on almost cylindrical languages and the decidability of the d0l and pwd0l primitivity problems abstract primitive words and their properties have always been of fundamental importance in the study of formal language theory head and lando in periodic d0l languages proposed the idea of deciding whether or not a given d0l language has the property that every word in it is a primitive word after reducing the general problem to the case in which h is injective it will be shown that primitivity is decidable when a h is an almost cylindrical set moreover in this case it is shown that the set of words which generate primitive sequences given a particular d0l scheme is an algorithmically constructible context sensitive language an undecidability result for the pwd0l primitivity problem and decidability results for cases of the rwd0l primitivity problem are also given

the cr geometry of weighted extremal kahler and sasaki metrics we establish an equivalence between conformally einstein maxwell kahler 4 manifolds recently studied in apostolov et al j reine angew math 721 109 147 2016 apostolov and maschler j eur math soc 21 1319 1360 2019 futaki and ono j math soc jpn 70 1493 1521 2018 koca et al ann glob anal geom 50 29 46 2016 lebrun einstein maxwell equations extremal kahler metrics and seiberg witten theory in the many facets of geometry a tribute to nigel hitchin oxford university press oxford pp 17 33 2009 lebrun j geom phys 91 171 2015 and lebrun commun math phys 344 621 653 2016 and extremal kahler 4 manifolds in the sense of calabi extremal kahler metrics seminar on differential geometry annals of mathematics studies vol 102 pp 259 290 princeton university press princeton 1982 with nowhere vanishing scalar curvature the corresponding pairs of kahler metrics arise as transversal kahler structures of sasaki metrics compatible with the same cr structure and having commuting sasaki reeb vector fields this correspondence extends to higher dimensions using the notion of a weighted extremal kahler metric apostolov et al in levi kahler reduction of cr structures product of spheres and toric geometry arxiv 1708 05253 apostolov et al in weighted extremal kahler metrics and the einstein maxwell geometry of projective bundles arxiv 1808 02813 lahdili in j geom anal 29 542 568 2019 lahdili in int math res not arxiv 1710 00235 lahdili in proc lond math soc 119 1065 1114 2019 illuminating and uniting several explicit constructions in kahler and sasaki geometry it also leads to new existence and non existence results for extremal sasaki metrics suggesting a link between the notions of relative weighted k stability of a polarized variety introduced in apostolov et al weighted extremal kahler metrics and the einstein maxwell geometry of projective bundles arxiv 1808 02813 and lahdili proc lond math soc 119 1065 1114 2019 and relative k stability of the kahler cone corresponding to a sasaki polarization studied in boyer and van coevering math res lett 25 1 19 2018 and collins and szekelyhidi j differ geom 109 81 109 2018

watson crick d0l systems with regular triggers watson crick complementarity has been used as a basis for massive parallelism in dna computing also its use in an operational sense has turned out to be very promising in the study of watson crick d0l systems the latter generalize d0l systems in a way not investigated so far in the theory of lindenmayer systems the complexity of the trigger is crucial for decidability properties concerning watson crick d0l systems the purpose of this paper is to settle the basic decision problems in the case of regular triggers

dimer monomer model on the sierpinski gasket abstract we present the numbers of dimer monomers m d n on the sierpinski gasket s g d n at stage n with dimension d equal to two three and four the upper and lower bounds for the asymptotic growth constant defined as z s g d lim v ln m d n v where v is the number of vertices on s g d n are derived in terms of the results at a certain stage as the difference between these bounds converges quickly to zero as the calculated stage increases the numerical value of z s g d can be evaluated with more than a hundred significant figures accurate from the results for d 2 3 4 we conjecture the upper and lower bounds of z s g d for general dimension the corresponding results on the generalized sierpinski gasket s g d b n with d 2 and b 3 4 are also obtained

complex symplectomorphisms and pseudo kahler islands in the quantization of toric manifolds let p be a delzant polytope we show that the quantization of the corresponding toric manifold x p in toric kahler polarizations and in the toric real polarization are related by analytic continuation of hamiltonian flows evaluated at time t sqrt 1 s we relate the quantization of x p in two different toric kahler polarizations by taking the time sqrt 1 s hamiltonian flow of strongly convex functions on the moment polytope p by taking s to infinity we obtain the quantization of x p in the singular real toric polarization recall that x p has an open dense subset which is biholomorphic to mathbb c n the quantization of x p in a toric kahler polarization can also be described by applying the complexified hamiltonian flow of the abreu guillemin symplectic potential g at time t sqrt 1 to an appropriate finite dimensional subspace of quantum states in the quantization of t mathbb t n in the vertical polarization by taking other imaginary times t k sqrt 1 k in mathbb r we describe toric kahler metrics with cone singularities along the toric divisors in x p for convex hamiltonian functions and sufficiently negative imaginary part of the complex time we obtain degenerate kahler structures which are negative definite in some regions of x p we show that the pointwise and l 2 norms of quantum states are asymptotically vanishing on negative definite regions

deterministic versus nondeterministic space in terms of synchronized alternating machines the study of synchronized alternating machines has enabled to characterize several natural complexity classes it is known that synchronized alternating space saspace s n c 0nspace ncs n for any space constructible function s n hromkovic et al 1991 in particular context sensitive languages are characterized by two way synchronized alternating finite automata furthermore pspace is characterized by synchronized alternating multihead finite automata and nlog by synchronized alternating two way finite automata with parallelism bounded by a constant in the present paper we prove analogous characterizations for deterministic space classes using a restricted form of synchronization globally deterministic synchronization this enables to study the well known open problems concerning nondeterminism versus determinism as problems about synchronization we also show that globally deterministic synchronization is strictly more powerful than deterministic synchronization

existential second order logic over graphs charting the tractability frontier fagin s theorem the first important result of descriptive complexity asserts that a property of graphs is in np if and only if it is definable by an existential second order formula in this article we study the complexity of evaluating existential second order formulas that belong to prefix classses of existential second order logic where a prefix class is the collection of all existential second order formulas in prenex normal form such that the second order and the first order quantifiers obey a certain quantifier pattern we completely characterize the computational complexity of prefix classes of existential second order logic in three different contexts 1 over directed graphs 2 over undirected graphs with self loops and 3 over undirected graphs without self loops our main result is that in each of these three contexts a dichotomy holds that is to say each prefix class of existential second order logic either contains sentences that can express np complete problems or each of its sentences expresses a polynomial time solvable problem although the boundary of the dichotomy coincides for the first two cases it changes as one moves to undirected graphs without self loops the key difference is that a certain prefix class based on the well known ackermann class of first order logic contains sentences that can express np complete problems over graphs of the first two types but becomes tractable over undirected graphs without self loops moreover establishing the dichotomy over undirected graphs without self loops turns out to be a technically challenging problem that requires the use of sophisticated machinery from graph theory and combinatorics including results about graphs of bounded tree width and ramsey s theorem

two applications of inductive counting for complementation problems following the recent independent proofs of immerman siam j comput 17 1988 pp 935 938 and szelepcsenyi bull european assoc theoret comput sci 33 1987 pp 96 100 that nondeterministic space bounded complexity classes are closed under complementation two further applications of the inductive counting technique are developed first an errorless probabilistic algorithm for the undirected graph s t connectivity problem that runs in o log n space and polynomial expected time is given then it is shown that the class logcfl is closed under complementation the latter is a special case of a general result that shows closure under complementation of classes defined by semi unbounded fan in circuits or equivalently nondeterministic auxiliary pushdown automata or tree size bounded alternating turing machines as one consequence it is shown that small numbers of role switches in two person pebbling can be eliminated

a space lower bound for st connectivity on node named jags abstract given a directed graph g and two of its nodes s and t the directed st connectivity problem stcon is to decide whether there is a directed path from s to t in g establishing a super logarithmic space lower bound for stcon on a general computation model such as turing machine or branching program has been a big challenge in complexity theory as an intermediate step cook and rackoff siam j comput 9 3 1980 636 652 introduce a structured model called jag jumping automaton for graphs and prove a space lower bound of log 2 n log log n on this model berman and simon proc 24th annual symp on foundations of computer science ieee press new york tucson az november 1983 show a similar lower bound for a probabilistic jag we take a step further by introducing a stronger model called nn jag node named jag and obtain the same space lower bound of log 2 n log log n on a probabilistic nnjag we show that s log 2 n log log n log log t where s is the space and t is the expected time used respectively this gives the best expected time lower bound on this model when the space s is o log 2 n log log n

quaternionic reduction and quaternionic orbifolds on considere un processus de reduction pour des varietes de kahler quaternioniques on montre qu il existe dans ce cas une certaine application impulsion qui se reduit a celle classique quand la courbure scalaire k de l espace est zero et les metriques deviennent hyperkahler quand k 0 cette application impulsion est definie de facon unique pour un groupe compact d automorphismes h

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

connecting toric manifolds by conical kahler einstein metrics abstract we give criterions for the existence of toric conical kahler einstein and kahler ricci soliton metrics on any toric manifold in relation to the greatest ricci and bakry emery ricci lower bound we also show that any two toric manifolds with the same dimension can be joined by a continuous path of toric manifolds with conical kahler einstein metrics in the gromov hausdorff topology

semi classical weights and equivariant spectral theory abstract we prove inverse spectral results for differential operators on manifolds and orbifolds invariant under a torus action these inverse spectral results involve the asymptotic equivariant spectrum which is the spectrum itself together with very large weights of the torus action on eigenspaces more precisely we show that the asymptotic equivariant spectrum of the laplace operator of any toric metric on a generic toric orbifold determines the equivariant biholomorphism class of the orbifold we also show that the asymptotic equivariant spectrum of a t n invariant schrodinger operator on r n determines its potential in some suitably convex cases in addition we prove that the asymptotic equivariant spectrum of an s 1 invariant metric on s 2 determines the metric itself in many cases finally we obtain an asymptotic equivariant inverse spectral result for weighted projective spaces as a crucial ingredient in these inverse results we derive a surprisingly simple formula for the asymptotic equivariant trace of a family of semi classical differential operators invariant under a torus action

the expressiveness of a family of finite set languages abstract in this paper we characterize exactly the complexity of a set based database language called srl which presents a unified framework for queries and updates by imposing simple syntactic restrictions on it we are able to express exactly the classes p and logspace we also discuss the role of ordering in database query languages and show that the hom operator of machiavelli language in ohori et al 1989 does not capture all the order independent properties

kahler metrics on toric orbifolds a theorem of e lerman and s tolman generalizing a result of t delzant states that compact symplectic toric orbifolds are classified by their moment polytopes together with a positive integer label attached to each of their facets in this paper we use this result and the existence of global actionangle coordinates to give an effective parametrization of all compatible toric complex structures on a compact symplectic toric orbifold by means of smooth functions on the corresponding moment polytope this is equivalent to parametrizing all toric kahler metrics and generalizes an analogous result for toric manifolds a simple explicit description of interesting families of extremal kahler metrics arising from recent work of r bryant is given as an application of the approach in this paper the fact that in dimension four these metrics are self dual and conformally einstein is also discussed this gives rise in particular to a one parameter family of self dual einstein metrics connecting the well known eguchi hanson and taub nut metrics

toric generalized kahler ricci solitons with hamiltonian 2 form we show that the generalized kahler ricci soliton equation on 4 dimensional toric kahler orbifolds reduces to odes assuming there is a hamiltonian 2 form this leads to an explicit resolution of this equation on labelled triangles and convex labelled quadrilaterals in particular we give the explicit expression of the kahler ricci solitons of weighted projective planes as well as new examples

kahler ricci solitons on toric fano orbifolds we prove the existence of kahler ricci solitons on toric fano orbifolds hence extend the theorem of wang and zhu adv math 188 87 103 2004 to the orbifold case

descriptional and computational complexity of finite automata a survey finite automata are probably best known for being equivalent to right linear context free grammars and thus for capturing the lowest level of the chomsky hierarchy the family of regular languages over the last half century a vast literature documenting the importance of deterministic nondeterministic and alternating finite automata as an enormously valuable concept has been developed in the present paper we tour a fragment of this literature mostly we discuss developments relevant to finite automata related problems like for example i simulation of and by several types of finite automata ii standard automata problems such as fixed and general membership emptiness universality equivalence and related problems and iii minimization and approximation we thus come across descriptional and computational complexity issues of finite automata we do not prove these results but we merely draw attention to the big picture and some of the main ideas involved

grassmannian representation of the two dimensional monomer dimer model we present an application of the grassmann algebra to the problem of the monomer dimer statistics on a two dimensional square lattice the exact partition function or total number of possible configurations of a system of dimers with a finite set of n monomers at fixed positions can be expressed via a quadratic fermionic theory we give an answer in terms of a product of two pfaffians and the solution is closely related to the kasteleyn result of the pure dimer problem correlation functions are in agreement with previous results both for monomers on the boundary where a simple exact expression is available in the discrete and continuous case and in the bulk where the expression is evaluated numerically

extremal kahler metrics on projective bundles over a curve let m p e be the complex manifold underlying the total space of the projectivization of a holomorphic vector bundle e over a compact complex curve of genus 2 building on ideas of fujiki 1992 27 we prove that m admits a kahler metric of constant scalar curvature if and only if e is polystable we also address the more general existence problem of extremal kahler metrics on such bundles and prove that the splitting of e as a direct sum of stable subbundles is necessary and sufficient condition for the existence of extremal kahler metrics in kahler classes sufficiently far from the boundary of the kahler cone the methods used to prove the above results apply to a wider class of manifolds called rigid toric bundles over a semisimple base which are fibrations associated to a principal torus bundle over a product of constant scalar curvature kahler manifolds with fibres isomorphic to a given toric kahler variety we discuss various ramifications of our approach to this class of manifolds

ale scalar flat kahler metrics on non compact weighted projective spaces we construct new explicit toric scalar flat kahler ale metrics with orbifold singularities which we use to obtain smooth extremal kahler metrics on appropriate resolutions of orbifolds

the logarithmic alternation hierarchy collapses aσ 2l aπ 2l abstract we show that a 2 l a k l k 2 by proving that a 2 l coincides with a 2 l essentially this is done by reducing the a 2 l complete set gap cogap to the question whether of two vectors a and b of n components a contains more solvable components i e components which are contained in gap than b moreover using a similar technique we show a 2 l l hd nl finally we consider the relevance of our proof technique for polynomial time classes e g the boolean np hierarchy

dynamical properties of pwdol systems the definitions of a piecewise deterministic zero lindenmayer pwd0l scheme and system are given and dynamical properties of such systems are introduced harrison 1994 showed that given an arbitrary finite alphabet a the emptiness problem is undecidable for the class of languages which are intersections of a d0l language and a context sensitive language this result is used to prove that many dynamical properties of pwd0l systems such as finiteness periodicity etc are in general undecidable over a two member context sensitive partition of a the idea of a morphic equivalence relation on a a is finite is defined and the idea of a finite morphic refinement is introduced harrison 1994 showed that every regular language and its complement is refined by a finite partition which is induced by a morphic congruence using this theorem it is shown that dynamical properties such as finiteness and periodicity are in general decidable for rwd0l systems i e a pwd0l system over a finite partition of a made up of all regular languages

equivariant inverse spectral theory and toric orbifolds abstract let o 2 n be a symplectic toric orbifold with a fixed t n action and with a toric kahler metric g in 10 we explored whether when o is a manifold the equivariant spectrum of the laplace operator g on c o determines o up to symplectomorphism in the setting of toric orbifolds we significantly improve upon our previous results and show that a generic toric orbifold is determined by its equivariant spectrum up to two possibilities this involves developing the asymptotic expansion of the heat trace on an orbifold in the presence of an isometry we also show that the equivariant spectrum determines whether the toric kahler metric has constant scalar curvature

unique decipherability in formal languages abstract we consider several language theoretic aspects of various notions of unique decipherability or unique factorization in formal languages given a language l at some position within the chomsky hierarchy we investigate the language of words ud l in l that have unique factorization over l we also consider similar notions for weaker forms of unique decipherability such as numerically decipherable words nd l multiset decipherable words msd l and set decipherable words sd l although these notions of unique factorization have been considered before it appears that the languages of words having these properties have not been positioned in the chomsky hierarchy up until now we show that ud l nd l msd l and sd l need not be context free if l is context free in fact nd l and msd l need not be context free even if l is finite although ud l and sd l are regular in this case we show that if l is context sensitive then so are ud l nd l msd l and sd l we also prove that the membership problem resp emptiness problem for these classes is pspace complete resp undecidable we finally determine upper and lower bounds on the length of the shortest word of l not having the various forms of unique decipherability into elements of l

periodicity and ultimate periodicity of dol systems a unified presentation of periodicity and ultimate periodicity of d0l systems is given bounds are provided for the period and index of periodic systems and simplified algorithms are obtained by using elementary morphisms it was shown previously harju and linna 1986 pansiot 1986 that if a h w is a d0l system with h w wy then it is decidable whether the word h w is ultimately periodic i e of the form xu in this paper a decision procedure is given to decide if there are an index i and a period p such that hp hi w hi w y and h p hi w is ultimately periodic given a morphism h a a bounds are obtained for the period and index of ultimately periodic systems it is also shown that the set w a h p hi w is ultimately periodic is a constructable regular language

on the structure of linear apex nlc graph grammars it is known that linear apex nlc lin a nlc grammars can generate np complete graph languages the present paper examines the source of this expressive power by analyzing complexity and decidability of the so called k connecting lin a nlc k lin a nlc grammars in which the right hand side of each production contains at most k nodes that can be connected to outside nodes the number of connecting nodes is indeed one source of the expressive power of graph grammars in that k lin a nlc k 1 lin a nlc for every k 0 there exists a 2 lin a nlc language which is np complete but every 1 lin a nlc language is in nlog the equivalence problem is undecidable for 1 lin a nlc languages but is decidable for 0 lin a nlc languages even when one of two input languages is an arbitrary b nlc language

on deciding readiness and failure equivalences for processes in this paper we study the complexity of deciding readiness and failure equivalences for finite state processes and recursively defined processes specified by normed context free grammars cfgs in greibach normal form gnf the results are as follows 1 readiness and failure equivalences for processes specified by normed gnf cfgs are both undecidable for this class of processes the regularity problem with respect to failure or readiness equivalence is also undecidable moreover all these undecidability results hold even for locally unary processes in the unary case these problems become decidable in fact they are p2 complete we also show that with respect to bisimulation equivalence the regularity for processes specified by normed gnf cfgs is nl complete 2 readiness and failure equivalences for finite state processes are pspace complete this holds even for locally unary finite state processes these two equivalences are co np complete for unary finite state processes further for acyclic finite state processes readiness and failure equivalences are co np complete and they are nl complete in the unary case 3 for finite tree processes we show that finite trace readiness and failure equivalences are all l complete further the results remain true for the unary case our results provide a complete characterization of the computational complexity of deciding readiness and failure equivalences for several important classes of processes

characterizations of context sensitive languages and other language classes in terms of symport antiport p systems we give syntactic characterizations of context sensitive languages csls in terms of some restricted models of symport antiport p systems these are the first such characterizations of csls in terms of p systems in particular we show the following for any language l over a binary alphabet 1 let m be any integer 1 then l is a csl if and only if it can be accepted by a restricted symport antiport p system with m membranes and multiple number of symbols objects moreover holding the number of membranes at m there is an infinite hierarchy in computational power within the class of binary csls with respect to the number of symbols 2 let s be any integer 14 then l is a csl if and only if it can be accepted by a restricted symport antiport p system with s symbols and multiple number of membranes moreover holding the number of symbols at s there is an infinite hierarchy in computational power with respect to the number of membranes similar results hold for languages over an alphabet of k 2 symbols thus 1 and 2 say that in order for the restricted symport antiport p systems to accept all binary csls at least one parameter either the number of symbols or the number of membranes must grow these are the first results of their kind in the p systems area they contrast a known result that unrestricted symport antiport p systems with s 2 symbols and m 1 membranes accept or generate exactly the recursively enumerable sets of numbers even for s m 6 we also note that previous characterizations of formal languages in the membrane computing literature are mostly for the parikh images of languages variations of our model yield characterizations of regular languages languages accepted by one way log n space bounded turing machines and recursively enumerable languages

a pfaffian formula for monomer dimer partition functions we consider the monomer dimer partition function on arbitrary finite planar graphs and arbitrary monomer and dimer weights with the restriction that the only non zero monomer weights are those on the boundary we prove a pfaffian formula for the corresponding partition function as a consequence of this result multipoint boundary monomer correlation functions at close packing are shown to satisfy fermionic statistics our proof is based on the celebrated kasteleyn theorem combined with a theorem on pfaffians proved by one of the authors and a careful labeling and directing procedure of the vertices and edges of the graph

observations on complete sets between linear time and polynomial time there is a single set that is complete for a variety of nondeterministic time complexity classes with respect to related versions of m reducibility this observation immediately leads to transfer results for determinism versus nondeterminism solutions also an upward transfer of collapses of certain oracle hierarchies built analogously to the polynomial time or the linear time hierarchies can be shown by means of uniformly constructed sets that are complete for related levels of all these hierarchies a similar result holds for difference hierarchies over nondeterministic complexity classes finally we give an oracle set relative to which the nondeterministic classes coincide with the deterministic ones for several sets of time bounds and we prove that the strictness of the tape number hierarchy for deterministic linear time turing machines does not relativize

on the power of alternation on reversal bounded alternating turing machines with a restriction whether or not there is a difference of the power among alternating turing machines with a bounded number of alternations is one of the most important problems in the field of computer science this paper presents the following result let r n be a space and reversal constructible function then for any k 1 we obtain that the class of languages accepted by off line 1 tape r k machines running in reversal o r n is equal to the class of languages accepted by off line 1 tape 1 machines running in reversal o r n an off line 1 tape k machine m is called an off line 1 tape r k machine if m always limits the non blank part of the work tape to at most o r n log n when making an alternation between universal and existential states during the computation

dimers on a simple quartic net with a vacancy a seminal milestone in lattice statistics is the exact solution of the enumeration of dimers on a simple quartic net obtained by fisher kasteleyn and temperley fkt in 1961 an outstanding related and yet unsolved problem is the enumeration of dimers on a net with vacant sites here we consider this vacant site problem with a single vacancy occurring at certain specific sites on the boundary of a simple quartic net first using a bijection between dimer and spanning tree configurations due to temperley kenyon propp and wilson we establish that the dimer generating function is independent of the location of the vacancy and deduce a closed form expression for the generating function we next carry out finite size analyses of this solution as well as that of the fkt solution our analyses lead to a logarithmic correction term in the large size expansion for the vacancy problem with free boundary conditions a concrete example exhibiting this difference is given we also find the central charge c 2 in the language of conformal field theory for the vacancy problem as versus the value c 1 when there is no vacancy

pfaffian solution of a dimer monomer problem single monomer on the boundary we consider the dimer monomer problem for the rectangular lattice by mapping the problem into one of close packed dimers on an extended lattice we rederive the tzeng wu solution for a single monomer on the boundary by evaluating a pfaffian we also clarify the mathematical content of the tzeng wu solution by identifying it as the product of the nonzero eigenvalues of the kasteleyn matrix

boundary monomers in the dimer model the correlation functions of an arbitrary number of boundary monomers in the system of close packed dimers on the square lattice are computed exactly in the scaling limit the equivalence of the 2n point correlation functions with those of a complex free fermion is proved thereby reinforcing the description of the monomer dimer model by a conformal free field theory with central charge c 1 comment 15 pages 2 figures

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

language theoretic aspects of dna complementarity the optimism about the possibilities of dna computing is based on two central issues the watson crick complementarity and the massive parallelism of dna strands while the latter issue renders exhaustive searches possible and thus may settle problems previously considered intractable the former issue is the cause behind the universality of many models of dna computing moreover complementarity can be viewed as a purely language theoretic operation undesirable circumstances in a string trigger a transition to the complementary string this aspect of complementarity is investigated in the present paper mainly from the point of view of l systems new types of word sequences will be discovered sometimes the resulting decision problems are equivalent to well known open problems from other areas

monomer dimer model on a scale free small world network abstract the explicit determination of the number of monomer dimer arrangements on a network is a theoretical challenge and exact solutions to monomer dimer problem are available only for few limiting graphs with a single monomer on the boundary e g rectangular lattice and quartic lattice however analytical research even numerical result for monomer dimer problem on scale free small world networks is still missing despite the fact that a vast variety of real systems display simultaneously scale free and small world structures in this paper we address the monomer dimer problem defined on a scale free small world network and obtain the exact formula for the number of all possible monomer dimer arrangements on the network based on which we also determine the asymptotic growth constant of the number of monomer dimer arrangements in the network we show that the obtained asymptotic growth constant is much less than its counterparts corresponding to two dimensional lattice and sierpinski fractal having the same average degree as the studied network which indicates from another aspect that scale free networks have a fundamentally distinct architecture as opposed to regular lattices and fractals without power law behavior

convexity properties of the moment mapping ii be its associated momen t mapping see w for definitions the set x is the union of co adjoint orbits the main result of this paper is a description of the orbit structure of this set to describe this result we first note that the coadjoint orbits in q can be parametr ized as follows let t be a caf tan subalgebra of g and let b be a positive definite g invariant bilinear form on by means of b we get a g equivariant identification q let t be the subspace of q corresponding to t then every co adjoint orbit intersects i in a weyl group orbit so there is a one one correspondence between co adjoint orbits in q and weyl group orbits in t to get an even sharper parametrization let t be a weyl chamber in then every weyl group orbit intersects t in a single point so t is a modul i space for the co adjoint orbits two orbits in x are said to be of the same type if they are isomorphic as homogeneous g spaces since x is compact there are at most a finite number of different types of orbits see 1113 let h be a closed subgroup of t of codimension r and let cit be the set of all orbits in x of type g h

morphic congruences and dol languages in a short note head 1991 showed that given an arbitrary finitely generated submonoid m of a finitely generated free monoid a and an endomorphism e of a such that m e m there exists an algorithmically computable natural number n such that for any x a l sx m if and only if x ei 0 i n m where sx a e x is a d0l system in this paper the idea of a morphic refinement of a finite partition of a is introduced to allow us to extend head s result to all regular languages in a moreover it is shown that such a bound n can be computed which only depends upon the regular language l and is independent of the endomorphism e

reducibility in sasakian geometry the purpose of this paper is to study reducibility properties in sasakian geometry first we give the sasaki version of the de rham decomposition theorem however we need a mild technical assumption on the sasaki automorphism group which includes the toric case next we introduce the concept of it cone reducible and consider s 3 bundles over a smooth projective algebraic variety where we give a classification result concerning contact structures admitting the action of a 2 torus of reeb type in particular we can classify all such sasakian structures up to contact isotopy on s 3 bundles over a riemann surface of genus greater than zero finally we show that in the toric case an extremal sasaki metric on a sasaki join always splits

vacancy localization in the square dimer model we study the classical dimer model on a square lattice with a single vacancy by developing a graph theoretic classification of the set of all configurations which extends the spanning tree formulation of close packed dimers with this formalism we can address the question of the possible motion of the vacancy induced by dimer slidings we find a probability 57 4 ensuremath 10 sqrt 2 for the vacancy to be strictly jammed in an infinite system more generally the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 9 8 on a finite system the probability that a vacancy in the bulk can reach the boundary falls off as a power law of the system size with exponent 1 4 the resultant weak localization of vacancies still allows for unbounded diffusion characterized by a diffusion exponent that we relate to that of diffusion on spanning trees we also implement numerical simulations of the model with both free and periodic boundary conditions

dimer coverings on the sierpinski gasket we present the number of dimer coverings nd n on the sierpinski gasket sgd n at stage n with dimension d equal to two three four or five when the number of vertices denoted as v n of the sierpinski gasket is an even number nd n is the number of close packed dimers when the number of vertices is an odd number no close packed configurations are possible and we allow one of the outmost vertices uncovered the entropy of absorption of diatomic molecules per site defined as s mathit sg d lim n to infty ln n d n v n is calculated to be ln 2 3 exactly for sg2 the numbers of dimers on the generalized sierpinski gasket sgd b n with d 2 and b 3 4 5 are also obtained exactly with entropies equal to ln 6 7 ln 28 12 ln 200 18 respectively the number of dimer coverings for sg3 is given by an exact product expression such that its entropy is given by an exact summation expression the upper and lower bounds for the entropy are derived in terms of the results at a certain stage for sgd n with d 3 4 5 as the difference between these bounds converges quickly to zero as the calculated stage increases the numerical value of s mathit sg d with d 3 4 5 can be evaluated with more than a hundred significant figures accurate

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

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

sublogarithmic bounds on space and reversals the complexity measure under consideration is mbox rm space times mbox rm reversals for turing machines that are able to branch both existentially and universally we show that for any function h n between log log n and log n pi 1 mbox rm space times mbox rm reversals h n is separated from sigma 1 mbox rm space times mbox rm reversals h n as well as from mbox sf co sigma 1 mbox rm space times mbox rm reversals h n for middle accept and weak modes of this complexity measure this also separates determinism from the higher levels of the alternating hierarchy for well behaved functions h n between log log n and log n almost all of the above separations can be obtained by using unary witness languages in addition the construction of separating languages contributes to the research on minimal resource requirements for computational devices capable of recognizing nonregular languages for any arbitrarily slow growing unbounded monotone recursive function f n a nonregular unary language is presented that can be accepted by a middle mbox pi 1 alternating turing machine in s n space and i n input head reversals with s n cdot i n in cal o log log n cdot f n thus there is no exponential gap for the optimal lower bound on the product s n cdot i n between unary and general nonregular language acceptance in sharp contrast with the one way case

relational queries computable in polynomial time we characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe we also show that even without the ordering one application of fixed point suffices to express any query expressible with several alternations of fixed point and negation this proves that the fixed point query hierarchy suggested by chandra and harel collapses at the first fixed point level it is also a general result showing that in finite model theory one application of fixed point suffices

hamiltonian 2 forms in kahler geometry ii global classification we present a classification of compact kahler manifolds admitting a hamiltonian 2 form which were classified locally in part i of this work this involves two components of independent interest the first is the notion of a rigid hamiltonian torus action this natural condition for torus actions on a kahler manifold was introduced locally in part i but such actions turn out to be remarkably well behaved globally leading to a fairly explicit classification up to a blow up compact kahler manifolds with a rigid hamiltonian torus action are bundles of toric kahler manifolds the second idea is a special case of toric geometry which we call orthotoric we prove that orthotoric kahler manifolds are diffeomorphic to complex projective space but we extend our analysis to orthotoric orbifolds where the geometry is much richer we thus obtain new examples of kahler einstein 4 orbifolds combining these two themes we prove that compact kahler manifolds with hamiltonian 2 forms are covered by blow downs of projective bundles over kahler products and we describe explicitly how the kahler metrics with a hamiltonian 2 form are parameterized we explain how this provides a context for constructing new examples of extremal kahler metrics in particular a subclass of such metrics which we call weakly bochner flat we also provide a self contained treatment of the theory of compact toric kahler manifolds since we need it and find the existing literature incomplete

bridging across the log n space frontier we believe that now is the opportune time to unify the theory of space bounded computations below log n with higher complexity classes this needs to review the basic concepts of the space complexity theory and clarify the role of the space constructibility despite of the fact that the space below log n behaves radically different from the higher bounds many important techniques do work on the both sides of this boundary in addition several important problems are closely related across the log n space bound