numerical solutions of forced vibration and whirling of a non linear string using the theory of a cosserat point abstract o reilly and holmes 1 performed experiments and analysis of non linear motion of a string subjected to vertical oscillation of one end their analysis suggested that differences between theoretical and experimental results were mainly due to uncertainty in the assumed form for the forcing function that was used to satisfy the forced boundary condition here a numerical solution of the non linear string problem is considered which incorporates the forced boundary condition directly and thus avoids the need to assume an arbitrary forcing function specifically the numerical formulation of string problems based on the theory of a cosserat point is used it is shown that the director inertia coefficient in the cosserat theory can be chosen so that the theory predicts the first modal frequency of small deformation free vibration exactly for each level of discretizational also examples of forced in plane motion and free non linear whirling motion are considered to validate the numerical model the resulting simulations indicate that the forcing amplitude for the onset of persistent whirling and aperiodic response is about five times smaller than that observed in the experiments even when the uncertainty in the forcing function is removed from the analysis additional attempts to bridge the gap between theory and experiment suggest that there is still some mechanism in the experiment that is not properly modelled

uniform global attractors for the nonautonomous 3d navier stokes equations abstract we obtain the existence and the structure of the weak uniform with respect to the initial time global attractor and construct a trajectory attractor for the 3d navier stokes equations nse with a fixed time dependent force satisfying a translation boundedness condition moreover we show that if the force is normal and every complete bounded solution is strongly continuous then the uniform global attractor is strong strongly compact and solutions converge strongly toward the trajectory attractor our method is based on taking a closure of the autonomous evolutionary system without uniqueness whose trajectories are solutions to the nonautonomous 3d nse the established framework is general and can also be applied to other nonautonomous dissipative partial differential equations for which the uniqueness of solutions might not hold it is not known whether previous frameworks can also be applied in such cases as we indicate in open problems related to the question of uniqueness of the leray hopf weak solutions

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

the complexity of pursuit on a graph abstract a robber and k cops choose starting vertices in a graph and move in alternation from vertex to vertex along the edges of the graph capture occurs if a cop ever shares a vertex with the robber if k is not fixed and if either the graph is directed or initial positions are given we show that the problem is exptime complete similar techniques lead to the pspace and exptime completeness of some other combinatorial games that were previously only known to be np and pspace hard

on global attractors of the 3d navier stokes equations abstract in view of the possibility that the 3d navier stokes equations nse might not always have regular solutions we introduce an abstract framework for studying the asymptotic behavior of multi valued dissipative evolutionary systems with respect to two topologies weak and strong each such system possesses a global attractor in the weak topology but not necessarily in the strong in case the latter exists and is weakly closed it coincides with the weak global attractor we give a sufficient condition for the existence of the strong global attractor which is verified for the 3d nse when all solutions on the weak global attractor are strongly continuous we also introduce and study a two parameter family of models for the navier stokes equations with similar properties and open problems these models always possess weak global attractors but on some of them every solution blows up in a norm stronger than the standard energy one in finite time

n by n checkers is exptime complete the game of checkers can easily be generalized to be played on an n by n board and the complexity of deciding questions about positions regarded as a function of n this paper considers mainly the question of whether a particular player can force a win from a given position and also the question of what is the best move in a given position each of these problems is shown to be complete in exponential time this means that any algorithm to solve them must take time which rises exponentially with respect to some power of n and moreover that they are amongst the hardest problems with such a time bound for instance if there are any problems solvable in exponential time but not in polynomial space then these two problems are amongst them

a new 3 d finite element for nonlinear elasticity using the theory of a cosserat point abstract the theory of a cosserat point has been used to formulate a new 3 d finite element for the numerical analysis of dynamic problems in nonlinear elasticity the kinematics of this element are consistent with the standard tri linear approximation in an eight node brick element specifically the cosserat point is characterized by eight director vectors which are determined by balance laws and constitutive equations for hyperelastic response the constitutive equations for the director couples are determined by derivatives of a strain energy function restrictions are imposed on the strain energy function which ensure that the element satisfies a nonlinear version of the patch test it is shown that the cosserat balance laws are in one to one correspondence with those obtained using a bubnov galerkin formulation nevertheless there is an essential difference between the two approaches in the procedure for obtaining the strain energy function specifically the cosserat approach determines the constitutive coefficients for inhomogeneous deformations by comparison with exact solutions or experimental data in contrast the bubnov galerkin approach determines these constitutive coefficients by integrating the 3 d strain energy function using the kinematic approximation it is shown that the resulting cosserat equations eliminate unphysical locking and hourglassing in large compression without the need for using assumed enhanced strains or special weighting functions

nondeterministic space is closed under complementation in this paper we show that nondeterministic space s n is closed under complementation for s n greater than or equal to log n it immediately follows that the context sensitive languages are closed under complementation thus settling a question raised by kuroda inform and control 7 1964 pp 207 233

alternation with restrictions on looping alternating turing machines with restrictions preventing them from returning to a previous configuration model games with rules enforcing such a restriction for instance the chinese version of go such restrictions do not affect the time complexity of problems for alternating turing machines but space s on a machine with the restriction is equivalent either to time or to space exponential in s on a normal alternating machine depending on the precise nature of the restriction

rush hour is psapce complete or why you should generously tip parking lot attendants rush hour is a children s game that consists of a grid board several cars that are restricted to move either vertically or horizontally but not both a special target car and a single exit on the perimeter of the grid the goal of the game is to find a sequence of legal moves that allows the target car to exit the grid we consider a slightly generalized version of the game that uses an nn grid and assume that we can place the single exit and target car at any location we choose on initialization of the game in this work we show that deciding if the target car can legally exit the grid is pspace complete our constructive proof uses a lazy form of dual rail reversible logic such that movement of output cars can only occur if logical combinations of input cars can also move emulating this logic only requires three types of devices two switches and one crossover thus our proof technique can be easily generalized to other games and planning problems in which the same three primitive devices can be constructed

recent results and questions in combinatorial game complexities abstract aim present a systematic development of part of the theory of combinatorial games from the ground up approach computational complexity combinatorial games are completely determined the questions of interest are efficiencies of strategies methodology divide and conquer isolate the various difficulties separating hard from easy games and attack them individually presentation informal examples of games sampled from various levels illustrate the theory with emphasis on formulating and motivating new and old research problems

on the complexity of connection games in this paper we study three connection games among the most widely played havannah twixt and slither we show that determining the outcome of an arbitrary input position is pspace complete in all three cases our reductions are based on the popular graph problem generalized geography and on hex itself we also consider the complexity of generalizations of hex parameterized by the length of the solution and establish that while short generalized hex is w1 hard short hex is fpt finally we prove that the ultra weak solution to the empty starting position in hex cannot be fully adapted to any of these three games the games of havannah twixt and slither are pspace complete the game of slither does not admit draws on finite planar grid boards short generalized hex is w1 hard and short hex is fixed parameter tractable

drawn k in a row games wu and huang 2005 12 and wu et al 2006 13 presented a generalized family of k in a row games called connect m n k p q two players black and white alternately place p stones on an mxn board in each turn black plays first and places q stones initially the player who first gets k consecutive stones of his her own horizontally vertically or diagonally wins both tie the game when the board is filled up with neither player winning a connect m n k p q game is drawn if neither has any winning strategy given p this paper derives the value k d r a w p such that connect m n k p q games are drawn for all k k d r a w p m 1 n 1 email protected email protected p as follows 1 k d r a w p 11 2 for all p 3 k d r a w p 3p 3d 1 where d is a logarithmic function of p so the ratio k d r a w p p is approximately 3 for sufficiently large p the first result was derived with the help of a program to our knowledge our k d r a w p values are currently the smallest for all email protected p 1000

lower bounds for multiplayer noncooperative games of incomplete information abstract this paper see also 1 extends the alternating turing machine a tm of chandra kozen and stockmeyer 2 the private and the blind alternating machines of reif 3 4 to model multiplayer games of incomplete information we use these machines to provide matching lower bounds for our decision algorithms described in our companion paper 5 we also apply multiple person alternation to other machine types we show that multiplayer games of incomplete information can be undecidable general however one form of incomplete information games that is decidable we term as hierarchical games defined later in this paper in hierarchical multiplayer games each additional clique subset of players with same information increases the complexity of the outcome problem by a further exponential consequently if a multiplayer game of incomplete information with k cliques has a space bound of s n then its outcome can be k repeated exponentials harder than games of complete information with the same space bound s n this paper proves that this exponential blow up must occur in the worst case we define team private peek and team blind peek extending the previous models of peek these new games can be shown to be complete for their respective classes we use these games to establish lower bounds on complexity of multiplayer games of incomplete information and blindfold multiplayer games we analyze the time bounded alternating machines and conclude that time is not a very critical resource for multiplayer alternation we also show dqbf a variant of qbf to be complete in nexptime

undirected edge geography abstract the game of edge geography is played by two players who alternately move a token on a graph from one vertex to an adjacent vertex erasing the edge in between the player who first has no legal move is the loser we show that the decision problem of determining whether a position in this game is a win for the first player is pspace complete further the problem remains pspace complete when restricted to planar graphs with maximum degree 3 however if the underlying graph is bipartite we provide 1 a linear algebraic characterization of the p and n positions yielding 2 a polynomial time algorithm for deciding whether any given position is p or n and also 3 a polynomial time algorithm to find winning moves

the subpower membership problem for bands abstract fix a finite semigroup s and let a 1 a k b be tuples in a direct power s n the subpower membership problem smp for s asks whether b can be generated by a 1 a k for bands idempotent semigroups we provide a dichotomy result if a band s belongs to a certain quasivariety then is in p otherwise it is np complete furthermore we determine the greatest variety of bands all of whose finite members induce a tractable finally we present the first example of two finite algebras that generate the same variety and have tractable and np complete smp s respectively

on the size of binary decision diagrams representing boolean functions we consider the size of the representation of boolean functions by several classes of binary decision diagrams bdds also called branching programs namely the classes of arbitrary bdds of real time bdd rbdd i e bdds where each computation path is limited to the number of variables of free bdds fbdds also called read once only branching programs of ordered bdds obdds i e fbdds where variables are tested in the same order along all paths and binary decision trees bdts using well known techniques we first establish asymptotically sharp bounds as a function of n on the minimum size of arbitrary bdds representing almost all boolean functions of n variables and provide asymptotic lower and upper bounds differing only by a factor of two on the minimum size obdds representing almost all boolean functions of n variables we then using a method to obtain exponential lower bounds on complexity of computation of boolean functions by rbdd fbdd and obdd that originated in breitbart 1968 present the highest such bounds to date and also present improved bounds on the relative economy of description of particular boolean functions by the above classes of bdds for each nontrivial pair of bdd classes considered we exhibit infinite families of boolean functions representable much more concisely by bdds in one class than by bdds in the other

planar formulae and their uses we define the set of planar boolean formulae and then show that the set of true quantified planar formulae is polynomial space complete and that the set of satisfiable planar formulae is np complete using these results we are able to provide simple and nearly uniform proofs of np completeness for planar node cover planar hamiltonian circuit and line geometric connected dominating set and of polynomial space completeness for planar generalized geography the np completeness of planar node cover and planar hamiltonian circuit and line were first proved elsewhere m r garey and d s johnson the rectilinear steiner tree is np complete siam j appl math 32 1977 pp 826 834 and m r garey d s johnson and r e tarjan the planar hamilton circuit problem is np complete siam j comp 5 1976 pp 704 714

energy preserving schemes for nonlinear hamiltonian systems of wave equations application to the vibrating piano string the problem of the vibration of a string is well known in its linear form describing the transversal motion of a string nevertheless this description does not explain all the observations well enough nonlinear coupling between longitudinal and transversal modes seams to better model the piano string as does for instance the geometrically exact model gem this report introduces a general class of nonlinear systems nonlinear hamiltonian systems of wave equations in which fits the gem mathematical study of these systems is lead in a first part showing central properties energy preservation existence and unicity of a global smooth solution finite propagation velocity ldots space discretization is made in a classical way variational formulation and time discretization aims at numerical stability using an energy technique a definition of preserving schemes is introduced and we show that explicit schemes or partially implicit schemes which are preserving according to this definition cannot be built unless the model is linear a general energy preserving second order accurate fully implicit scheme is built for any continuous system that fits the nonlinear hamiltonian systems of wave equations class

conservative numerical methods for nonlinear strings in this article a class of numerical schemes for the simulation of nonlinear coupled longitudinal transverse string vibration is presented though there are various ways of arriving at such schemes special attention is paid here to energy conservation in nonlinear model systems and its transfer to an analogous discrete quantity in a difference scheme such exact numerical energy conservation can lead to simple global stability conditions which can be otherwise difficult to ascertain for nonlinear difference schemes in particular such conditions may be arrived at without any reliance on frequency domain concepts i e fourier or laplace transforms which are of only moderate utility in the analysis of nonlinear systems implementation details are discussed and numerical results are presented

ip pspace in this paper it is proven that when both randomization and interaction are allowed the proofs that can be verified in polynomial time are exactly those proofs that can be generated with polynomial space

attractors for nonautonomous 2d navier stokes equations with less regular normal forces abstract first the existence and structure of uniform attractors in h is proved for nonautonomous 2d navier stokes equations on bounded domain with a new class of distribution forces termed normal in l loc 2 r v see definition 3 1 which are translation bounded but not translation compact in l loc 2 r v then the properties of the kernel section are investigated last the fractal dimension is estimated for the kernel sections of the uniform attractors obtained

the othello game on an n n board is pspace complete abstract given an arbitrary position of the othello game played on an n n board the problem of determining the winner is shown to be pspace complete it can be reduced from generalized geography played on bipartite graphs with maximum degree 3

internal resonances in whirling strings involving longitudinal dynamics and material non linearities abstract internal resonance mechanisms between near commensurate longitudinal and transverse modes of a taut spatial string are identified and studied using an asymptotic method and the influence of material non linearities on the resulting solutions is considered geometrical non linearities couple longitudinal motions to in plane and out of plane transverse motions resulting in resonant and non resonant interactions between linearly orthogonal string modes past studies have included only transverse modes in the description of string motions and have predicted periodic quasi periodic and chaotic whirling motions arising from the geometrical non linearities this study considers further the inclusion of longitudinal motions and a non linear material law which are both appropriate for the study of rubber like strings an asymptotic analysis captures the aforementioned whirling motions as well as a new class of whirling motions with significant longitudinal content periodic quasi periodic and aperiodic likely chaotic responses are included among these motions their existence hardening softening characterization and stability are found to be highly dependent on the magnitude of the material non linearities

an algorithmic analysis of the honey bee game the honey bee game is a two player board game that is played on a connected hexagonal colored grid or in a generalized setting on a connected graph with colored nodes in a single move a player calls a color and thereby conquers all the nodes of that color that are adjacent to his own current territory both players want to conquer the majority of the nodes we show that winning the game is pspace hard in general np hard on series parallel graphs but easy on outer planar graphs in the solitaire version the goal of the single player is to conquer the entire graph with the minimum number of moves the solitaire version is np hard on trees and split graphs but can be solved in polynomial time on co comparability graphs

complexity of path forming games abstract for a number of two player games where players alternately choose the next vertex of a simple or an elementary path in a graph we consider the problem to determine whether for a given game instance there is a winning strategy for the first player we show several of these problems to be pspace complete in some special cases we obtain polynomial time algorithms based on graph rewriting or an intricate form of dynamic programming e g we show generalized geography and some other pspace complete problems to be linear time solvable on graphs with constant bounded treewidth

phutball is pspace hard we consider the nxn game of phutball it is shown that given an arbitrary position of stones on the board it is a pspace hard problem to determine whether the specified player can win the game regardless of the opponent s choices made during the game

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

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

complexity of path discovery game problems in this paper path discovery games are introduced and complexity of the game problems is studied it is shown that the path discovery game problem played on directed graphs is pspace complete and the path discovery game problem played on undirected graphs is in the class sspace nlogn moreover it is shown that the acyclic path discovery game problems played on directed graphs and on undirected graphs are both np complete

on the fairness and complexity of generalized k in a row games recently wu and huang i c wu d y huang a new family of k in a row games in the 11th advances in computer games conference acg 11 taipei taiwan september 2005 introduced a new game called connect6 where two players black and white alternately place two stones of their own color black and white respectively on an empty go like board except for that black the first player places one stone only for the first move the one who gets six consecutive horizontally vertically or diagonally stones of his color first wins the game unlike go moku connect6 appears to be fairer and has been adopted as an official competition event in computer olympiad 2006 connect m n k p q is a generalized family of k in a row games where two players place p stones on an mxn board alternatively except black places q stones in the first move the one who first gets his stones k consecutive in a line horizontally vertically or diagonally wins connect6 is simply the game of connect m n 6 2 1 in this paper we study two interesting issues of connect m n k p q fairness and complexity first we prove that no one has a winning strategy in connect m n k p q starting from an empty board when k 4p 7 and p q second we prove that for any fixed constants k p such that k p max 3 p and a given connect m n k p q position it is pspace complete to determine whether the first player has a winning strategy consequently this implies that connect6 played on an mxn board i e connect m n 6 2 1 is pspace complete

numerical solution procedures for nonlinear elastic rods using the theory of a cosserat point the theory of a cosserat point is developed as a continuum model which is inherently nonlinear and is valid for arbitrary constitutive equations here attention is confined to nonlinear elastic response which is hyperelastic with a strain energy function but large displacements deformations and rotations are allowed it is shown that the theory of a cosserat point can be used to formulate a numerical solution procedure for the dynamic three dimensional motion of nonlinear curved rods by modeling the rod as a set of n connected cosserat points like finite elements specifically the cosserat model allows for axial extension tangential shear deformation normal cross sectional extension normal cross sectional shear deformation and rotary inertia the cosserat approach ensures that the global forms of the balances of linear and angular momentum are satisfied and the hyperelastic nature of the constitutive equations is preserved since the response functions are determined by derivatives of a strain energy function a number of static example problems have been considered which examine the influence of shear deformation by comparing cosserat solutions with nonlinear solutions of an elastica

all structured programs have small tree width and good register allocation the register allocation problem for an imperative program is often modelled as the coloring problem of the interference graph of the control flow graph of the program the interference graph of a flow graph g is the intersection graph of some connected subgraphs of g these connected subgraphs represent the lives or life times of variables so the coloring problem models that two variables with overlapping life times should be in different registers for general programs with unrestricted gotos the interference graph can be any graph and hence we cannot in general color within a factor o n from optimality unless np p

a finite set of functions with an exptime complete composition problem we exhibit a finite family of functions over a finite set i e a finite algebra such that the problem whether a given function can be obtained as a composition of the members of this family i e is a member of the clone generated by the algebra is exptime complete

graph nonisomorphism has subexponential size proofs unless the polynomial time hierarchy collapses traditional hardness versus randomness results focus on time efficient randomized decision procedures we generalize these trade offs to a much wider class of randomized processes we work out various applications most notably to derandomizing arthur merlin games we show that every language with a bounded round arthur merlin game has subexponential size membership proofs for infinitely many input lengths unless exponential time coincides with the third level of the polynomial time hierarchy and hence the polynomial time hierarchy collapses since the graph nonisomorphism problem has a bounded round arthur merlin game this provides the first strong evidence that graph nonisomorphism has subexponential size proofs we also establish hardness versus randomness trade offs for space bounded computation

the monadic second order logic of graphs i recognizable sets of finite graphs abstract the notion of a recognizable set of finite graphs is introduced every set of finite graphs that is definable in monadic second order logic is recognizable but not vice versa the monadic second order theory of a context free set of graphs is decidable

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

complexity of some problems concerning varieties and quasi varieties of algebras in this paper we consider the complexity of several problems involving finite algebraic structures given finite algebras a and b these problems ask the following 1 do a and b satisfy precisely the same identities 2 do they satisfy the same quasi identities 3 do a and b have the same set of term operations in addition to the general case in which we allow arbitrary finite algebras we consider each of these problems under the restrictions that all operations are unary and that a and b have cardinality two we briefly discuss the relationship of these problems to algebraic specification theory

the accelerated k in a row game we investigate two versions of the well known k in a row game while in the most intriguing k 5 case the outcome of the game has been recently settled very little is known about what happens when the rules are changed a natural modification is that the players take more than one square of the board per move in order to speed up the game our main goal is to improve the quadratic bound on the error term given by csirmaz in csirmaz discrete math 29 1980 19 23 to a logarithmic one for the accelerated k in a row the other issue is the extreme sensitivity of k in a row under biased rules beck proposed in beck unpublished lecture notes that a player may trade some of his freedom of choice for the right of taking more squares than his opponent we prove logarithmic bounds on the error term in that case too

monadic second order evaluations on tree decomposable graphs abstract every graph generated by a hyperedge replacement graph grammar can be represented by a tree namely the derivation tree of the derivation sequence that produced it certain functions on graphs can be computed recursively on the derivation trees of these graphs by using monadic second order logic and semiring homomorphisms we describe in a single formalism a large class of such functions polynomial and even linear algorithms can be constructed for some of these functions we unify similar results obtained by takamizawa 1982 bern 1987 arnborg 1991 and habel 1989

efficient solution to connectivity problems on hierarchically defined graphs using hierarchical definitions we can describe very large graphs in small spaces in this paper we discuss how such succinct graph descriptions can be used to speed up the solution of graph problems we present the bottom up method that solves graph problems without expanding the hierarchical description this allows solutions that are efficient in terms of the hierarchical graph description instead of the size of the expanded graph we exemplify the method by giving efficient solutions to connectivity problems on hierarchical graphs our results have applications in computer aided design for integrated circuit design and other engineering problems

inertial manifolds for the 3d modified leray α model abstract in this paper we investigate the critical modified leray model in t 3 and prove the existence of an n dimensional inertial manifold for this problem

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

on the complexity of vlsi implementations and graph representations of boolean functions with application to integer multiplication lower bound results on boolean function complexity under two different models are discussed the first is an abstraction of tradeoffs between chip area and speed in very large scale integrated vlsi circuits the second is the ordered binary decision diagram obdd representation used as a data structure for symbolically representing and manipulating boolean functions the lower bounds demonstrate the fundamental limitations of vlsi as an implementation medium and that of the obdd as a data structure it is shown that the same technique used to prove that any vlsi implementation of a single output boolean function has area time complexity at sup 2 omega n sup 2 also proves that any obdd representation of the function has omega c sup n vertices for some c 1 but that the converse is not true an integer multiplier for word size n with outputs numbered 0 least significant through 2n 1 most significant is described for the boolean function representing either output i 1 or output 2n i 1 where 1

symmetric space bounded computation abstract a symmetric turing machine is one such that the yields relation between configurations is symmetric the space complexity classes for such machines are found to be intermediate between the corresponding deterministic and nondeterministic space complexity classes certain natural problems are shown to be complete for symmetric space complexity classes and the relationship of symmetry to determinism and nondeterminism is investigated

the biased distance restricted n in a row game for small p the biased n in a row game was shown to be a win for the first player for any n by j beck to limit the advantage of picking more than one point per move he suggested a weak form of the game where the first player s p points for each move must be contained in a circle of radius r for p 2 we give a tight bound for the maximum length of the line where the first player can force a win answering an open problem posed by csorba

decision algorithms for multiplayer noncooperative games of incomplete information abstract extending the complexity results of reif 1 2 for two player games of incomplete information this paper see also 3 presents algorithms for deciding the outcome for various classes of multiplayer games of incomplete information i e deciding whether or not a team has a winning strategy for a particular game our companion paper 4 shows that these algorithms are indeed asymptotically optimal by providing matching lower bounds the classes of games to which our algorithms are applicable include games which were not previously known to be decidable we apply our algorithms to provide alternative upper bounds and new time space trade offs on the complexity of multiperson alternating turing machines 3 we analyze the algorithms to characterize the space complexity of multiplayer games in terms of the complexity of deterministic computation on turing machines in hierarchical multiplayer games each additional clique subset of players with the same information increases the complexity of the outcome problem by a further exponential we show that an s n space bounded k player game of incomplete information has a deterministic time upper bound of k 1 repeated exponentials of s n furthermore s n space bounded k player blindfold games have a deterministic space upper bound of k repeated exponentials of s n this paper proves that this exponential blow up can occur we also show that time bounded games do not exhibit such hierarchy a t n time bounded blindfold multiplayer game as well as a t n time bounded multiplayer game of incomplete information has a deterministic space bound of t n

preprocessing of intractable problems some computationally hard problems e g deduction in logical knowledge bases are such that part of an instance is known well before the rest of it and remains the same for several subsequent instances of the problem in these cases it is useful to preprocess off line this known part so as to simplify the remaining on line problem in this paper we investigate such a technique in the context of intractable i e np hard problems recent results in the literature show that not all np hard problems behave in the same way for some of them preprocessing yields polynomial time on line simplified problems we call them compilable while for other ones their compilability implies some consequences that are considered unlikely our primary goal is to provide a sound methodology that can be used to either prove or disprove that a problem is compilable to this end we define new models of computation complexity classes and reductions we find complete problems for such classes completeness meaning they are the less likely to be compilable we also investigate preprocessing that does not yield polynomial time on line algorithms but generically decreases complexity this leads us to define hierarchies of compilability that are the analog of the polynomial hierarchy a detailed comparison of our framework to the idea of parameterized tractability shows the differences between the two approaches

the complexity of propositional linear temporal logics the complexity of satisfiability and determination of truth in a particular finite structure are considered for different propositional linear temporal logics it is shown that these problems are np complete for the logic with f and are pspace complete for the logics with f x with u with u s x operators and for the extended logic with regular operators given by wolper

computation of equilibriain noncooperative games this paper presents algorithms for finding equilibria of mixed strategy in multistage noncooperative games of incomplete information like probabilistic blindfold chess where at every opportunity a player can perform different moves with some probability these algorithms accept input games in extensive form our main result is an algorithm for computing aeguential equilibrium which is the most widely accepted notion of equilibrium for mixed strategies of noncooperative probabilistic games in mainstream economic game theory previously there were no known algorithms for computing sequential equilibria strategies except for the special case of single stage games the computational aspects of passage from a recursive presentation of a game to its extensive form are also discussed for nontrivial inputs the concatenation of this procedure with the equilibrium computation is time intensive but has low spatial requirements given a recursively represented game with a position space bound s n and a log space computable next move relation we can compute an example mixed strategy satisfying the sequential equilibria condition all in space bound o s n 2 furthermore in space o s n 3 we can compute the connected components of mixed strategies satisfying sequential equilibria

games on interval and permutation graph representations we describe combinatorial games on graphs in which two players antagonistically build a representation of a subgraph of a given graph we show that for a large class of these games determining whether a given instance is a winning position for the next player is pspace hard in contrast we give polynomial time algorithms for solving some versions of the games on trees

reaching and distinguishing states of distributed systems some systems interact with their environment at physically distributed interfaces called ports and in testing such a system it is normal to place a tester at each port each tester observes only the events at its port and it is known that this limited observational power introduces additional controllability and observability problems into testing given a multiport finite state machine fsm m we consider the problems of defining strategies for the testers either to reach a given state of m or to distinguish two states of m these are important problems since most techniques for testing from a single port fsm use sequences that reach and distinguish states both problems can be solved in low order polynomial time for single port fsms but we prove that the corresponding decision problems are undecidable for multiport fsms however we also show that they can be solved in low order polynomial times for deterministic fsms if we restrict our attention to controllable tests these results have important ramifications for testing from a multiport fsm since they suggest that methods for testing from a single port fsm cannot be easily adapted in addition two fsms can be distinguished if and only if their initial states can be distinguished and so the results suggest that in contrast to single port fsms we cannot expect to produce general complete test generation methods for multiport fsms