogeneous su 2 lattice vertex model render in the quasiclassical limit the solutions of the knizhnik zamolodchikov equation

reasoning about partially ordered events abstract this paper describes a class of temporal reasoning problems involving events whose order is not completely known we examine the complexity of such problems and show that for all but trivial cases these problems are likely to be intractable as an alternative to a complete but potentially exponential time decision procedure we provide a partial decision procedure that reports useful results and runs in polynomial time

integrated common sense learning and planning in pomdps we formulate a new variant of the problem of planning in an unknown environment for which we can provide algorithms with reasonable theoretical guarantees in spite of large state spaces and time horizons partial observability and complex dynamics in this variant an agent is given a collection of example traces produced by a reference policy which may for example capture the agent s past behavior the agent is only asked to find policies that are supported by regularities in the dynamics that are observable on these example traces we describe an efficient algorithm that uses such common sense knowledge reflected in the example traces to construct decision tree policies for goal oriented factored pomdps more precisely our algorithm provably succeeds at finding policy for a given input goal when 1 there is a cnf that is almost always observed satisfied on the traces of the pomdp capturing a sufficient approximation of its dynamics and 2 for a decision tree policy of bounded complexity there exist small space resolution proofs that the goal is achieved on each branch using the aforementioned cnf capturing the common sense rules such a cnf always exists for noisy strips domains for example our results thus essentially establish that the possession of a suitable exploration policy for collecting the necessary examples is the fundamental obstacle to learning to act in such environments

state set branching leveraging bdds for heuristic search in this article we present a framework called state set branching that combines symbolic search based on reduced ordered binary decision diagrams bdds with best first search such as a and greedy best first search the framework relies on an extension of these algorithms from expanding a single state in each iteration to expanding a set of states we prove that it is generally sound and optimal for two a implementations and show how a new bdd technique called branching partitioning can be used to efficiently expand sets of states the framework is general it applies to any heuristic function evaluation function and transition cost function defined over a finite domain moreover branching partitioning applies to both disjunctive and conjunctive transition relation partitioning an extensive experimental evaluation of the two a implementations proves state set branching to be a powerful framework the algorithms outperform the ordinary a algorithm in almost all domains in addition they can improve the complexity of a exponentially and often dominate both a and blind bdd based search by several orders of magnitude moreover they have substantially better performance than bdda the currently most efficient bdd based implementation of a

exact analytical solution of the n level landau zener type bow tie model the non stationary schrodinger equation in a finite basis of states is considered for the hamiltonian matrix linearly depending on time exact analytical solutions of asymptotic transition probabilities are obtained for a bow tie model in which an arbitrary number of linear time dependent diabatic potential curves cross at one point and only a particular horizontal curve has interactions with the others based on the contour integral method used some mathematical aspects such as a possible generalization of the whittaker functions are also briefly discussed

a probabilistic analysis of prepositional strips planning abstract i present a probabilistic analysis of prepositional strips planning the analysis considers two assumptions one is that each possible precondition likewise postcondition of an operator is selected independently of other pre and postconditions the other is that each operator has a fixed number of preconditions likewise postconditions under both assumptions i derive bounds for when it is highly likely that a planning instance can be efficiently solved either by finding a plan or proving that no plan exists roughly if planning instances under either assumption have n propositions ground atoms and g goals and the number of operators is less than an o n in g bound then a simple efficient algorithm can prove that no plan exists for most instances if the number of operators is greater than an n in g bound then a simple efficient algorithm can find a plan for most instances the two bounds differ by a factor that is exponential in the number of pre and postconditions a similar result holds for plan modification i e solving a planning instance that is close to another planning instance with a known plan thus it appears that prepositional strips planning a pspace complete problem exhibits a easy hard easy pattern as the number of available operators increases with a narrow range of hard problems an empirical study demonstrates this pattern for particular parameter values because prepositional strips planning is pspace complete this extends previous phase transition analyses which have focused on np complete problems also the analysis shows that surprisingly simple algorithms can solve a large subset of the planning problem

limitations of acyclic causal graphs for planning causal graphs are widely used in planning to capture the internal structure of planning instances researchers have paid special attention to the subclass of planning instances with acyclic causal graphs which in the past have been exploited to generate hierarchical plans to compute heuristics and to identify classes of planning instances that are easy to solve this naturally raises the question of whether planning is easier when the causal graph is acyclic in this article we show that the answer to this question is no proving that in the worst case the problem of plan existence is pspace complete even when the causal graph is acyclic since the variables of the planning instances in our reduction are propositional this result applies to strips planning with negative preconditions we show that the reduction still holds if we restrict actions to have at most two preconditions having established that planning is hard for acyclic causal graphs we study two subclasses of planning instances with acyclic causal graphs one such subclass is described by propositional variables that are either irreversible or symmetrically reversible another subclass is described by variables with strongly connected domain transition graphs in both cases plan existence is bounded away from pspace but in the latter case the problem of bounded plan existence is hard implying that optimal planning is significantly harder than satisficing planning for this class

on the undecidability of probabilistic planning and related stochastic optimization problems automated planning the problem of how an agent achieves a goal given a repertoire of actions is one of the foundational and most widely studied problems in the ai literature the original formulation of the problem makes strong assumptions regarding the agent s knowledge and control over the world namely that its information is complete and correct and that the results of its actions are deterministic and known recent research in planning under uncertainty has endeavored te relax these assumptions providing formal and computation models wherein the agent has incomplete or noisy information about the world and has noisy sensors and effectors this research has mainly taken one of two approaches extend the classical planning paradigm to a semantics that admits uncertainty or adopt another framework for approaching the problem most commonly the markov decision process mdp model this paper presents a complexity analysis of planning under uncertainty it begins with the probabilistic classical planning problem showing that problem to be formally undecidable this fundamental result is then applied to a broad class of stochastic optimization problems in brief any problem statement where the agent a operates over an infinite or indefinite time horizon and b has available only probabilistic information about the system s state undecidability is established for policy existence problems for partially observable infinite horizon markov decision processes under discounted and undiscounted total reward models average reward models and state avoidance models the results also apply to corresponding approximation problems with undiscounted objective functions the paper answers a significant open question raised by papadimitriou and tsitsiklis math oper res 12 3 1987 441 450 about the complexity of infinite horizon pomdps

understanding planning with incomplete information and sensing pks is the framework for planning with incomplete information and sensing recently introduced by bacchus and petrick proc kr 98 pp 432 443 the fact that pks generalizes strips to domains with incomplete information and sensing opens up the possibility of proposing it as a reference for comparisons with other formalisms that approach the problem from different perspectives to this end we first provide a formal semantics for pks then analyze and extend it the formal definition of the extended pks entails the identification of a number of properties of this planning framework in particular we prove that for any finite instance of the pks planning problem the reachable states are finite on the basis of this result we propose an improved planning algorithm that is not only sound as the one proposed by petrick and bacchus proc aips 02 pp 212 221 but also complete we extend pks to include conditional plans with cycles and introduce the distinction between different classes of solutions strong strong cyclic weak acyclic and weak cyclic in contrast with current belief we prove that some weak acyclic solutions are more likely to succeed for a limited execution than some strong cyclic solutions revealing the lack of a method for judging the quality of different solutions finally we introduce a quality measure for solutions of any class and a quantitative method for comparing them

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

the strong second order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications for a locally optimal solution to the nonlinear semidefinite programming problem under robinson s constraint qualification the following conditions are proved to be equivalent the strong second order sufficient condition and constraint nondegeneracy the nonsingularity of clarke s jacobian of the karush kuhn tucker system the strong regularity of the karush kuhn tucker point and others

s matrix for generalized landau zener problem the schrodinger equation i psi a bt psi with constant hermitian matrices a and b is studied in the form where b is diagonalized this equation is a generalization of the landau zener problem to an arbitrary number of crossing energy levels an approach the independent crossing approximation leading to a partial understanding of the general case in terms of the two level problem is introduced it is found that certain s matrix elements and thus the corresponding transition probabilities for the general problem are exactly given by formulae of unexpected simplicity suggesting that some kind of general analytic solution might exist the full s matrix is calculated for a solvable special case of the problem the solution of another special case previously discovered for systems with three states is generalized to any number of states the asymptotic behaviour of the system is discussed in general and given explicitly to lowest order in 1 t

a new non interior continuation method for solving the second order cone complementarity problem abstract in this paper based on a symmetrically perturbed smoothing fischer burmeister function a non interior continuation method is proposed for solving the second order cone complementarity problem soccp the proposed algorithm solves only one linear system of equations and performs only one line search at each iteration under monotonicity it is shown that our algorithm is globally and locally superlinearly convergent without requiring strict complementarity assumption at the soccp solution furthermore the proposed algorithm has local quadratic convergence under mild conditions some numerical results are reported which indicate the effectiveness of the proposed algorithm