computational complexity of holant problems we propose and explore a novel alternative framework to study the complexity of counting problems called holant problems compared to counting constraint satisfaction problems csp it is a refinement with a more explicit role for the constraint functions both graph homomorphism and csp can be viewed as special cases of holant problems we prove complexity dichotomy theorems in this framework our dichotomy theorems apply to local constraint functions which are symmetric functions on boolean input variables and evaluate to arbitrary real or complex values we discover surprising tractable subclasses of counting problems which could not easily be specified in the csp framework when all unary functions are assumed to be free mathrm holant problems the tractable ones consist of functions that are degenerate or of arity at most two or holographic transformations of fibonacci gates when only two special unary functions the constant zero and constant one functions are assumed to be free mathrm holant c problems we further identify three special families of tractable cases then we prove that all other cases are p hard the main technical tool we use and develop is holographic reductions another technical tool used in combination with holographic reductions is polynomial interpolations

a collapse theorem for holographic algorithms with matchgates on domain size at most 4 holographic algorithms with matchgates are a novel approach to design polynomial time computation they use kasteleyn s algorithm for perfect matchings and more importantly a holographic reduction the two fundamental parameters of a holographic reduction are the domain size k of the underlying problem and the basis size a holographic reduction transforms the computation to matchgates by a linear transformation that maps to a tensor product space of a linear space of dimension 2 we prove a sharp basis collapse theorem which shows that for domain size 3 and 4 all non trivial holographic reductions can be expressed with a basis of size 1 or 2 respectively the main proof techniques are matchgate identities and a group property of matchgate signatures

an effective dichotomy for the counting constraint satisfaction problem bulatov proceedings of the 35 th international colloquium on automata languages and programming part 1 lecture notes in comput sci 5125 springer new york 2008 pp 646 661 gave a dichotomy for the counting constraint satisfaction problem csp a problem from csp is characterized by a constraint language gamma a fixed finite set of relations over a finite domain d an instance of the problem uses these relations to constrain an arbitrarily large finite set of variables bulatov showed that the problem of counting the satisfying assignments of instances of any problem from csp is either in polynomial time fp or is p complete his proof draws heavily on techniques from universal algebra and cannot be understood without a secure grasp of that field we give an elementary proof of bulatov s dichotomy based on succinct representations which we call frames of a class of highly structured relations which we call strongly rectangular we show that these are precisely the relation

the complexity of counting cuts and of computing the probability that a graph is connected several enumeration and reliability problems are shown to be p complete and hence at least as hard as np complete problems included are important problems in network reliability analysis namely computing the probability that a graph is connected and counting the number of minimum cardinality s t cuts or directed network cuts also shown to be p complete are counting vertex covers in a bipartite graph counting antichains in a partial order and approximating the probability that a graph is connected and the probability that a pair of vertices is connected

periodic solutions of semilinear equations of evolution of compact type abstract the existence of solutions in a weak sense of x a b t x x f t x x 0 x t is established under the conditions that a generates a semigroup of compact type on a hilbert space h b t x is a bounded linear operator and f t x a function with values in h for each square integrable t the problem with b t t and f t t in place of b t x and f t x has a unique solution and b and f satisfy certain boundedness and continuity conditions

periodicity in the α norm for partial functional differential equations in fading memory spaces abstract the aim of this work is to study the existence of periodic solutions in the norm for some partial functional differential equations of neutral type in fading memory spaces we assume that a linear part is densely defined and is the generator of an analytic semigroup the delayed part is assumed to be periodic with respect to the first argument in the nonhomogeneous linear case we show that the existence of a bounded solution in r implies the existence of the periodic solution in the nonlinear case we use two approaches the first one is based on the ultimate boundedness of solutions and the second one is based on the multivalued fixed point theorem

existence of a periodic solution for some partial functional differential equations with infinite delay abstract this paper deals with the existence of periodic solutions for some partial functional differential equations with infinite delay we suppose that the linear part is nondensely defined and satisfies the hille yosida condition in the nonlinear case we give several criteria to ensure the existence of a periodic solution in the nonhomogeneous linear case we prove the existence of a periodic solution under the existence of a bounded solution

a class of linear partial neutral functional differential equations with nondense domain abstract we consider a system of linear partial neutral functional differential equations with nondense domain a natural generalized notion of solutions is provided by the integral solutions we derive a variation of constants formula which allows us to transform the integral solutions of the neutral equation to solutions of an abstract volterra integral equation the basic existence and uniqueness results are given and the solutions are shown to generate an integrated semigroup

periodic solutions of delay impulsive differential equations abstract we study the following semilinear impulsive differential equation with delay u t a u t f t u t u t t 0 t t i u s s s r 0 u t i i i u t i i 1 2 0 t 1 t 2 in a banach space x with an unbounded operator a where r 0 is a constant and u t s u t s s r 0 here u t i u t i u t i constitutes an impulsive condition which can be used to model more physical phenomena than the traditional initial value problems we assume that f t u w is t periodic in t and then prove with some compactness conditions that if solutions of the equation are ultimately bounded then the differential equation has a t periodic solution the new results obtained here extend some results in this area for differential equations without impulsive conditions or without delays

the complexity of symmetric boolean parity holant problems for certain subclasses of np oplus p or p characterized by local constraints it is known that if there exist any problems within that subclass that are not polynomial time computable then all the problems in the subclass are np complete oplus p complete or p complete such dichotomy results have been proved for characterizations such as constraint satisfaction problems and directed and undirected graph homomorphism problems often with additional restrictions here we give a dichotomy result for the more expressive framework of holant problems for example these additionally allow for the expression of matching problems which have had pivotal roles in the development of complexity theory as our main result we prove the dichotomy theorem that for the class oplus p every set of symmetric holant signatures of any arities that is not polynomial time computable is oplus p complete the result exploits some special properties of the class oplus p and characterizes four distinct tractable

ultimate boundedness and periodicity for some partial functional differential equations with infinite delay abstract in this work we study the existence of periodic solutions for some partial functional differential equation with infinite delay we assume that the linear part is not necessarily densely defined and satisfies the known hille yosida condition firstly we give some estimates of the solutions secondly we prove that the poincare map is condensing which allows us to prove the existence of periodic solutions when the solutions are ultimately bounded

bounded and periodic solutions of differential equations in banach space abstract we study the equation u t au t f t t 0 1 in a banach space x with a the generator of an analytic or a strongly continuous semigroup s and prove that if solutions of 1 are bounded and ultimate bounded with f t periodic and s t compact then 1 has a t periodic solution we also show that the existence of a proper liapunov function implies the boundedness and ultimate boundedness of solutions of 1 these results extend earlier results in finite dimensional spaces we then apply the results to a parabolic partial differential equation u t t x 2m c x d u t x f t x 2

some notes on the fourier transform methods for error rate analysis of equal gain combining transform techniques based on moment generating functions mgfs and characteristic functions chfs have recently provided efficient analytical tools for the performance evaluation of digital communication systems over fading channels more recently the convolution theorem of the fourier transform has been employed to obtain unified expressions for the average error probabilities of equal gain combining egc diversity reception in terms of the chfs of the branches amplitude gains in this paper we prove that these expressions include redundant terms furthermore simpler analytical expressions for the average error rates of egc diversity reception can be obtained when the convolutional theorem of the sine and cosine transforms are used instead of the conventional fourier transform

boundedness and periodicity in impulsive ordinary and functional differential equations abstract in this paper we study the boundedness and periodicity of solutions for impulsive ordinary differential equations odes and functional differential equations fdes by using horn s fixed point theorem hale yoshizawa type criteria for the existence of t periodic solutions are established to use these criteria we also give two new boundedness theorems and establish new existence results for t periodic solutions which show that the impulsive perturbations do contribute to yielding periodic solutions even when the underlying systems do not enjoy periodic solutions

a massera type theorem for almost automorphic solutions of differential equations abstract in this note we present a massera type theorem for the existence of almost automorphic solutions of periodic linear evolution equations of the form x t a t x t f t where a t is unbounded linear operator depending on t periodically and generates a periodic evolutionary process f is almost automorphic the main results are stated in terms of the almost automorphy of solutions and their carleman spectra

generic error probabilities this paper presents new forms for an error probability associated with the phase angle between two vectors perturbed by gaussian noise an interesting consequence of the underlying generic form is a new expression for the symbol error rate in mdpsk that is very similar to its counterpart for mpsk the generic error probability is further shown to contain as special cases mpsk mdpsk cpfsk and digital fm and to give a new expression for the marcum q function the generic error probability also simplifies the error probability expressions in other situations such as nonorthogonal signaling maximum likelihood differential detection of dpsk with block by block detection and gray coding of mdpsk

massera problem for non autonomous retarded differential equations abstract in this paper under acquistapace terreni conditions we study the existence of periodic solutions for some non autonomous semilinear partial functional differential equation with delay we assume that the linear part is non densely defined the delayed part is assumed to be periodic with respect to the first argument using a fixed point theorem for multivalued mapping some sufficient conditions are given to prove the existence of periodic solutions an example is shown to illustrate our results

existence and uniqueness of periodic solution for a class of semilinear evolution equations this paper deals with the existence and uniqueness for the periodic boundary value problem of the semilinear evolution equation in a hilbert space h u t au t f t u t 0 t u 0 u where a d a h h is a positive definite self adjoint operator 0 and f 0 h h satisfy caratheodory condition we present some spectral conditions for the nonlinearity f t u to guarantee the existence and uniqueness these spectral conditions are the generalization for nonresonance condition of the self adjoint elliptic boundary value problems

periodic solutions for a class of neutral functional differential equations with infinite delay abstract in this paper we study the existence and uniqueness of periodic solutions of the nonlinear neutral functional differential equation with infinite delay of the form d d t x t 0 g s x t s d s a t x t x t f t x t in the process we use the fundamental matrix solution of x t a t u t x t and construct appropriate mappings where u c r r n is an periodic function then we employ matrix measure and the leray schauder fixed point theorem to show the existence of periodic solutions of this neutral differential equation in the special case where g s u 0 and a t x a t some sufficient conditions which ensure the uniform stability and global attractivity of a unique periodic solution are derived

differential modulations for multinode cooperative communications this paper proposes and analyzes differential modulation schemes for two cooperation protocols in multinode cooperative wireless networks namely multinode differential amplify and forward scheme diffaf and multinode differential decode and forward scheme diffdf in the diffaf scheme with knowledge of long term average of received signals from all communication links the destination efficiently combines signals from direct and all multiple relay links to improve communication reliability in the diffdf scheme by utilizing a decision threshold at each relay destination link the destination efficiently combines signals from the direct link and each relay link whose signal amplitude is larger than the threshold for the diffaf scheme an exact bit error rate ber formulation based on optimum combining is provided for differential m ary phase shift keying dmpsk modulation and it serves as a performance benchmark of the proposed diffaf scheme in addition ber upper bounds ber lower bounds and simple ber approximations are derived then optimum power allocation is provided to further improve performance of the diffaf scheme based on the tight ber approximation the optimum power allocation can be simply obtained through a single dimensional search in case of the diffdf scheme the performance of dmpsk modulation is analyzed first a ber formulation for dmpsk modulation is derived next an approximate ber formulation of the diffdf scheme is obtained and a tractable ber lower bound is derived to provide further insights then the performance of the diffdf scheme is enhanced by jointly optimizing power allocation and decision thresholds with an aim to minimize the ber finally simulation results under the two proposed cooperation protocols are given to validate their merit and support the theoretical analysis

the effects of noise correlation and power imbalance on terrestrial and satellite dpsk channels new results are given for the bit error probability for binary dpsk modulation over both terrestrial and satellite channels taking into account noise correlation and power imbalance the new expressions are remarkably simpler than their previously published counterparts for the terrestrial channel the results are in closed form in terms of tabulated functions and for the hard limiting satellite channel both in terms of integrals readily evaluated by quadrature and in terms of infinite series using the results it is shown that the error rate does not depend on the noise correlation down link in the satellite case so long as the a priori symbol probabilities are equal thereby solving an open problem posed by lee french and hong also the satellite case in which each of the up link and down link channels contains nonzero noise correlations is briefly treated

a general method for calculating error probabilities over fading channels signal fading is a ubiquitous problem in mobile and wireless communications in digital systems fading results in bit errors and evaluating the average error rate under fairly general fading models and multichannel reception is often required predominantly to date most researchers perform the averaging using the probability density function method or the moment generating function mgf method this paper presents a third method called the characteristic function chf method for calculating the average error rates and outage performance of a broad class of coherent differentially coherent and noncoherent communication systems with or without diversity reception in a myriad of fading environments unlike the mgf technique the proposed chf method based on parseval s theorem enables us to unify the average error rate analysis of different modulation formats and all commonly used predetection diversity techniques i e maximal ratio combining equal gain combining selection diversity and switched diversity within a single common framework the chf method also lends itself to the averaging of the conditional error probability involving the complementary incomplete gamma function and the confluent hypergeometric function over fading amplitudes which heretofore resisted to a simple form as an aside we show some previous results as special cases of our unified framework

complexity of generalized satisfiability counting problems abstract the class of generalized satisfiability problems introduced in 1978 by schaefer presents a uniform way of studying the complexity of satisfiability problems with special conditions the complexity of each decision and counting problem in this class depends on the involved logical relations in 1979 valiant defined the class p the class of functions definable as the number of accepting computations of a polynomial time nondeterministic turing machine clearly all satisfiability counting problems belong to this class p we prove a dichotomy theorem for generalized satisfiability counting problems that is if all logical relations involved in a generalized satisfiability counting problem are affine then the number of satisfying assignments of this problem can be computed in polynomial time otherwise this function is p complete this gives us a comparison between decision and counting generalized satisfiability problems we can determine exactly the polynomial satisfiability decision problems whose number of solutions can be computed in polynomial time and also the polynomial satisfiability decision problems whose counting counterparts are already p complete moreover taking advantage of a similar dichotomy result proved in 1978 by schaefer for generalized satisfiability decision problems we get as a corollary the implication that the counting counterpart of each np complete generalized satisfiability decision problem is p complete

the complexity of weighted boolean csp with mixed signs we give a complexity dichotomy for the problem of computing the partition function of a weighted boolean constraint satisfaction problem such a problem is parameterized by a set c of rational valued functions which generalize constraints each function assigns a weight to every assignment to a set of boolean variables our dichotomy extends previous work in which the weight functions were restricted to being non negative we represent a weight function as a product of the form 1 sg where the polynomial s determines the sign of the weight and the non negative function g determines its magnitude we show that the problem of computing the partition function the sum of the weights of all possible variable assignments is in polynomial time if either every function in c can be defined by a pure affine magnitude with a quadratic sign polynomial or every function can be defined by a magnitude of product type with a linear sign polynomial in all other cases computing the partition function is fp p complete

existence and asymptotic stability of periodic solution for evolution equations with delays abstract in this paper we discuss the existence and asymptotic stability of the time periodic solution for the evolution equation with multiple delays in a hilbert space h u t a u t f t u t u t 1 u t n t r where a d a h h is a positive definite selfadjoint operator f r h n 1 h is a nonlinear mapping which is periodic in t and 1 2 n are positive constants we present essential conditions on the nonlinearity f to guarantee that the equation has periodic solutions or an asymptotically stable periodic solution the discussion is based on analytic semigroups theory and an integral inequality with delays

quantum circuits that can be simulated classically in polynomial time a model of quantum computation based on unitary matrix operations was introduced by feynman and deutsch it has been asked whether the power of this model exceeds that of classical turing machines we show here that a significant class of these quantum computations can be simulated classically in polynomial time in particular we show that two bit operations characterized by 4 4 matrices in which the sixteen entries obey a set of five polynomial relations can be composed according to certain rules to yield a class of circuits that can be simulated classically in polynomial time this contrasts with the known universality of two bit operations and demonstrates that efficient quantum computation of restricted classes is reconcilable with the polynomial time turing hypothesis therefore it is possible that the techniques introduced bring the quantum computational model within the realm of algebraic complexity theory in a manner consistent with one view of quantum physics the wave function is simulated deterministically and randomization arises only in the course of making measurements the results generalize the quantum model in that they do not require the matrices to be unitary in a different direction these techniques also yield deterministic polynomial time algorithms for the decision and parity problems for certain classes of read twice boolean formulae all our results are based on the use of gates that are defined in terms of their graph matching properties

self sustained oscillations in a ring array of coupled lossless transmission lines abstract in this paper we derive a neutral difference differential system with diffusion which arises from a ring array of coupled lossless transmission lines we investigate the problem of self sustained oscillations of the considered transmission lines and apply a global hopf bifurcation theorem to establish the existence of multiple large amplitude phase locked periodic solutions in the corresponding neutral system

holographic algorithms by fibonacci gates abstract we introduce fibonacci gates as a polynomial time computable primitive and develop a theory of holographic algorithms based on these gates the fibonacci gates play the role of matchgates in valiant s theory valiant 2008 19 they give rise to polynomial time computable counting problems on general graphs while matchgates mainly work over planar graphs only we develop a signature theory and characterize all realizable signatures for fibonacci gates for bases of arbitrary dimensions we prove a basis collapse theorem we apply this theory to give new polynomial time algorithms for certain counting problems we also use this framework to prove that some slight variations of these counting problems are p hard holographic algorithms with fibonacci gates prove to be useful as a general tool for classification results of counting problems dichotomy theorems cai et al 2009 7

schaefer type theorem and periodic solutions of evolution equations abstract two fixed point theorems for the sum of contractive and compact operators are obtained in this paper which generalize and improve the corresponding results in h schaefer uber die methode der a priori schranken math ann 129 1955 415 416 t a burton integral equations implicit functions and fixed points proc amer math soc 124 1996 2383 2390 v i istr tescu fixed point theory an introduction reidel dordrecht 1981 t a burton k colleen a fixed point theorem of krasnoselskii schaefer type math nachr 189 1998 23 31 d r smart fixed point theorems cambridge univ press cambridge 1980 as the applications for the results we obtain the existence of periodic solutions for some evolution equations with delay which extend the corresponding results in t a burton b zhang periodic solutions of abstract differential equations with infinite delay j differential equations 90 1991 357 396

accurate evaluation for mdpsk with noncoherent diversity the error probability analysis of m ary differential phase shift keying signals with noncoherent diversity combining over general fading channels is not available in the literature except for some simple cases the difficulty lies in the philosophy which attempts to explicitly determine the phase distribution expressions of the received signal and this often leads to a mathematically intractable issue in this paper we take a novel approach by formulating the phase distribution in terms of joint moment generating functions of the real and imaginary parts of the decision variable at the receiver output we further derive fast convergent techniques for two dimensional 2 d inverse laplace transform enabling us to accurately evaluate the phase distribution the error probability formulas thus obtained involve a twofold integral which can be efficiently evaluated by using our algorithms developed on the basis of the 2 d trapezoidal summation and gauss chebyshev quadrature the new technique is very general taking into account the effects of arbitrary diversity order symbol alphabet size m and arbitrary diversity branches correlation numerical results are also presented for illustration

periodic solutions for dynamic equations on time scales massera type criteria are established for the existence of periodic solutions of linear and nonlinear dynamic equations on time scales some interesting properties of the exponential function on time scales are presented furthermore a sufficient condition guaranteeing the boundedness of the solutions of the equation is presented

periodic solutions of infinite delay evolution equations abstract for a t and f t x y t periodic in t we consider the differential equation with infinite delay in a general banach space x u t a t u t f t u t u t t 0 u s s s 0 0 1 where the resolvent of the unbounded operator a t is compact and f is continuous in its variables and ut s u t s s 0 we first show that the poincare operator given by p ut i e t units along the unique solution u determined by the initial function is a condensing operator with respect to kuratowski s measure of non compactness in a phase space cg and then derive periodic solutions from bounded solutions by using sadovskii s fixed point theorem this extends the study of deriving periodic solutions from bounded solutions to infinite delay differential equations in general banach spaces

bounded and periodic solutions of infinite delay evolution equations abstract for a t and f t x y t periodic in t we consider the following evolution equation with infinite delay in a general banach space x 0 1 u t a t u t f t u t u t t 0 u s s s 0 where the resolvent of the unbounded operator a t is compact and ut s u t s s 0 by utilizing a recent asymptotic fixed point theorem of hale and lunel 1993 for condensing operators to a phase space cg we prove that if solutions of eq 0 1 are ultimate bounded then eq 0 1 has a t periodic solution this extends and improves the study of deriving periodic solutions from boundedness and ultimate boundedness of solutions to infinite delay evolution equations in general banach spaces it also improves a corresponding result in j math anal appl 247 2000 627 644 where the local strict boundedness is used

polynomial time approximation algorithms for the ising model the paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic ising system to any specified degree of accuracy the running time of the algorithm in

existence of periodic solutions for abstract neutral non autonomous equations with infinite delay in this paper by using sadovskii fixed point theorem we study the existence of solutions and periodic solutions for a class of abstract neutral functional evolution equations with infinite delay an example is presented in the end to show the applications of the obtained results

performance analysis of linear modulation schemes with generalized diversity combining on rayleigh fading channels with noisy channel estimates generalized diversity combining gdc also known as hybrid selection maximal ratio combining or generalized selection combining is a low complexity diversity combining technique by which a fixed subset of a large number of available diversity channels is chosen and then combined using the rules of maximal ratio combining in this paper we analyze the performance of gdc on time correlated rayleigh fading channels with noisy channel estimates we derive expressions for the probability of error for various linear modulation schemes with coherent detection and discuss the conditions under which the analysis can be extended to noncoherent and differentially coherent receiver structures throughout the paper using a fundamental approach to obtain the decision statistic at the combiner output a number of new expressions for the error probabilities are obtained in a rigorous way along with a presentation of their performance with channel estimation errors the final expressions have roughly the same complexity of evaluation as that for the channel with only additive gaussian noise our results correct various inaccuracies in the literature and show that coherent receivers based on imperfectly estimated channel knowledge incur a significant performance loss

holographic algorithms the power of dimensionality resolved valiant s theory of holographic algorithms is a novel methodology to achieve exponential speed ups in computation a fundamental parameter in holographic algorithms is the dimension of the linear basis vectors we completely resolve the problem of the power of higher dimensional bases we prove that 2 dimensional bases are universal for holographic algorithms

a complete dichotomy rises from the capture of vanishing signatures we prove a complexity dichotomy theorem for holant problems over an arbitrary set of complex valued symmetric constraint functions mathcal f on boolean variables this extends and unifies all previous dichotomies for holant problems on symmetric constraint functions taking values without a finite modulus we define and characterize all symmetric vanishing signatures they turn out to be essential to the complete classification of holant problems the dichotomy theorem has an explicit tractability criterion expressible in terms of holographic transformations a holant problem defined by a set of constraint functions mathcal f is solvable in polynomial time if it satisfies this tractability criterion and is p hard otherwise the tractability criterion can be intuitively stated as follows a set mathcal f is tractable if 1 every function in mathcal f has arity at most two or 2 mathcal f is transformable to an affine type or 3 mathcal f is transformable to a product type o

some new twists to problems involving the gaussian probability integral using an alternate form of the gaussian probability integral discovered a number of years ago it is shown that the solution to a number of previously considered communication problems can be simplified and in some cases made more accurate i e exact rather than bounded these problems include the evaluation of 1 the bit error probability of uncoded phase shift keying psk with costas loop tracking 2 word error probability of antipodal modulation in the presence of fading 3 bit error probability of coded m ary psk mpsk over the memoryless fading channel with given channel state information 4 conditional symbol error probability of mpsk in the presence of carrier synchronization error and 5 the average error probability for the binary additive white gaussian noise awgn intersymbol interference channel also obtained is a generalization of this new alternate form to the case of a two dimensional gaussian probability integral with arbitrary correlation which can be used to evaluate the symbol error probability of mpsk with i q unbalance

existence of periodic solutions in abstract semilinear equations and applications to biological models abstract in this paper we study the existence of mild periodic solutions of abstract semilinear equations in a setting that includes several other types of equations such as delay differential equations first order hyperbolic partial differential equations and reaction diffusion equations under different assumptions on the linear operator and the nonhomogeneous function sufficient conditions are derived to ensure the existence of mild periodic solutions in the abstract semilinear equations when the semigroup generated by the linear operator is not compact banach fixed point theorem is used whereas when the semigroup generated by the linear operator is compact schauder fixed point theorem is employed in applications we apply the main results to establish the existence of periodic solutions in delayed red blood cell models age structured models with periodic harvesting and the diffusive logistic equation with periodic coefficients

holographic algorithms with matchgates capture precisely tractable planar csp valiant introduced matchgate computation and holographic algorithms a number of seemingly exponential time problems can be solved by this novel algorithmic paradigm in polynomial time we show that in a very strong sense matchgate computations and holographic algorithms based on them provide a universal methodology to a broad class of counting problems studied in the statistical physics community for decades they capture precisely those problems which are p hard on general graphs but computable in polynomial time on planar graphs more precisely we prove complexity dichotomy theorems in the framework of counting csp problems the local constraint functions take boolean inputs and can be arbitrary real valued symmetric functions we prove that every problem in this class belongs to precisely three categories 1 those which are tractable i e polynomial time computable on general graphs or 2 those which are p hard on general graphs but tractable on planar graphs or 3 those which are p har

beyond csp a dichotomy for counting weighted eulerian orientations with ars abstract we define and explore a notion of unique prime factorization for constraint functions and use this as a new tool to prove a complexity classification for counting weighted eulerian orientation problems with arrow reversal symmetry ars we prove that all such problems are either polynomial time computable or p hard we show that the class of weighted eulerian orientation problems subsumes all weighted counting constraint satisfaction problems csp on boolean variables more significantly we establish a novel connection between csp and counting weighted eulerian orientation problems that is global in nature this connection is based on a structural determination of all half weighted affine linear subspaces over z 2 which is proved using mobius inversion

reflection positivity rank connectivity and homomorphism of graphs it is shown that a graph parameter can be realized as the number of homomorphisms into a fixed weighted graph if and only if it satisfies two linear algebraic conditions reflection positivity and exponential rank connectivity in terms of statistical physics this can be viewed as a characterization of partition functions of vertex models

solvability of the cauchy problem for infinite delay equations abstract in this paper we study the solvability of the cauchy problem for functional differential equations with infinite delay in a banach space x which are more general than those in many previous publications we undertake our study under suitable hypotheses based on noncompactness measures and kamke type functions and in a general setting of admissible phase space p including the space lp 0 x therefore our results extend and unify many existing results for finite and infinite delay equations as a sample of possible applications we analyze the solvability of the cauchy problem for a schrodinger type partial functional integro differential equation in l1 r

expressiveness of matchgates matchgates have been used to simulate classically in polynomial time assemblies of quantum gates in this paper it is shown that every matchgate for 2 input 2 output functions has to obey a certain set of five polynomial identities it is also shown that no matchgate can realize a nontrivial control gate for any number of inputs on the other hand it is proved that classical boolean formulae can be expressed as matchcircuits of polynomial size

the complexity of weighted boolean csp this paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted boolean constraint satisfaction problem the problem is parameterized by a finite set mathcal f of nonnegative functions that may be used to assign weights to the configurations feasible solutions of a problem instance classical constraint satisfaction problems correspond to the special case of 0 1 valued functions we show that computing the partition function i e the sum of the weights of all configurations is text sf fp text sf p complete unless either 1 every function in mathcal f is of product type or 2 every function in mathcal f is pure affine in the remaining cases computing the partition function is in p

blow up and global existence of solutions to integral equations with infinite delay in banach spaces abstract we present new blow up theorems which are only in terms of the ordinary limit for the solutions to the cauchy problem for integral equations with infinite delay in banach spaces moreover we provide an example to illustrate our abstract result

holographic algorithm with matchgates is universal for planar csp over boolean domain we prove a complexity classification theorem that classifies all counting constraint satisfaction problems csp over boolean variables into exactly three classes 1 polynomial time solvable 2