the complexity of mean payoff games on graphs abstract we study the complexity of finding the values and optimal strategies of mean payoff games on graphs a family of perfect information games introduced by ehrenfeucht and mycielski and considered by gurvich karzanov and khachiyan we describe a pseudo polynomial time algorithm for the solution of such games the decision problem for which is in np conp finally we describe a polynomial reduction from mean payoff games to the simple stochastic games studied by condon these games are also known to be in np conp but no polynomial or pseudo polynomial time algorithm is known for them

computing logcfl certificates the complexity class logcfl consists of all languages or decision problems which are logspace reducible to a context free language since logcfl is included in ac1 the problems in logcfl are highly parallelizable by results of ruzzo jcss 21 1980 218 the complexity class logcfl can be characterized as the class of languages accepted by alternating turing machines atms which use logarithmic space and have polynomially sized accepting computation trees we show that for each such atm m recognizing a language a in logcfl it is possible to construct an llogcfl transducer tm such that tm on input w e a outputs an accepting tree for m on w it follows that computing single logcfl certificates is feasible in functional ac1 and is thus highly parallelizable wanke j algorithms 16 1994 470 has recently shown that for any fixed k deciding whether the treewidth of a graph is at most k is in the complexity class logcfl as an application of our general result we show that the task of computing a tree decomposition for a graph of constant treewidth is in functional logcfl and thus in ac1 we also show that the following tasks are all highly parallelizable computing a solution to an acyclic constraint satisfaction problem computing an m coloring for a graph of bounded treewidth computing the chromatic number and minimal colorings for graphs of bounded tree width

objective analyses and mapping techniques for rainfall fields an objective comparison many methods have been proposed and applied individually to rainfall fields in order to estimate point or average values at ungauged sites this paper reviews some of the usual as well as some of the more recent techniques they are classified according to their fundamental principles optimality criteria and practical aspects some theoretical developments mostly for the statistically based techniques are offered and the practical aspects are mainly directed to the particular case of rainfall fields a case study is presented for a region with particularly high rainfall variability providing a good sample of events for testing the sensitivity of the estimation to the different methods used the identification of statistical structure functions required by certain methods using regionalized variable concepts is discussed in detail for the case considered method evaluation is based on a classical validation technique that divides the available stations into two separate networks i e a base network is used to perform estimations at the stations of a test network for a set of independent storm events careful attention is paid to result interpretation and visualisation finally conclusions are drawn as to which method should be implemented taking into account cost efficiency considerations

membership in constant time and almost minimum space this paper deals with the problem of storing a subset of elements from the bounded universe mathcal m 0 ldots m 1 so that membership queries can be performed efficiently in particular we introduce a data structure to represent a subset of n elements of mathcal m in a number of bits close to the information theoretic minimum b left lceil lg m choose n right rceil and use the structure to answer membership queries in constant time

estimation of spatial covariance structures by adjoint state maximum likelihood cross validation 1 theory this series of three papers describes a cross validation method to estimate the spatial covariance structure of intrinsic or nonintrinsic random functions from point or spatially averaged data that may be corrupted by noise any number of relevant parameters including nugget effect can be estimated the theory described in this paper is based on a maximum likelihood approach which treats the cross validation errors as gaussian various a posteriori statistical tests are used to verify this hypothesis and to show that in many cases correlation between these errors is weak the log likelihood criterion is optimized through a combination of conjugate gradient algorithms an adjoint state theory is used to efficiently calculate the gradient of the estimation criterion optimize the step size downgradient and compute a lower bound for the covariance matrix of the estimation errors issues related to the identifiability stability and uniqueness of the resulting adjoint state maximum likelihood cross validation asmlcv method are discussed this paper also describes the manner in which asmlcv allows one to use model structure identification criteria to select the best covariance model among a given set of alternatives practical aspects of asmlcv and its application to synthetic data are presented in paper 2 samper and neuman this issue a applications to real hydrogeological data transmissivities and groundwater levels have been presented elsewhere while hydrochemical and isotopic data are analyzed by asmlcv in paper 3 samper and neuman this issue b

succinct representations of graphs for a fixed graph property q the complexity of the problem given a graph g does g have property q is usually investigated as a function of v the number of vertices in g with the assumption that the input size is polynomial in v in this paper the complexity of these problems is investigated when the input graph is given by a succinct representation by a succinct representation it is meant that the input size is polylog in v it is shown that graph problems which are approached this way become intractable actually no nontrivial problem could be found which can be solved in polynomial time the main result is characterizing a large class of graph properties for which the respective succinct problem is np hard trying to locate these problems within the p time hierarchy shows that the succinct versions of polynomially equivalent problems may not be polynomially equivalent

succinct representation leaf languages and projection reductions abstract in this article the following results are shown 1 for succinctly encoded problems s a completeness under polynomial time reductions is equivalent to completeness under projection reductions an extremely weak reduction defined by a quantifier free projective formula 2 the succinct version s a of a computational problem a is complete under projection reductions for the class of problems characterizable with leaf language a but not complete under monotone projections 3 a strong conversion lemma if a is reducible to b in polylogarithmic time then the succinct version of a is monotone projection reducible to the succinct version of b this result strengthens previous results by papadimitriou and yannakakis and balcazar and lozano it allows iterated application for multiple succinct problems 4 for all syntactic complexity classes there exist complete problems under monotone projection reductions this positively answers a question by stewart for a large number of complexity classes

interpolation methods comparison abstract in many fields spatial interpolation is used to evaluate physical data in a continuous domain the many different techniques offer different performances according to the characteristics of initial data points the aim of this paper is to provide help in choosing and evaluating the technique that best suits the data set a few indices measure the quality of interpolation by different viewpoints an extensive test case is reported involving four different interpolation methods data sets are generally connected with environmental topics or taken from literature

linear estimation of random fields with second order increments and its application abstract the purpose of this paper is to develop a mathematical model of a class of nonstationary random fields with second order increments and to consider the estimation problem of the random field from noisy observation data obtained at scattered locations first a theory of random field which is nonstationary with second order increments is developed concerning several mathematical properties extending the discussion to the intrinsic random field and its ergodic property secondly minimum variance estimators for a state of the random field at an arbitrary location in the two dimensional domain are considered for both cases where the information about statistical properties of the random field is a priori available and not the estimators obtained are compared with the kriging which is a useful interpolation method used in geostatistics and hydrosciences finally a numerical example is presented for examining the estimators for identifying the variogram of the given random field and the proposed estimators are tested for the real meteorological data to establish a weather map

a stochastic inverse solution for transient groundwater flow parameter identification and reliability analysis in this paper a stochastic approach is developed for solving the inverse problem of parameter identification for transient groundwater flow adjoint state equations are derived for the stochastic partial differential equation spde relating transient head and log hydraulic conductivity perturbations the derived equations can be used to calculate the covariance matrix of head observations and the cross covariance matrix between head observations and log hydraulic conductivity measurements for each observation time as well as the covariance and cross covariance matrices between different observation times the number of simulation runs required for obtaining these matrices is equal to the number of head observations the reliability of model prediction is evaluated through the variance estimate method using adjoint sensitivity analysis and the cokriging estimate the reliability evaluation of model prediction can be used as an aid in the optimization of experimental design for sampling strategies a numerical example is given to illustrate the stochastic inverse procedure for a general transient flow problem the example shows that using head observations of all observation times simultaneously produces much better results than using them sequentially commonly known as the quasi steady approach the example also shows that it is possible to obtain a reliable stochastic inverse solution for meeting a given prediction objective based on a limited number of observations

on the complexity of kings a king in a directed graph is a vertex from which each vertex in the graph can be reached through paths of length at most two there is a broad literature on tournaments completely oriented digraphs and it has been known for more than half a century that all tournaments have at least one king recently kings have proven useful in theoretical computer science in particular in the study of the complexity of reachability problems and semifeasible sets in this article we study the complexity of recognizing kings for each succinctly specified family of tournaments the king problem is already known to belong to p 2 p we prove that the complexity of kingship problems is a rich enough vocabulary to pinpoint every nontrivial many one degree in p 2 p that is we show that every set in p 2 p other than 0 and s is equivalent to a king problem under m p reductions indeed we show that the equivalence can even be realized by relatively simple padding and holds even if the notion of kings is redefined to refer to k kings for any fixed k 2 vertices from which all vertices can be reached through paths of length at most k in contrast we prove that for each succinctly specified family of tournaments the source problem the problem of deciding whether a given vertex v has the property that there exists a k such that v is a k king also falls within p 2 p yet cannot be p 2 p complete or even np hard unless p np using these and related techniques we obtain a broad range of additional results about the complexity of king problems diameter problems and radius problems it follows easily from our proof approach that the problem of testing kingship in succinctly specified graphs which need not be tournaments is p 2 p complete we show that the radius problem for arbitrary succinctly represented graphs is s 3 p complete but that in contrast the diameter problem for arbitrary succinctly represented graphs or even tournaments is p 2 p complete

the complexity of bayesian networks specified by propositional and relational languages abstract we examine the complexity of inference in bayesian networks specified by logical languages we consider representations that range from fragments of propositional logic to function free first order logic with equality in doing so we cover a variety of plate models and of probabilistic relational models we study the complexity of inferences when network query and domain are the input the inferential and the combined complexity when the network is fixed and query and domain are the input the query data complexity and when the network and query are fixed and the domain is the input the domain complexity we draw connections with probabilistic databases and liftability results and obtain complexity classes that range from polynomial to exponential levels we identify new languages with tractable inference and we relate our results to languages based on plates and probabilistic relational models

on the complexity of data disjunctions we study the complexity of data disjunctions in disjunctive deductive databases dddbs a data disjunction is a disjunctive ground clause r c 1pt1 r ck k 2 which is derived from the database such that all atoms in the clause involve the same predicate r we consider the complexity of deciding existence and uniqueness of a minimal data disjunction as well as actually computing one both for propositional data and nonground program complexity of the database our results extend and complement previous results on the complexity of disjunctive databases and provide newly developed tools for the analysis of the complexity of function computation

a fast general methodology for information theoretically optimal encodings of graphs we propose a fast methodology for encoding graphs with information theoretically minimum numbers of bits specifically a graph with property pi is called a em pi graph if pi satisfies certain properties then an n node m edge pi graph g can be encoded by a binary string x such that 1 g and x can be obtained from each other in o n log n time and 2 x has at most beta n o beta n bits for any continuous superadditive function beta n so that there are at most 2 beta n o beta n distinct n node pi graphs the methodology is applicable to general classes of graphs this paper focuses on planar graphs examples of such pi include all conjunctions over the following groups of properties 1 g is a planar graph or a plane graph 2 g is directed or undirected 3 g is triangulated triconnected biconnected merely connected or not required to be connected 4 the nodes of g are labeled with labels from 1 ldots ell 1 for ell 1 leq n 5 the edges of g are labeled with labels from 1 ldots ell 2 for ell 2 leq m and 6 each node respectively edge of g has at most ell 3 o 1 self loops respectively ell 4 o 1 multiple edges moreover ell 3 and ell 4 are not required to be o 1 for the cases of pi being a plane triangulation these examples are novel applications of small cycle separators of planar graphs and are the only nontrivial classes of graphs other than rooted trees with known polynomial time information theoretically optimal coding schemes

on ram priority queues priority queues are some of the most fundamental data structures for example they are used directly for task scheduling in operating systems moreover they are essential to greedy algorithms we study the complexity of integer priority queue operations on a ram with arbitrary word size modeling the possibilities in standard imperative programming languages such as c we present exponential improvements over previous bounds and we show tight relations to sorting our first result is a ram priority queue supporting find min in constant time and insert and delete min in time o log log n where n is the current number of keys in the queue this is an exponential improvement over the o sqrt log n bound of fredman and willard proceedings of the 22nd acm symposium on the theory of computing baltimore md pp 1 7 plugging this priority queue into dijkstra s algorithm gives an o mlog log m algorithm for the single source shortest path problem on a graph with m edges as compared with the previous o m sqrt log m bound based on fredman and willard s priority queue the above bounds assume o n 2 varepsilon w space where w is the word length and varepsilon 0 they can however be achieved in linear space using randomized hashing our second result is a general equivalence between sorting and priority queues a priority queue is monotone if the minimum is nondecreasing over time as in many greedy algorithms we show that on a ram the amortized operation cost of a monotone priority queue is equivalent to the per key cost of sorting for example the equivalence implies that the single source shortest paths problem on a graph with m edges is no harder than that of sorting m keys with the current ram sorting this gives an o m log log m time bound as above but the relation holds regardless of the future developments in ram sorting from the equivalence result for any fixed varepsilon 0 we derive a randomized monotone o sqrt log n 1 varepsilon priority queue with expected constant time decrease key plugging this into dijkstra s algorithm gives an o n sqrt log n 1 varepsilon m algorithm for the single source shortest path problem on a graph with n nodes and m edges complementing the above o mlog log m algorithm if m gg n this improves the o nlog n log log n m bound by fredman and willard proceedings of the 31st ieee symposium on the foundations of computer science st louis mo 1990 pp 719 725 based on their o log n log log n priority queue with constant decrease key

statistical estimation of polynomial generalized covariance functions and hydrologic applications minimum variance unbiased linear estimation theory has found many applications in the analysis of spatial rainfall and hydrogeologic data estimation of point values or areal averages calculation of variances of estimation error and network design however the important problem of inferring the spatial structure or interdependence of the function of interest has received relatively less attention three methods for the estimation of the parameters of matheron s polynomial generalized covariance function a useful model for nonstationary functions are presented and evaluated maximum likelihood ml minimum variance unbiased quadratic mvuq and minimum norm least squares the estimation error covariance matrix of the parameters is calculated with each of these methods ml and mvuq estimation have very good properties and for reasonably large samples give very similar results minimum norm estimation is appropriate for preliminary data analysis the application of these methodologies is illustrated with a set of rainfall data and problems of implementation are discussed it is shown that the estimation of the parameters of the covariance function involves sizeable errors it is suggested that in practice it may be rather difficult to identify the parameters of all but simple models it is important that future research evaluate the effects of parameter uncertainty in the circulation of estimation error variances of point or areal averages and in the design of hydrologic data collection networks

succinct representation of labeled trees we give a representation for labeled ordered trees that supports labeled queries such as finding the i th ancestor of a node with a given label our representation is succinct namely the redundancy is small o of the optimal space for storing the tree this improves the representation of he et al isaac 2012 8 which is succinct only when the entropy of the labels is 1

memoryless determinacy of parity and mean payoff games a simple proof we give a simple direct and constructive proof of memoryless determinacy for parity and mean payoff games first we prove by induction that the finite duration versions of these games played until some vertex is repeated are determined and both players have memoryless winning strategies in contrast to the proof of ehrenfeucht and mycielski internat j game theory 8 1979 109 113 our proof does not refer to the infinite duration versions second we show that memoryless determinacy straightforwardly generalizes to infinite duration versions of parity and mean payoff games

mean payoff games with partial observation mean payoff games are important quantitative models for open reactive systems they have been widely studied as games of perfect information in this paper we investigate the algorithmic properties of several subclasses of mean payoff games where the players have asymmetric information about the state of the game these games are in general undecidable and not determined according to the classical definition we show that such games are determined under a more general notion of winning strategy we also consider mean payoff games where the winner can be determined by the winner of a finite cycle forming game this yields several decidable classes of mean payoff games of asymmetric information that require only finite memory strategies including a generalization of perfect information games where positional strategies are sufficient we give an exponential time algorithm for determining the winner of the latter

floor planning by graph dualization 2 concave rectilinear modules given a planar triangulated graph ptg g the problem of constructing a floor plan f such that g is the dual of f and the boundary of f is rectangular is studied it is shown that if only zero concave rectilinear modules crm or rectangular modules and 1 crm i e l shaped are allowed there are ptgs that do not admit any floor plan however if 2 bend modules e g t shaped and z shaped are also allowed then every biconnected ptg admits a floor plan thus the employment of 2 bend modules is necessary and sufficient for graph dualization floor planning a linear time algorithm for constructing a 2 crm floor plan of an arbitrary ptg is proposed

succinct representation of balanced parentheses and static trees we consider the implementation of abstract data types for the static objects binary tree rooted ordered tree and a balanced sequence of parentheses our representations use an amount of space within a lower order term of the information theoretic minimum and support in constant time a richer set of navigational operations than has previously been considered in similar work in the case of binary trees for instance we can move from a node to its left or right child or to the parent in constant time while retaining knowledge of the size of the subtree at which we are positioned the approach is applied to produce a succinct representation of planar graphs in which one can test adjacency in constant time

functions computable in polynomial space consider nondeterministic polynomial time turing machine that on input x outputs a 3 3 matrix with entries from 1 0 1 on each of its paths define the function f where f x is the upper left entry in the product of all these matrices in an order of the paths to be made precise below we show that the class of functions f computable as just described is exactly the class fpspace of integer valued functions computable by polynomial space turing machines along the way we obtain characterizations of fpspace in terms of arithmetic circuits and straight line programs

on some deterministic space complexity problems in this paper we give a complete problem in text dspace n the problem is whether there exists a cycle in the connected component containing 0 0 cdots 0 in the graph g p of the zeros of a polynomial p over gf 2 under a suitable natural coding hence the deterministic space complexity of this problem is o n but not o n we give as well several problems for which we can obtain very close upper and lower deterministic space bounds for example the deterministic space complexity to determine whether there exists a cycle in the graph of the set of assignments satisfying a boolean formula is o n log n but not o n log 2 n

good spanning trees in graph drawing introduces a good spanning tree of a plane graph solves two open problems on monotone drawings using good spanning trees finds a 2 visibility drawing of a planar graph using a good spanning tree gives algorithms to find an spike vpg and t shaped drawings of a planar graph a plane graph is a planar graph with a fixed planar embedding in this paper we define a special spanning tree of a plane graph which we call a good spanning tree not every plane graph has a good spanning tree we show that every connected planar graph has a planar embedding with a good spanning tree using a good spanning tree we show that every connected planar graph g of n vertices has a straight line monotone grid drawing on an o n o n 2 grid and such a drawing can be found in o n time our results solve two open problems on monotone drawings of planar graphs posed by angelini et al using good spanning trees we also give simple linear time algorithms for finding a 2 visibility representation of a connected planar graph g of n vertices on a 2 n 1 2 n 1 grid and for finding a spike vpg representation of g on a 2 n 1 n grid

linear connectivity problems in directed hypergraphs we introduce a notion of hyperconnection formally called l hyperpath between vertices in a directed hypergraph and relate this notion to existing notions of hyperpaths in directed hypergraphs we show that some interesting questions in problem domains such as distributed secret sharing and routing in packet filtered networks are basically questions about the existence of l hyperpaths in directed hypergraphs we study the computational complexity of problems related to l hyperpaths and the l cyclomatic number of directed hypergraphs the minimum number of hyperedges that need to be deleted to make a directed hypergraph free of l hypercycles we prove that the l hyperpath existence problem the l cyclomatic number problem the minimum l cyclomatic set problem and the minimal l cyclomatic set problem are each complete for the complexity class np s 2 p p 2 p and dp respectively

the complexity of searching implicit graphs abstract the standard complexity classes of complexity theory do not allow for direct classification of most of the problems solved by heuristic search algorithms the reason is that almost always these are defined in terms of implicit graphs of state or problem reduction spaces while the standard definitions of all complexity classes are specifically tailored to explicit inputs to allow for more precise comparisons with standard complexity classes we introduce here a model for the analysis of algorithms on graphs given by vertex expansion procedures it is based on previously studied concepts of succinct representation techniques and allows us to prove pspace completeness or exptime completeness of specific natural problems on implicit graphs such as those solved by a ao and other best first search strategies

effective algebraic degeneracy we show that for every smooth projective hypersurface x n 1 of degree d and of arbitrary dimension n 2 if x is generic then there exists a proper algebraic subvariety y x such that every nonconstant entire holomorphic curve f x has image f which lies in y as soon as its degree satisfies the effective lower bound d geqslant 2 n 5

regular edge labeling of 4 connected plane graphs and its applications in graph drawing problems abstract in this paper we extend the concept of the regular edge labeling for general plane graphs and for triconnected triangulated plane graphs to 4 connected triangulated plane graphs we present two different linear time algorithms for constructing such a labeling by using regular edge labeling we present a new linear time algorithm for constructing rectangular dual of planar graphs our algorithm is simpler than previously known algorithms the coordinates of the rectangular dual constructed by our algorithm are integers while the one constructed by known algorithms are real numbers our second regular edge labeling algorithm is based on canonical ordering of 4 connected triangulated plane graphs by using this technique we present a new algorithm for constructing visibility representation of 4 connected planar graphs our algorithm reduces the size of the representation by a factor of 2 for such graphs

the complexity of counting self avoiding walks in subgraphs of two dimensional grids and hypercubes valiant siam j comput 8 1979 410 421 showed that the problem of computing the number of simple s t paths in graphs is p complete both in the case of directed graphs and in the case of undirected graphs welsh complexity knots colourings and counting cambridge university press cambridge 1993 p 17 asked whether the problem of computing the number of self avoiding walks of a given length in the complete two dimensional grid is complete for p1 the tally version of p this paper offers a partial answer to the question of welsh it is p complete to compute the number of self avoiding walks of a given length in a subgraph of a two dimensional grid several variations of the problem are also studied and shown to be p complete this paper also studies the problem of computing the number of self avoiding walks in a subgraph of a hypercube similar completeness results are shown for the problem by scaling the computation time to exponential it is shown that computing the number of self avoiding walks in hypercubes is a complete problem for exp in the case when a subgraph of a hypercube is specified by its dimension and a boolean circuit that accepts the nodes finally this paper studies the complexity of testing whether a given word over the four letter alphabet u d l r represents a self avoiding walk in a two dimensional grid a linear space lower bound is shown for nondeterministic turing machines with a 1 way input head to make this test

thom polynomials of morin singularities we prove a formula for thom polynomials of a d singularities in any codimension we use a combination of the test curve model of porteous and the localization methods in equivariant cohomology our formulas are independent of the codimension and are computationally effective up to d 6

local optimization of observed points with no need to observations abstract for a second order stationary random field this paper presents a new formula which strictly ensures the unbiasedness and optimality of the common kriging to calculate the unknown parameters in variogram or covariance function based upon this formula an algorithm is developed to locate the observed points bearing no observations with the purpose of minimizing the maximal estimator variances on a networked domain

paper identification and optimal estimation of random fields from scattered point wise data a self contained presentation of the interpolation problem in two dimensional spatial random fields is given we investigate the case where the random field is not necessarily stationary where the data are so scarce and so scattered in space that sample covariance function estimates are not meaningful and where therefore an analytical parametric variogram model is used in lieu of the covariance we discuss several variogram parameter estimation techniques ls gls ml interpolation error method and we show how to derive estimates of various functionals of the random field from the variogram a numerical simulation and two typical engineering applications illustrate the variogram estimation techniques and provide a good measure of their respective performances

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

existence of global invariant jet differentials on projective hypersurfaces of high degree let x subset mathbb p n 1 be a smooth complex projective hypersurface in this paper we show that if the degree of x is large enough then there exist global sections of the bundle of invariant jet differentials of order n on x vanishing on an ample divisor we also prove a logarithmic version effective in low dimension for the log pair mathbb p n d where d is a smooth irreducible divisor of high degree moreover these result are sharp i e one cannot have such jet differentials of order less than n

lattices in the cohomology of shimura curves we prove the main conjectures of breuil j reine angew math 2012 including a generalisation from the principal series to the cuspidal case and dembele j reine angew math 2012 subject to a mild global hypothesis that we make in order to apply certain r mathbb t theorems more precisely we prove a multiplicity one result for the mod p cohomology of a shimura curve at iwahori level and we show that certain apparently globally defined lattices in the cohomology of shimura curves are determined by the corresponding local p adic galois representations we also indicate a new proof of the buzzard diamond jarvis conjecture in generic cases our main tools are the geometric breuil mezard philosophy developed in emerton and gee j inst math jussieu 2012 and a new and more functorial perspective on the taylor wiles kisin patching method along the way we determine the tamely potentially barsotti tate deformation rings of generic two dimensional mod p representations generalising a result of breuil and mezard bull soc math de france 2012 in the principal series case

thom polynomials symmetries and incidences of singularities as an application of the generalized pontryagin thom construction rsz here we introduce a new method to compute cohomological obstructions of removing singularities i e thom polynomials t with the aid of this method we compute some sample results such as the thom polynomials associated to all stable singularities of codimension 8 between equal dimensional manifolds and some other thom polynomials associated to singularities of maps n n p n k for k 0 we also give an application by reproving a weak form of the multiple point formulas of herbert and ronga h ro2 as a byproduct of the theory we define the incidence class of singularities which the author believes may turn to be an interesting useful and simple tool to study incidences of singularities

cnf and dnf succinct graph encodings abstract it is well known that succinct encodings of computational problems using circuits or formulas to encode large instances generally result in an exponential complexity blow up compared to their original complexity we introduce a new way to encode graph problems based on cnf or dnf formulas we show that contrary to the other existing succinct models there are examples of problems whose complexity does not increase when encoded in the new form or increases to an intermediate complexity class less powerful than the exponential blow up we also study the complexity of the succinct versions of the graph isomorphism problem we show that all the versions are hard for pspace although the exact complexity of these problems is still unknown we show that under most existing succinct models the different versions of the problem are equivalent we also give an algorithm for the dnf encoded version of gi whose running time depends mainly on the number of terms in the succinct representation

orderly spanning trees with applications we introduce and study orderly spanning trees of plane graphs this algorithmic tool generalizes canonical orderings which exist only for triconnected plane graphs although not every plane graph admits an orderly spanning tree we provide an algorithm to compute an orderly pair for any connected planar graph g consisting of an embedded planar graph h isomorphic to g and an orderly spanning tree of h we also present several applications of orderly spanning trees 1 a new constructive proof for schnyder s realizer theorem 2 the first algorithm for computing an area optimal 2 visibility drawing of a planar graph and 3 the most compact known encoding of a planar graph with o 1 time query support all algorithms in this paper run in linear time

finite monoids from word to circuit evaluation the problem of evaluating a circuit whose wires carry values from a finite monoid m and whose gates perform the monoid operation provides a meaningful generalization to the well studied problem of evaluating a word over m evaluating words over monoids is closely tied to the fine structure of the complexity class nc 1 and in this paper analogous ties between evaluating circuits over monoids and the structure of the complexity class p are exhibited it is shown that circuit evaluation in the case of any nonsolvable monoid is p complete while circuits over solvable monoids can be evaluated in det subseteq nc 2 then the case of aperiodic monoids is completely elucidated their circuit evaluation problems are either in ac 0 or l or nl complete depending on the precise algebraic properties of the monoids finally it is shown that the evaluation of circuits over the cyclic group bbb z q for fixed q geq 2 is complete for the logspace counting class co mod ql that the problem for p groups p a prime is complete for mod pl and that the more general case of nilpotent groups of exponent q belongs to the boolean closure of mod ql

mcnaughton families of languages in 1988 the church rosser languages were introduced by mcnaughton et al as those languages that are recognized by finite length reducing and confluent string rewriting systems using extra non terminal symbols here we generalize this concept by considering classes of languages that are obtained by other types of string rewriting systems to honour robert mcnaughton s original contribution we call the resulting families of languages mcnaughton families here it is shown that the concept of mcnaughton families is as powerful as the notion of turing machine or the notion of phrase structure grammar we investigate the relationships between the various mcnaughton families obtaining an extensive hierarchy of classes that includes many well known language and complexity classes as well as some new classes further we consider some closure and non closure properties for those mcnaughton families that are contained in the class of context free languages and we address the complexity of the fixed and the general membership problems for these families

symbolic model checking for m calculus requires exponential time we investigate the complexity of symbolic model checking for calculus the exponential time lower bound is proved moreover this lower bound holds even for a fixed alternation free formula

a note on succinct representations of graphs galperin and wigderson inform and control 56 1983 183 198 showed that certain trivial graph properties become np complete when the graph is represented in a particular exponentially succinct way we show that under the same representation graph properties that are ordinarily np complete become complete for non deterministic exponential time

word problems and membership problems on compressed words we consider a compressed form of the word problem for finitely presented monoids where the input consists of two compressed representations of words over the generators of a monoid m and we ask whether these two words represent the same monoid element of m words are compressed using straight line programs i e context free grammars that generate exactly one word for several classes of finitely presented monoids we obtain completeness results for complexity classes in the range from p to expspace as a by product of our results on compressed word problems we obtain a fixed deterministic context free language with a pspace complete compressed membership problem the existence of such a language was open so far finally we will investigate the complexity of the compressed membership problem for various circuit complexity classes

succinct representations of planar maps this paper addresses the problem of representing the connectivity information of geometric objects using as little memory as possible as opposed to raw compression issues the focus here is on designing data structures that preserve the possibility of answering incidence queries in constant time we propose in particular the first optimal representations for 3 connected planar graphs and triangulations which are the most standard classes of graphs underlying meshes with spherical topology optimal means that these representations asymptotically match the respective entropy of the two classes namely 2 bits per edge for 3 connected planar graphs and 1 62 bits per triangle or equivalently 3 24 bits per vertex for triangulations these representations support adjacency queries between vertices and faces in constant time

on floor plan of plane graphs a floor plan is a rectangle partitioned into a set of disjoint rectilinear polygonal regions called modules a floor plan f represents a plane graph g as follows each vertex of g corresponds to a module of f and two vertices are adjacent in g iff their corresponding modules share a common boundary floor plans find applications in vlsi chip design if a module m is a union of k disjoint rectangles m is called a k rectangle module it was shown in k h yeap and m sarrafzadeh siam j comput 22 1993 pp 500 526 that every triangulated plane graph g has a floor plan using 1 2 and 3 rectangle modules in this paper we present a simple linear time algorithm that constructs a floor plan for g using only 1 and 2 rectangle modules

the complexity of computing the size of an interval given a p order a over a universe of strings i e a transitive reflexive antisymmetric relation such that if x y in a then x is polynomially bounded by y an interval size function of a returns for each string x in the universe the number of strings in the interval between strings b x and t x with respect to a where b x and t x are functions that are polynomial time computable in the length of x by choosing sets of interval size functions based on feasibility requirements for their underlying p orders we obtain new characterizations of complexity classes we prove that the set of all interval size functions whose underlying p orders are polynomial time decidable is exactly mp we show that the interval size functions for orders with polynomial time adjacency checks are closely related to the class fpspace poly indeed fpspace poly is exactly the class of all nonnegative functions that are an interval size function minus a polynomial time computable function we study two important functions in relation to interval size functions the function mdiv maps each natural number n to the number of nontrivial divisors of n we show that mdiv is an interval size function of a polynomial time decidable partial p order with polynomial time adjacency checks the function mmonsat maps each monotone boolean formula f to the number of satisfying assignments of f we show that mmonsat is an interval size function of a polynomial time decidable total p order with polynomial time adjacency checks finally we explore the related notion of cluster computation

a taxonomy of problems with fast parallel algorithms the class nc consists of problems solvable very fast in time polynomial in log n in parallel with a feasible polynomial number of processors many natural problems in nc are known in this paper an attempt is made to identify important subclasses of nc and give interesting examples in each subclass the notion of nc 1 reducibility is introduced and used throughout problem r is nc 1 reducible to problem s if r can be solved with uniform log depth circuits using oracles for s problems complete with respect to this reducibility are given for many of the subclasses of nc a general technique the parallel greedy algorithm is identified and used to show that finding a minimum spanning forest of a graph is reducible to the graph accessibility problem and hence is in nc 2 solvable by uniform boolean circuits of depth o log 2 n and polynomial size the class logcfl is given a new characterization in terms of circuit families the class det of problems reducible to integer determinants is defined and many examples given a new problem complete for deterministic polynomial time is given namely finding the lexicographically first maximal clique in a graph this paper is a revised version of s a cook 1983 in proceedings 1983 intl found comut sci conf lecture notes in computer science vol 158 pp 78 93 springer verlag berlin new york

nonuniform acc circuit lower bounds the class acc consists of circuit families with constant depth over unbounded fan in and or not and modm gates where m 1 is an arbitrary constant we prove the following nexp the class of languages accepted in nondeterministic exponential time does not have nonuniform acc circuits of polynomial size the size lower bound can be slightly strengthened to quasipolynomials and other less natural functions enp the class of languages recognized in 2o n time with an np oracle doesn t have nonuniform acc circuits of 2no 1 size the lower bound gives an exponential size depth tradeoff for every d m there is a 0 such that enp doesn t have depth d acc circuits of size 2n with modm gates previously it was not known whether expnp had depth 3 polynomial size circuits made out of only mod6 gates the high level strategy is to design faster algorithms for the circuit satisfiability problem over acc circuits then prove that such algorithms entail these lower bounds the algorithms combine known properties of acc with fast rectangular matrix multiplication and dynamic programming while the second step requires a strengthening of the author s prior work

on symbolic obdd based algorithms for the minimum spanning tree problem the minimum spanning tree problem is one of the most fundamental algorithmic graph problems and obdds are a very common dynamic data structure for boolean functions since in some applications graphs become larger and larger a research branch has emerged which is concerned with the design and analysis of so called symbolic algorithms for classical graph problems on obdd represented graph instances here a symbolic minimum spanning tree algorithm using o log 3 v functional operations is presented where v is the set of vertices of the input graph moreover the computation of the transitive closure is investigated and it is proved that there can be an exponential blow up from input to output size furthermore answering an open problem posed by sawitzki 37 it is shown that every symbolic obdd based algorithm for the minimum spanning tree problem needs exponential space with respect to the obdd size of the input graph this result even holds for planar input graphs

automatic interpolation methods for mapping piezometric surfaces abstract the purpose of analysis of spatial data should determine the approach to be adopted if estimation is concerned with detailed local interpretation rather than some form of global averaging then kriging would seem to be an inappropriate method this is especially so for the interpolation of precise observations which consequently are better estimated by deterministic methods five such efficient direct automatic interpolation methods are discussed and applied to the contour mapping of a piezometric surface