computational complexity of inner and outer j radii of polytopes in finite dimensional normed spaces this paper studies the complexity of computing or approximating or bounding the various inner and outer radii of ann dimensional convex polytope in the space n equipped with an lp norm or a polytopal norm the polytopep is assumed to be presented as the convex hull of finitely many points with rational coordinates v presented or as the intersection of finitely many closed halfspaces defined by linear inequalities with rational coefficients presented the innerj radius ofp is the radius of a largestj ball contained inp it isp s inradius whenj n and half ofp s diameter whenj 1 the outerj radius measures how wellp can be approximated in a minimax sense by an n j flat it isp s circumradius whenj n and half ofp s width whenj 1 the binary turing machine model of computation is employed the primary concern is not with finding optimal algorithms but with establishing polynomial time computability or np hardness special attention is paid to the case in whichp is centrally symmetric when the dimensionn is permitted to vary the situation is roughly as follows a for general presented polytopes in lp spaces with 1

a new approach to the derivation of binary non markovian kinetic equations abstract a universal method of derivation of infinite hierarchies for partial distribution functions and correlation forms in the thermodynamic limit has been developed it is based on the consideration of reacting systems in the fock space hierarchy closure methods available in the literature are shown to give incorrect binary kinetic equations of the reaction a b b in some critical cases a new approach to hierarchy closure has been proposed it consists in neglecting contributions from four particle correlations and in adapting the faddeev method of the three body theory to the extraction of a binary part of three particle evolution for the model of the reaction a b b the proposed method gives correct kinetic equations obtained earlier on the basis of diagram summation it gives the theoretical basis for derivation of binary kinetic equations for realistic reacting systems

hard promise problems and nonuniform complexity for every recursive set a let pp a denote the following promise problem input x and y promise x a y a property x a we show that if l is a solution of pp a then a p l poly from this result it follows that if a is t p hard for np then all solutions of pp a are hard for np under a reduction that generalizes both t p and t sn specifically if a is np hard then all solutions of pp a are generalized high2 bbs86b the main theorem that leads to this result states that if b is a self reducible set b t p a and a p l poly then 2 p b 2 p l several interesting connections between uniform and nonuniform complexity follow directly from this theorem

a semidefinite hierarchy for containment of spectrahedra a spectrahedron is the positivity region of a linear matrix pencil and thus the feasible set of a semidefinite program we propose and study a hierarchy of sufficient semidefinite conditions to certify the containment of a spectrahedron in another one this approach comes from applying a moment relaxation to a suitable polynomial optimization formulation the hierarchical criterion is stronger than a solitary semidefinite criterion discussed earlier by helton klep and mccullough as well as by the authors moreover several exactness results for the solitary criterion can be brought forward to the hierarchical approach the hierarchy also applies to the equivalent question of checking whether a map between matrix sub spaces is positive in this context the solitary criterion checks whether the map is completely positive and thus our results provide a hierarchy between positivity and complete positivity

the cauchy integral in cn for domains with minimal smoothness abstract we prove l p b d regularity of the cauchy leray integral for bounded domains d c n whose boundary satisfies the minimal regularity condition of class c 1 1 together with a naturally occurring notion of convexity

exploiting functional dependencies in declarative problem specifications in this paper we tackle the issue of the automatic recognition of functional dependencies among guessed predicates in constraint problem specifications functional dependencies arise frequently in pure declarative specifications because of the intermediate results that need to be computed in order to express some of the constraints or due to precise modeling choices e g to provide multiple viewpoints of the search space in order to increase constraint propagation in either way the recognition of dependencies greatly helps solvers allowing them to avoid spending search on unfruitful branches while maintaining the highest degree of declarativeness by modeling constraint problem specifications as second order formulae we provide a characterization of functional dependencies in terms of semantic properties of first order ones and prove undecidability of the problem of their recognition despite such negative result we advocate the in many cases effective possibility of using automated tools to mechanize this task additionally we show how suitable search procedures can be automatically synthesized in order to exploit recognized dependencies we present opl examples of various problems taken from bio informatics planning and resource allocation and show how in many cases opl greatly benefits from the addition of such search procedures moreover we also give evidence that writing sophisticated ad hoc search procedures that handle dependencies exploiting the peculiarities of the particular problem is a very difficult and error prone task which in many cases does not seem to pay off

a many particle derivation of non markovian kinetic equations of reversible reaction a b c in solutions based on the effective pairs approach abstract the non markovian kinetic equations for local concentrations have been derived in the effective pairs approximation on the basis of the hierarchy for correlation patterns of the reversible reaction a b c the equations are shown to agree with the kinetic and thermodynamic detailed balancing principles as compared to the integral encounter theory equations obtained earlier the above equations have a wider time range of applicability and may form the basis for the development of a binary approximation for the reversible reaction a b c in solutions

consideration of initial correlations of the same type in reactions a b b and a b c b abstract a new method is used to derive the binary non markovian integro differential kinetic equations of irreversible reactions with respect to initial correlations of the same type the source of inhomogeneous integro differential equation is determined by initial correlations which is in full accord with the properties of kinetic equations of non equilibrium statistical mechanics a procedure is found to reduce the derived equations into the differential form of the equations of chemical kinetics

parameterized learnability of juntas we study the parameterized complexity of learning k juntas and some variations of juntas we show the hardness of learning k juntas and subclasses of k juntas in the pac model by reductions from a w 2 complete problem on the other hand as a consequence of a more general result we show that k juntas are exactly learnable with improper equivalence queries and access to a w p oracle

polyhedral boundary projection we consider the problem of projecting a point in a polyhedral set onto the boundary of the set using an arbitrary norm for the projection two types of polyhedral sets one defined by a convex combination of k points in rn and the second by the intersection of m closed half spaces in rn lead to disparate optimization problems for finding such a projection the first case leads to a mathematical program with a linear objective function and constraints that are linear inequalities except for a single nonconvex cylindrical constraint interestingly for the 1 norm this nonconvex problem can be solved by solving 2n linear programs the second polyhedral set leads to a much simpler problem of determining the minimum of m easily evaluated numbers these disparate mathematical complexities parallel known ones for the related problem of finding the largest ball with radius measured by an arbitrary norm that can be inscribed in the polyhedral set for a polyhedral set of the first type this problem is np hard for the 2 norm and the infty norm r m freund and j b orlin math programming 33 1985 pp 139 145 and solvable by a single linear program for the 1 norm p gritzmann and v klee math programming 59 1993 pp 163 213 while for the second type this problem leads to a single linear program even for a general norm p gritzmann and v klee discrete comput geom 7 1992 pp 255 280

deciding uniqueness in norm maximization np hardness is established for the problem whose instance is a system of linear inequalities defining a polytopep and whose question is whether onp the global maximum of the euclidean norm is attained at more than one vertex ofp the np hardness persists even for the restricted problem in whichp is a full dimensional parallelotope with one vertex at the origin this makes it possible to establish np hardness for other uniqueness problems including some from pseudoboolean programming and computational convexity

t matrix representation and long time behavior of observables in the theory of migration influenced irreversible reactions in liquid solutions abstract the theory of migration influenced irreversible reactions upon binary encounters of reactants in liquid solutions is formulated in terms similar to those of quantum scattering theory free motion of a reacting pair in the configuration space is a random walk in three dimensional infinite space and arbitrary markovian motion over internal degrees of freedom in the case of mixing by free motion general asymptotic properties of the free resolvent describing this motion have been established general long time kinetic law of the attainment of steady state values by the observables in bulk and geminate reactions has been deduced thermodynamically not only the universality of their long time dependence is important but also the fact that the rate of attaining the steady state values is completely determined by macroscopic quasi equilibrium observables

calculus of fuzzy vector valued functions and almost periodic fuzzy vector valued functions on time scales abstract in this paper we establish an embedding theorem for the fuzzy multidimensional space and introduce the new types of multiplications of fuzzy vectors determined by the determinant algorithm then some fundamental results of calculus of fuzzy vector valued functions on time scales are established based on these results we introduce the concept of shift almost periodic fuzzy vector valued functions and develop a theory of almost periodic fuzzy functions on time scales this function theory can be used to study almost periodic fuzzy dynamic equations on time scales including a new type of fuzzy dynamic equations called fuzzy q dynamic equation i e quantum fuzzy dynamic equation

a natural encoding scheme proved probabilistic polynomial complete abstract we prove a natural encoding scheme to be intractable by showing it ur complete a technique which may be used when a problem does not yield to a proof of np completeness this is the first non number theoretic problem that is ur complete but not known to be np complete we also redefine ur completeness henceforth referred to as pr completeness in probabilistic terms thus making the notion conceptually simpler our result suggests that pr completeness may be a more widely applicable technique than was previously believed

containment problems for polytopes and spectrahedra we study the computational question of whether a given polytope or spectrahedron s a as given by the positive semidefiniteness region of a linear matrix pencil a x is contained in another s b first we classify the computational complexity extending results on the polytope polytope case by gritzmann and klee to the polytope spectrahedron case for various restricted containment problems np hardness is shown we then study in detail semidefinite conditions to certify containment building upon work by ben tal and nemirovski and helton klep and mccullough in particular we discuss variations of a sufficient semidefinite condition to certify containment of a spectrahedron in a spectrahedron it is shown that these sufficient conditions even provide exact semidefinite characterizations for containment in several important cases including containment of a spectrahedron in a polyhedron moreover in the case of bounded s a the criteria will always succeed in certifying containment of some scale

hard core theorems for complexity classes nancy lynch proved that if a decision problem a is not solvable in polynomial time then there exists an infinite recursive subset x of its domain on which the decision is almost everywhere complex in this paper general theorems of this kind that can be applied to several well known automata based complexity classes including a common class of randomized algorithms are proved

lower bounds for lovasz schrijver systems and beyond follow from multiparty communication complexity we prove that an omega log 4 n lower bound for the three party number on the forehead nof communication complexity of the set disjointness function implies an n omega 1 size lower bound for treelike lovasz schrijver systems that refute unsatisfiable formulas in conjunctive normal form cnfs more generally we prove that an n omega 1 lower bound for the k 1 party nof communication complexity of set disjointness implies a 2 n omega 1 size lower bound for all treelike proof systems whose formulas are degree k polynomial inequalities

on the unique satisfiability problem unique sat is the problem of deciding whether a given boolean formula has exactly one satisfying truth assignment this problem is a typical moreover complete representative of a natural class of problems about unique solutions all these problems belong to the class dife l1 l2 l1 lz np studied by papadimitriou and yannakakis we consider the relationship between these two classes particularly whether unique sat is dife complete it is if np co np we construct an oracle relative to which unique sat is not complete for dif and another oracle relative to which unique sat is complete for dif e whereas np v co np

linear time algorithms for linear programming in r 3 and related problems linear time algorithms for linear programming in r 2 and r 3 are presented the methods used are applicable for other graphic and geometric problems as well as quadratic programming for exam

intrinsic volumes and successive radii motivated by a problem of teissier to bound the intrinsic volumes of a convex body in terms of the inradius and the circumradius of the body we give upper and lower bounds for the intrinsic volumes of a convex body in terms of the elementary symmetric functions of the so called successive inner and outer radii these results improve on former bounds and in particular they also provide bounds for the elementary symmetric functions of the roots of steiner polynomials in terms of the elementary symmetric functions of these radii

approximating the radii of point sets we consider the problem of computing the outer radii of point sets in this problem we are given integers n d and k where k le d and a set p of n points in re d the goal is to compute the outer k radius of p denoted by cal r k p which is the minimum over all d k dimensional flats f of max p in p d p f where d p f is the euclidean distance between the point p and flat f computing the radii of point sets is a fundamental problem in computational convexity with many significant applications the problem admits a polynomial time algorithm when the dimension d is constant u faigle w kern and m streng math program 73 1996 pp 1 5 here we are interested in the general case in which the dimension d is not fixed and can be as large as n where the problem becomes np hard even for k 1 it is known that r k p can be approximated in polynomial time by a factor of 1 varepsilon for any varepsilon 0 when d k is a fixed constant m babdoiu s har peled and p indyk in proceedings of the acm symposium on the theory of computing 2002 s har peled and k varadarajan in proceedings of the acm symposium on computing geometry 2002 a polynomial time algorithm that guarantees a factor of o sqrt log n approximation for r 1 p the width of the point set p is implied by the results of nemirovski roos and terlaky math program 86 1999 pp 463 473 and nesterov handbook of semidefinite programming theory algorithms kluwer academic publishers norwell ma 2000 in this paper we show that r k p can be approximated by a ratio of o sqrt log n for any 1 leq k leq d thus matching the previously best known ratio for approximating the special case r 1 p the width of point set p our algorithm is based on semidefinite programming relaxation with a new mixed deterministic and randomized rounding procedure we also prove an inapproximability result that gives evidence that our approximation algorithm is doing well for a large range of k we show that there exists a constant delta 0 such that the following holds for any 0 eps 1 there is no polynomial time algorithm that approximates r k p within log n delta for all k such that k leq d d varepsilon unless np subseteq dtime 2 log m o 1 our inapproximability result for r k p extends a previously known hardness result of brieden discrete comput geom 28 2002 pp 201 209 and is proved by modifying brieden s construction using basic ideas from probabilistically checkable proofs pcp theory

on computing the diameter of a point set in high dimensional euclidean space we consider the problem of computing the diameter of a set of n points in d dimensional euclidean space under euclidean distance function we describe an algorithm that in time o dnlogn n2 finds with high probability an arbitrarily close approximation of the diameter for large values of d the complexity bound of our algorithm is a substantial improvement over the complexity bounds of previously known exact algorithms computing and approximating the diameter are fundamental primitives in high dimensional computational geometry and find practical application for example in clustering operations for image databases

note on the computational complexity of j radii of polytopes in r n we show that for fixed dimensionn the approximation of inner and outer j radii of polytopes in n endowed with the euclidean norm is in our method is based on the standard polynomial time algorithms for solving a system of polynomial inequalities over the reals in fixed dimension

a many particle approach to the derivation of binary non markovian kinetic equations for the reaction a b b abstract many particle methods of physical kinetics have been adapted to a many particle consideration of irreversible reactions a b b in liquid solutions the correctness of the diagrammatic approach developed is demonstrated using the exactly solvable problem appropriate scaling procedure has been devised for the extraction of a binary kinetics on its basis the conception of pair uncorrelated encounters of reactants in liquid solutions has been generalized and the concept of the effective pair has been introduced binary non markovian kinetic equations of the reaction for uniform initial distribution of b species obtained earlier are reproduced for the first time integro differential kinetic equations of the reaction in spatially non uniform normal systems have been derived

a many particle derivation of the integral encounter theory non markovian kinetic equations of the reversible reaction a b c in solutions the non markovian binary kinetic equations for a rather realistic model of association dissociation reaction a b c in liquid solutions are derived using a newly developed method based on a many particle consideration the method leads to an infinite hierarchy for correlation patterns that can be truncated at the first step on a two particle level to give the integral encounter theory result it is shown that although being restricted in time the theory predicts true equilibrium concentrations of reactants and the equilibrium constant corresponding to the thermodynamic detailed balancing principle

np is as easy as detecting unique solutions abstract for every known np complete problem the number of solutions of its instances varies over a large range from zero to exponentially many it is therefore natural to ask if the inherent intractability of np complete problem is caused by this wide variation we give a negative answer to this question using the notion of randomized polynomial time reducibility we show that the problems of distinguishing between instances of sat having zero or one solution or of finding solutions to instances of sat having a unique solution are as hard as sat under randomized reductions several corollaries about the difficulty of specific problems follow for example computing the parity of the number of solutions of a sat formula is shown to be np hard and deciding if a sat formula has a unique solution is shown to be d p hard under randomized reduction central to the study of cryptography is the question as to whether there exist np problems whose instances have solutions that are unique but are hard to find our result can be interpreted as strengthening the belief that such problems exist

mind change optimal learning of bayes net structure from dependency and independency data this paper analyzes the problem of learning the structure of a bayes net in the theoretical framework of gold s learning paradigm bayes nets are one of the most prominent formalisms for knowledge representation and probabilistic and causal reasoning we follow constraint based approaches to learning bayes net structure where learning is based on observed conditional dependencies and independencies between variables of interest e g the data are of the form x is dependent on y given any assignment to variables s or of the form x is independent of y given any assignment to variables s applying learning criteria in this model leads to the following results 1 the mind change complexity of identifying a bayes net graph over variables v from either dependency data or from independency data are v 2 the maximum number of edges 2 there is a unique fastest mind change optimal bayes net learner for either data type convergence speed is evaluated using gold s dominance notion of uniformly faster convergence for dependency data the optimal learner conjectures a graph if it is the unique bayes net pattern that satisfies the observed dependencies with a minimum number of edges and outputs no guess otherwise for independency data the optimal learner conjectures a graph if it is the unique bayes net pattern that satisfies the observed dependencies with a maximum number of edges and outputs no guess otherwise we investigate the complexity of computing the output of the fastest mind change optimal learner for either data type and show that each of these two problems is np hard assuming p rp to our knowledge these are the first np hardness results concerning the existence of a uniquely optimal bayes net structure

non commutative arithmetic circuits depth reduction and size lower bounds abstract we investigate the phenomenon of depth reduction in commutative and non commutative arithmetic circuits we prove that in the commutative setting uniform semi unbounded arithmetic circuits of logarithmic depth are as powerful as uniform arithmetic circuits of polynomial degree and unrestricted depth earlier proofs did not work in the uniform setting this also provides a unified proof of the circuit characterizations of the class logcfl and its counting variant logcfl we show that ac1 has no more power than arithmetic circuits of polynomial size and degree no log log n improving the trivial bound of no log n connections are drawn between tc1 and arithmetic circuits of polynomial size and degree then we consider non commutative computation we show that over the algebra max concat arithmetic circuits of polynomial size and polynomial degree can be reduced to o log2 n depth and even to o log n depth if unbounded fanin gates are allowed this establishes that optlogcfl is in ac1 this is the first depth reduction result for arithmetic circuits over a non commutative semiring and it complements the lower bounds of kosaraju and nisan showing that depth reduction cannot be done in the general non commutative setting we define new notions called short left paths and short right paths and we show that these notions provide a characterization of the classes of arithmetic circuits for which optimal depth reduction is possible this class also can be characterized using the auxpda model finally we characterize the languages generated by efficient circuits over the semiring 2 union concat in terms of simple one way machines and we investigate and extend earlier lower bounds on non commutative circuits

the complexity of vertex enumeration methods the computational complexity of problems relating to the enumeration of all the vertices of a convex polyhedron defined by linear inequalities is examined several published approaches are evaluated in this light a new algorithm is described and shown to have a better complexity estimate than existing methods empirical evidence supporting the theoretical superiority is presented finally vertex enumeration is discussed when the space containing the polyhedra is of fixed dimension and only the size of the inequality system is permitted to vary

a solution operator for bar partial on the hartogs triangle and l p lp estimates an integral solution operator for bar partial is constructed on product domains that include the punctured bidisc this operator is shown to satisfy l p estimates for all 1 le p infty though with non standard relative to strongly pseudoconvex domains bounding term these estimates imply l p estimates for bar partial on the hartogs triangle with greater range of p than the canonical solution satisfies

on polynomial time turing and many one completeness in pspace meyer and paterson 1979 investigated pm reducibility of pspace complete sets to sparse sets we point out that their observation indicates the difference between the powers of pt and pm reducibilities and establish a machinery that uses this difference for separating pt completeness from pm completeness in pspace by using this machinery we show the difference between pt and pm completeness notions in pspace from each of the following assumptions i a randomized completeness notion differs from a deterministic one in pspace and ii pspace has a dense set almost every element of which is hard to produce by any polynomial time computation

some np complete problems in quadratic and nonlinear programming in continuous variable smooth nonconvex nonlinear programming we analyze the complexity of checking whether a a given feasible solution is not a local minimum and b the objective function is not bounded below on the set of feasible solutions we construct a special class of indefinite quadratic programs with simple constraints and integer data and show that checking a or b on this class is np complete as a corollary we show that checking whether a given integer square matrix is not copositive is np complete

constant round interactive proofs for delegating computation the celebrated sf ip sf pspace theorem lund fortnow karloff and nisan j acm 39 1992 pp 859 868 shamir j acm 39 1992 pp 869 877 allows an all powerful but untrusted pro

largest j simplices in d cubes some relatives of the hadamard maximum determinant problem abstract this paper studies the computationally difficult problem of finding a largest j dimensional simplex in a given d dimensional cube the case in which j d is of special interest for it is equivalent to the hadamard maximum determinant problem it has been solved for infinitely many values of d but not for d 14 the subcase in which j d 3 mod 4 subsumes the famous problem on the existence of hadamard matrices the known results for the case j d are here summarized and used but the main focus is on fixed small values of j when j 1 the problem is trivial and when j 2 or j 3 it is here solved completely i e for all d beyond that the results are fragmentary but numerous and they lead to several attractive conjectures some other problems involving simplices in cubes are mentioned and the relationship of largest simplices to d optimal weighing designs is discussed

on computing all abductive explanations from a propositional horn theory abduction is a fundamental mode of reasoning with applications in many areas of ai and computer science the computation of abductive explanations is an important computational problem which is at the core of early systems such as the atms and clause management systems and is intimately related to prime implicate generation in propositional logic many algorithms have been devised for computing some abductive explanation and the complexity of the problem has been well studied however little attention has been paid to the problem of computing multiple explanations and in particular all explanations for an abductive query we fill this gap and consider the computation of all explanations of an abductive query from a propositional horn theory or of a polynomial subset of them our study pays particular attention to the form of the query ranging from a literal to a compound formula to whether explanations are based on a set of abducible literals and to the representation of the horn theory either by a horn conjunctive normal form cnf or model based in terms of its characteristic models for these combinations we present either tractability results in terms of polynomial total time algorithms intractability results in terms of nonexistence of such algorithms unless p e np or semi tractability results in terms of solvability in quasi polynomial time established by polynomial time equivalence to the problem of dualizing a monotone cnf expression our results complement previous results in the literature and refute a longstanding conjecture by selman and levesque they elucidate the complexity of generating all abductive explanations and shed light on related problems such as generating sets of restricted prime implicates of a horn theory the algorithms for tractable cases can be readily applied for generating a polynomial subset of explanations in polynomial time

optimal scaling of balls and polyhedra the concern is with solving as linear or convex quadratic programs special cases of the optimal containment and meet problems the optimal containment or meet problem is that of finding the smallest scale of a set for which some translation contains a set or meets each element in a collection of sets respectively these sets are unions or intersections of cells where a cell is either a closed polyhedral convex set or a closed solid ball

real hypersurfaces orders of contact and applications a fundamental problem in the modem theory of several complex variables concerns the boundary behavior of the cauchy riemann equations suppose that d is an open domain in cn and that its boundary m is a smooth real submanifold of cn how does the geometry of m influence the function theory on d one approach to this question is the a neumann problem 6 there one studies the inhomogeneous cauchy riemann equations au a where a is a 0 q form with distribution coefficients on the closed domain d u m satisfying the necessary compatibility condition a a 0 the a neumann problem constructs a particular solution u which is orthogonal to the null space of the complex laplacian kohn 10a has solved this problem and has shown that good local regularity properties for u in terms of a follow from so called subelliptic estimates it is natural to seek geometric conditions on m that are necessary and sufficient for these estimates in this paper we will be concerned with a certain geometric condition on m that we feel is the right one for subellipticity although the motivation for the questions discussed here comes from partial differential equations the techniques come from algebraic geometry to see why we state theorems of kohn greiner and catlin concerning subellipticity kohn 1oa has discovered a sufficient condition for a subelliptic estimate near a fixed point p in m in case d is pseudoconvex and is contained in c2 this condition is equivalent to the finiteness of order of tangency of every complex analytic one dimensional manifold with m at p greiner 13 established the necessity of this condition in

an integral kernel for weakly pseudoconvex domains a new explicit construction of cauchy fantappie kernels is introduced for an arbitrary weakly pseudoconvex domain with smooth boundary while not holomorphic in the parameter the new kernel reflects the complex geometry and the levi form of the boundary some estimates are obtained for the corresponding integral operator which provide evidence that this kernel and related constructions give useful new tools for complex analysis on this general class of domains

exactly solvable models in the theory of irreversible reactions in liquids abstract exact kinetic equations defining the a b b reaction in liquid solutions are obtained on the basis of a many particle approach and the notion of point reacting particles with remote reactivity for any initial correlations in the system of reactants the calculation of many particle kinetics is shown to reduce to the calculation of survival probability of one particle a in the ensemble of particles b in the context of the most general model the exact equations in the thermodynamic limit are obtained the equations define the process which develops from two classes of initial correlations those of the same type corresponding to the reactions in the bulk and polytypic correlations corresponding to the reactions in non isolated geminate pairs

the complexity of promise problems with applications to public key cryptography a promise problem is a formulation of partial decision problem complexity issues about promise problems arise from considerations about cracking problems for public key cryptosystems using a notion of turing reducibility between promise problems this paper disproves a conjecture made by even and yacobi 1980 that would imply nonexistence of public key cryptosystems with np hard cracking problems in its place a new conjecture is raised having the same consequence in addition the new conjecture implies that np complete sets cannot be accepted by turing machines that have at most one accepting computation for each input word

semi analytical computation of laplacian green functions in three dimensional domains with disconnected spherical boundaries abstract the generalized method of separation of variables gmsv is applied to solve boundary value problems for the laplace operator in three dimensional domains with disconnected spherical boundaries e g an arbitrary configuration of non overlapping partially reactive spherical sinks or obstacles we consider both exterior and interior problems and all most common boundary conditions dirichlet neumann robin and conjugate one using the translational addition theorems for solid harmonics to switch between the local spherical coordinates we obtain a semi analytical expression of the green function as a linear combination of partial solutions whose coefficients are fixed by boundary conditions although the numerical computation of the coefficients involves series truncation and solution of a system of linear algebraic equations the use of the solid harmonics as basis functions naturally adapted to the intrinsic symmetries of the problem makes the gmsv particularly efficient especially for exterior problems the obtained green function is the key ingredient to solve boundary value problems and to determine various characteristics of stationary diffusion such as reaction rate escape probability harmonic measure residence time and mean first passage time to name but a few the relevant aspects of the numerical implementation and potential applications in chemical physics heat transfer electrostatics and hydrodynamics are discussed

on the complexity of unique solutions on montre que le probleme de savoir si un cas du probleme du commis voyageur a une solution uniquement optimale est complet pour 2 p