bottom up tree pushdown automata classification and connection with rewrite systems we define different types of bottom up tree pushdown automata and study their connections with rewrite systems along this line of research we complete and generalize the results of gallier book and salomaa we define the notion of a tail reduction free trf rewrite system using the decidability of ground reducibility we prove the decidability of the trf property monadic rewrite systems of book gallier and salomaa become a natural particular case of trf rewrite systems we associate a deterministic bottom up tree pushdown automaton with any left linear trf rewrite system finally we generalize monadic rewrite systems by introducing the notion of a semi monadic rewrite system and show that like a monadic rewrite system it preserves recognizability

congruential complements of ground term rewrite systems abstract let a and b be ground term rewrite systems over some ranked alphabet with a b we say that a ground term rewrite system c over is a congruential complement of a for b if a c b and a c is the identity relation over t we show that given ground term rewrite systems a b c over some ranked alphabet with a b one can effectively decide if c is a congruential complement of a for b

linear generalized semi monadic rewrite systems effectively preserve recognizability abstract we introduce the notion of the generalized semi monadic rewrite system which is a generalization of well known rewrite systems the ground rewrite system the monadic rewrite system and the semi monadic rewrite system we show that linear generalized semi monadic rewrite systems effectively preserve recognizability we show that a tree language l is recognizable if and only if there exists a rewrite system r such that r r 1 is a linear generalized semi monadic rewrite system and that l is the union of finitely many r classes we show several decidability and undecidability results on rewrite systems effectively preserving recognizability and on generalized semi monadic rewrite systems for example we show that for a rewrite system r effectively preserving recognizability it is decidable if r is locally confluent moreover we show that preserving recognizability and effectively preserving recognizability are modular properties of linear collapse free rewrite systems finally as a consequence of our results on trees we get that restricted right left overlapping string rewrite systems effectively preserve recognizability

levels of undecidability in rewriting undecidability of various properties of first order term rewriting systems is well known an undecidable property can be classified by the complexity of the formula defining it this classification gives rise to a hierarchy of distinct levels of undecidability starting from the arithmetical hierarchy classifying properties using first order arithmetical formulas and continuing into the analytic hierarchy where quantification over function variables is allowed in this paper we give an overview of how the main properties of first order term rewriting systems are classified in these hierarchies we consider properties related to normalization strong normalization weak normalization and dependency problems and properties related to confluence confluence local confluence and the unique normal form property for all of these we distinguish between the single term version and the uniform version where appropriate we also distinguish between ground and open terms most uniform properties are p 2 0 complete the particular problem of local confluence turns out to be p 2 0 complete for ground terms but only p 2 0 complete and thereby recursively enumerable for open terms the most surprising result concerns dependency pair problems without minimality flag we prove this problem to be p 1 1 complete hence not in the arithmetical hierarchy but properly in the analytic hierarchy some of our results are new or have appeared in our earlier publications others are based on folklore constructions and are included for completeness as their precise classifications have hardly been noticed previously

a two phase method for selecting imrt treatment beam angles branch and prune and local neighborhood search this paper presents a new two phase solution approach to the beam angle and fluence map optimization problem in intensity modulated radiation therapy imrt planning we introduce branch and prune b p to generate a robust feasible solution in the first phase a local neighborhood search algorithm is developed to find a local optimal solution from the phase i starting point in the second phase the goal of the first phase is to generate a clinically acceptable feasible solution in a fast manner based on a branch and bound tree in this approach a substantially reduced search tree is iteratively constructed in each iteration a merit score based branching rule is used to select a pool of promising child nodes then pruning rules are applied to select one child node as the branching node for the next iteration the algorithm terminates when we obtain a desired number of angles in the current node although phase i generates quality feasible solutions it does not guarantee optimality therefore the second phase is designed to converge phase i starting solutions to local optimality our methods are tested on two sets of real patient data results show that not only can b p alone generate clinically acceptable solutions but the two phase method consistently generates local optimal solutions some of which are shown to be globally optimal

restricted ground tree transducers we consider restricted versions of ground tree transducers total deterministic and symmetric subclasses and all other subclasses created by applying any combination of these restrictions we present the inclusion diagram of the tree transformation classes induced by these restricted ground tree transducers we show that the following four classes of term relations are the same i tree transformations induced by symmetric deterministic ground tree transducers ii congruence relations on term algebras induced by reduced ground term rewriting systems iii congruence relations on term algebras induced by convergent ground term rewriting systems and iv finitely generated congruence relations on term algebras as a by product of our results we obtain a new ground completion algorithm moreover we show that the following three classes of term relations on term algebras with at least one non nullary function symbol are also the same i tree transformations induced by total symmetric deterministic ground tree transducers ii congruence relations on term algebras of finite index iii finitely generated congruence relations on term algebras of which the trunk is the whole set of terms

decidability of the confluence of finite ground term rewrite systems and of other related term rewrite systems abstract the aim of this paper is to propose an algorithm to decide the confluence of finite ground term rewrite systems actually a more general class of possibly infinite ground term rewrite systems is studied it is well known that the confluence is not decidable for general term rewrite systems but this paper proves it is for ground term rewrite systems following a conjecture made by huet and oppen in their survey the result is also applied to the confluence of left linear and right ground term rewrite systems we also sketch an algorithm for checking this property this algorithm is based on tree automata and tree transducers here we regard them as rewrite systems and specialists in automata theory would translate that easily in their language

the church rosser property for ground term rewriting systems is decidable abstract a term rewriting system is said to be a ground system if no variable occurs in any of its rewrite rules this paper shows that the church rosser property i e confluence problem for ground term rewriting systems is decidable this is an affirmative solution to this problem posed by huet and oppen 1980

term rewriting restricted to ground terms we study rewriting of ground terms for an arbitrary term rewrite system r over a ranked alphabet we restrict the rewriting relation r to ground terms we introduce the relation r g r t t we show that r g r t t we show that for a given term rewrite system r and a given ground term rewrite system s over a ranked alphabet it is decidable if r g s we show that for a given left linear right ground term rewrite system r over a ranked alphabet it is decidable if there is a ground term rewrite system s over such that r g s

stability conditions on k3 surfaces this article contains a description of one connected component of the space of stability conditions on the bounded derived category of coherent sheaves on a complex algebraic k3 surface

a gradient formula for linear chance constraints under gaussian distribution we provide an explicit gradient formula for linear chance constraints under a possibly singular multivariate gaussian distribution this formula allows one to reduce the calculus of gradients to the calculus of values of the same type of chance constraints in smaller dimension and with different distribution parameters this is an important aspect for the numerical solution of stochastic optimization problems because existing efficient codes for e g calculating singular gaussian distributions or regular gaussian probabilities of polyhedra can be employed to calculate gradients at the same time moreover the precision of gradients can be controlled by that of function values which is a great advantage over using finite difference approximations finally higher order derivatives are easily derived explicitly the use of the obtained formula is illustrated for an example of a transportation network with stochastic demands

decidable call by need computations in term rewriting the theorem of huet and levy stating that for orthogonal rewrite systems i every reducible term contains a needed redex and ii repeated contraction of needed redexes results in a normal form if the term under consideration has a normal form forms the basis of all results on optimal normalizing strategies for orthogonal rewrite systems however needed redexes are not computable in general in the paper we show how the use of approximations and elementary tree automata techniques allows one to obtain decidable conditions in a simple and elegant way surprisingly by avoiding complicated concepts like index and sequentiality we are able to cover much larger classes of rewrite systems we also study modularity aspects of the classes in our hierarchy it turns out that none of the classes is preserved under signature extension by imposing various conditions we recover the preservation under signature extension by imposing some more conditions we are able to strengthen the signature extension results to modularity for disjoint and constructor sharing combinations

probabilistically constrained linear programs and risk adjusted controller design the focal point of this paper is the probabilistically constrained linear program pclp and how it can be applied to control system design under risk constraints the pclp is the counterpart of the classical linear program where it is assumed that there is random uncertainty in the constraints and therefore the deterministic constraints are replaced by probabilistic ones it is shown that for a wide class of probability density functions called log concave symmetric densities the pclp is a convex program an equivalent formulation of the pclp is also presented which provides insight into numerical implementation this concept is applied to control system design it is shown how the results in this paper can be applied to the design of controllers for discrete time systems to obtain a closed loop system with a well defined risk of violating the so called property of superstability furthermore we address the problem of risk adjusted pole placement

derivation trees of ground term rewriting systems a notion of derivation tree is introduced for ground term rewriting systems using standard tree language theory new proofs are given for some old results

optimal inequalities in probability theory a convex optimization approach we propose a semidefinite optimization approach to the problem of deriving tight moment inequalities for p x in s for a set s defined by polynomial inequalities and a random vector x defined on omega subseteq cal r n that has a given collection of up to kth order moments in the univariate case we provide optimal bounds on p x in s when the first k moments of x are given as the solution of a semidefinite optimization problem in k 1 dimensions in the multivariate case if the sets s and omega are given by polynomial inequalities we obtain an improving sequence of bounds by solving semidefinite optimization problems of polynomial size in n for fixed k we characterize the complexity of the problem of deriving tight moment inequalities we show that it is np hard to find tight bounds for k geq 4 and omega cal r n and for k geq 2 and omega cal r n when the data in the problem is rational for k 1 and omega cal r n we show that we can find tight upper bounds by solving n convex optimization problems when the set s is convex and we provide a polynomial time algorithm when s and omega are unions of convex sets over which linear functions can be optimized efficiently for the case k 2 and omega cal r n we present an efficient algorithm for finding tight bounds when s is a union of convex sets over which convex quadratic functions can be optimized efficiently

convex approximations of chance constrained programs we consider a chance constrained problem where one seeks to minimize a convex objective over solutions satisfying with a given close to one probability a system of randomly perturbed convex constraints this problem may happen to be computationally intractable our goal is to build its computationally tractable approximation i e an efficiently solvable deterministic optimization program with the feasible set contained in the chance constrained problem we construct a general class of such convex conservative approximations of the corresponding chance constrained problem moreover under the assumptions that the constraints are affine in the perturbations and the entries in the perturbation vector are independent of each other random variables we build a large deviation type approximation referred to as bernstein approximation of the chance constrained problem this approximation is convex and efficiently solvable we propose a simulation based scheme for bounding the optimal value in the chance constrained problem and report numerical experiments aimed at comparing the bernstein and well known scenario approximation approaches finally we extend our construction to the case of ambiguous chance constrained problems where the random perturbations are independent with the collection of distributions known to belong to a given convex compact set rather than to be known exactly while the chance constraint should be satisfied for every distribution given by this set

a fast algorithm for constructing a tree automaton recognizing a congruential tree language abstract it is well known that congruential tree languages are the same as recognizable tree languages in this paper we construct in o n log n time for a given ground term equation system e and given ground trees p 1 p k a deterministic tree automaton a recognizing the congruential tree language p1 e pk e where n is the number of occurrences of symbols in e and p 1 p k

braid group actions on derived categories of coherent sheaves this paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety x the motivation for this is m kontsevich s homological mirror conjecture together with the occurrence of certain braid group actions in symplectic geometry one of the main results is that when dim x geq 2 our braid group actions are always faithful we describe conjectural mirror symmetries between smoothings and resolutions of singularities which lead us to find examples of braid group actions arising from crepant resolutions of various singularities relations with the mckay correspondence and with exceptional sheaves on fano manifolds are given moreover the case of an elliptic curve is worked out in some detail

a chance constrained programming framework to handle uncertainties in radiation therapy treatment planning abstract a stochastic programming framework is proposed for radiation therapy treatment planning this framework takes into account uncertainty in setting up or positioning patients identically day to day during the treatment period because uncertainties are unavoidable constraint violations are tolerated to some degree in practice under this assumption a chance constrained programming ccp framework is developed to handle setup uncertainties in treatment planning the proposed framework can be employed under different distributional assumptions the goal of the proposed approach is to maximize both the statistical confidence level of a treatment plan and the homogeneity of the dose distributions this novel perspective provides a user centric and personalized optimization model that allows a trade off between sufficient tumor coverage and sparing healthy tissues under uncertainty we describe testing of the performance of the proposed ccp models in terms of plan quality robustness and homogeneity and confidence level of the constraints using clinical data for a prostate cancer patient optimized ccp plans are also compared to plans developed using a deterministic approach that does not take uncertainties into account numerical experiments confirmed that the ccp is able to control setup uncertainties in target coverage and sparing of organs at risk

moduli spaces of stable sheaves on abelian surfaces in this paper we consider basic problems on moduli spaces of stable sheaves on abelian surfaces our main assumption is the primitivity of the associated mukai vector we determine the deformation types albanese maps bogomolov factors and their weight 2 hodge structures we also discuss the deformation types of moduli spaces of stable sheaves on k3 surfaces

intersection of finitely generated congruences over term algebra we show that it is decidable for any given ground term rewrite systems r and s if there is a ground term rewrite system u such that u r s if the answer is yes then we can effectively construct such a ground term rewrite system u in other words for any given finitely generated congruences and over the term algebra it is decidable if is a finitely generated congruence if the answer is yes then we can effectively construct a ground term rewrite system u such that u

on ground tree transformations and congruences induced by tree automata for a tree automaton a over a ranked alphabet we study the ground tree transformation a induced by a and the restriction a of the congruence a to terms over we define a congruence relation a a on a called the determiner of a and the quotient tree automaton a we show the following results it is decidable if a a if a is deterministic then a a the determiner of a can be effectively constructed a is deterministic and a a for a connected tree automaton a a a if and only if a b for some deterministic tree automaton b if and only if a a