separating k separated ence graph languages an ence graph grammar is k separated k 1 if the distance between any two nonterminal nodes in any of its sentential forms is at least k let sepk denote the class of graph languages generated by k separated grammars then sep1 sep2 is the class of ence boundary ence graph languages and so sep2 sep1 recently engelfriet 1991 showed that sep3 sep2 and conjectured that in fact sepk 1 sepk for each k 1 we prove this conjecture affirmatively

graph grammars with neighbourhood controlled embedding abstract a central feature that distinguishes graph grammars we consider grammars generating sets of node labelled undirected graphs only from string grammars is that in the former one has to provide a mechanism by which a daughter graph the right hand side of a production can be embedded in the rest of the mother graph while in the latter this embedding is provided automatically by the structure that all strings possess left to right orientation in this paper we consider a possible classification of embedding mechanisms for node rewriting graph grammars this classification originates from the basic ideas of 9 on the one hand it allows one to fit a number of existing notions of a graph grammar into a common framework and on the other hand it points out new natural possibilities for defining the embedding mechanism in a graph grammar the relationship between the graph language generating power of graph grammars using various embedding mechanisms is established

a note on higher order symmetric duality in this paper a pair of wolfe type higher order symmetric dual multiobjective programs is formulated strong and converse duality theorems are established under invexity assumptions duality relations for mond weir type dual models have also been obtained under pseudoinvexity assumptions

finite graph automata for linear and boundary graph languages graph grammars can be regarded as a generalization of context free grammars from strings to graphs over the past 30 years a rich theory of graph grammars and their languages has been developed however there are no graph automata there is no duality between generative and recognizing devices as it is known for the chomsky hierarchy of formal languages here we introduce graph automata as devices for the recognition of sets of undirected node labelled graphs a graph automaton consists of a finite state control a finite set of instructions and a collection of heads or guards it reads an input graph in a systematic way and performs a graph search directed by the instructions as our main results we show that finite graph automata recognize exactly the set of graph languages generated by linear nce graph grammars and that alternating finite graph automata recognize exactly the languages of boundary graph grammars finally we generalize some automata theoretic properties from string to graph automata integrate the connectivity of graphs into graph automata and explain why graph automata cannot be generalized to deal with dynamic edge relabellings and ence graph languages

multiobjective symmetric duality involving cones abstract in this paper a pair of multiobjective symmetric dual programs over arbitrary cones are formulated for cone convex functions weak strong converse and self duality theorems are proved for these programs

boundary nlc graph grammars basic definitions normal forms and complexity node label controlled nlc grammars are graph grammars operating on node labeled undirected graphs which rewrite single nodes only and establish connections between the embedded graph and the neighbors of the rewritten node on the basis of the labels of the involved nodes only they define possibly infinite languages of undirected node labeled graphs or if we just omit the labels languages of unlabeled graphs here we consider a restriction of nlc grammars so called boundary nlc bnlc grammars distinguished by the property that whenever in a graph already generated two nodes may be rewritten then these nodes are not adjacent the graph languages generated by this type of grammars are called bnlc languages although we show that this restriction leads to a smaller class of languages still enough generative power remains to define interesting graph languages for example trees complete bipartite graphs maximal outerplanar graphs k trees graphs of bandwidth k graphs of cyclic bandwidth k graphs of binary tree bandwidth k graphs of cutwidth k always for a fixed positive integer k turn out all to be bnlc languages we prove a number of normal forms for bnlc grammars and then we indicate their usefulness by various applications in particular we show that for connected graphs of bounded degree the membership problem for bnlc languages is solvable in deterministic polynomial time

the complexity of the kn n problem for node replacement graph languages the bounded kn n problem is the question whether or not a graph language of a given graph grammar contains arbitrarily large complete bipartite subgraphs kn n in this paper we investigate the complexity of this problem for all relevant classes of node replacement graph grammers our main result states that the bounded kn n problem is nl complete for reduced nonblocking ence graph grammars and for reduced linear nce graph grammars as an application our results settle the complexity of the problems whether or not the graph language of a given confluent boundary or linear graph grammar has bounded tree width and whether or not it is an hr graph language

higher order duality in multiobjective fractional programming with square root term under generalized higher order f α β p σ d v type i univex functions in this paper a new generalized class of higher order f d v type i univex function is introduced with some examples for a differentiable multiobjective programming mp then multiobjective fractional programming problem mfp is considered in which the numerator and denominator of objective functions contain square root of positive semidefinite quadratic form and the necessary and sufficient conditions for efficient solution for mfp are established under generalized higher order f d v type i univex functions again higher order dual program is proposed for mfp and the duality results are established under generalized of higher order f d v type i univex functions also some computational work has been done to substantiate the analysis

multiobjective second order symmetric duality with f convexity we suggest a pair of second order symmetric dual programs in multiobjective nonlinear programming for these second order symmetric dual programs we prove the weak strong and converse duality theorems under f convexity conditions

second order f α ρ d convexity and duality in multiobjective programming a class of second order f a r d convex functions and their generalizations is introduced using the assumptions on the functions involved weak strong and strict converse duality theorems are established for a second order mond weir type multiobjective dual

multiobjective mixed symmetric duality involving cones a pair of multiobjective mixed symmetric dual programs is formulated over arbitrary cones weak strong converse and self duality theorems are proved for these programs under k preinvexity and k pseudoinvexity assumptions this mixed symmetric dual formulation unifies the symmetric dual formulations of suneja et al 2002 14 and khurana 2005 15

node rewriting in graphs and hypergraphs a categorical framework vertex rewriting in graphs is a very powerful mechanism which has been studied for quite a long time in this paper we eventually provide a categorical theory of vertex rewriting and show how it can extend in a uniform way to node and pattern rewriting mechanisms in hypergraphs copyright 2001 elsevier science b v

second order symmetric duality in multiobjective programming abstract a pair of mond weir type multiobjective second order symmetric dual programs are formulated without non negativity constraints weak duality strong duality and converse duality theorems are established under bonvexity and pseudobonvexity assumptions a second order self duality theorem is given by assuming the functions involved to be skew symmetric

the bounded degree problem for ence graph grammars the complexity of the bounded degree problem is analyzed for graph languages generated by ence graph grammars in particular the bounded degree problem is shown to be undecidable for ence graph grammars dexptime complete for confluent boundary ence graph grammars pspace complete for linear ence graph grammars and p complete for non blocking ence graph grammars in our main theorem we show that the bounded degree problem is nl complete for reduced non blocking ence graph grammars many of the shown results carry over to other types of graph grammars

higher order f α ρ d convexity and symmetric duality in multiobjective programming a pair of higher order wolfe type and mond weir type multiobjective symmetric dual programs over arbitrary cones is formulated weak strong and converse duality theorems are then established using the notion of higher order f a r d convexity pseudoconvexity assumptions special cases are also discussed to show that this paper extends some known results of the literature

the monadic second order logic of graphs vii graphs as relational structures abstract relational structures form a unique framework in which various types of graphs and hypergraphs can be formalized and studied we define operations on structures that are compatible with monadic second order logic and that are powerful enough to represent context free graph and hypergraph grammars of various types namely the so called hyperedge replacement c ednce and separated handle rewriting grammars several results concerning monadic second order properties of the generated sets are obtained in a uniform way we also give a logical characterization of the equational sets of structures that generalizes the ones obtained by engelfriet and courcelle for hyperedge replacement and c ednce sets of graphs

second order symmetric duality with cone constraints wolfe and mond weir type second order symmetric duals are formulated and appropriate duality theorems are established under h bonvexity h pseudobonvexity assumptions this formulation removes several omissions in an earlier second order primal dual pair introduced by devi symmetric duality for nonlinear programming problems involving h bonvex functions european j oper res 104 1998 615 621

node replacement graph languages squeezed with chains trees and forests we present results on language theoretic properties such as closure membership and other decision properties of node replacement graph languages such as nlc b nlc and lin nlc languages squeezed with chains trees and forests

on multiobjective second order symmetric duality with cone constraints abstract a pair of wolfe type multiobjective second order symmetric dual programs with cone constraints is formulated and usual duality results are established under second order invexity assumptions these results are then used to investigate symmetric duality for minimax version of multiobjective second order symmetric dual programs wherein some of the primal and dual variables are constrained to belong to some arbitrary sets i e the sets of integers this paper points out certain omissions and inconsistencies in the earlier work of mishra s k mishra multiobjective second order symmetric duality with cone constraints european journal of operational research 126 2000 675 682 and mishra and wang s k mishra s y wang second order symmetric duality for nonlinear multiobjective mixed integer programming european journal of operational research 161 2005 673 682

a comparison of boundary graph grammars and context free hypergraph grammars context free hypergraph grammars and boundary graph grammars of bounded nonterminal degree have the same power both for generating sets of graphs and for generating sets of hypergraphs arbitrary boundary graph grammars have more graph generating power than context free hypergraph grammars but they have the same hypergraph generating power to obtain these results several normal forms for boundary graph grammars are given it is also shown that the class of boundary graph languages is closed under the operation of edge contraction where the label of the edge indicates whether or not the edge should be contracted

on bergman completeness and bergman stability it is proved that any bounded pseudoconvex domain in bf c n is complete w r t the bergman metric if its boundary can be described locally as the graph of a continuous function in suitable coordinates for bf c n further arguments are given concerning the stability problems of the bergman kernel on non smooth pseudoconvex domains

higher order symmetric duality in nondifferentiable multiobjective programming problems abstract in this paper a pair of nondifferentiable multiobjective programming problems is first formulated where each of the objective functions contains a support function of a compact convex set in rn for a differentiable function h r n r n r we introduce the definitions of the higher order f convexity f pseudo convexity f quasi convexity of function f r n r with respect to h when f and h are taken certain appropriate transformations all known other generalized invexity such as invexity type i invexity and higher order type i invexity can be put into the category of the higher order f invex functions under these the higher order f convexity assumptions we prove the higher order weak higher order strong and higher order converse duality theorems related to a properly efficient solution

an axiomatic definition of context free rewriting and its application to nlc graph grammars abstract an abstract notion of context free grammar is introduced it deals with abstract objects that can be words trees graphs or other combinatorial objects it is applied to nlc graph grammars introduced by rozenberg and janssens the monadic second order theory of a context free nlc set of graphs is decidable

the bergman metric on a stein manifold with a bounded plurisubharmonic function in this article we use the pluricomplex green function to give a sufficient condition for the existence and the completeness of the bergman metric as a consequence we proved that a simply connected complete kahler manifold possesses a complete bergman metric provided that the riemann sectional curvature a 2 which implies a conjecture of greene and wu moreover we obtain a sharp estimate for the bergman distance on such manifolds

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

linear graph grammars power and complexity abstract a graph grammar is linear if it generates graphs with at most one nonterminal node linear graph grammars can simulate nonterminal bounded graph grammars which generate graphs with a bounded number of nonterminal nodes and derivation bounded graph grammars if a linear graph language contains connected graphs of bounded degree only then it is in nspace log n these results are shown for graph grammars with neighbourhood controlled embedding and with dynamic edge relabeling ence grammars

a hierarchy of ence families of graph languages abstract even though ence and its subclasses have been studied intensively their inclusion relations are not completely known this paper proves some unknown relations among ence families of graph languages which yield together with other known relations a solid hierarchy of graph languages that completely determines equivalence proper inclusion and incomparability among nlc nce enlc ence and their boundary linear and apex subclasses the bottom level of this hierarchy i e lin a nlc contains an np complete graph language

nonterminal separation in graph grammars abstract the notion of nonterminal separation in ence graph grammars is introduced such a graph grammar is k separated with k 1 if the distance between any two nonterminal nodes in any of its sentential forms is at least k 2 separated ence grammars are known as boundary ence graph grammars there exists a 2 separated ence graph language that is not 3 separated apex ence graph grammars can be arbitrarily separated every apex ence graph language can be generated by a k separated apex ence grammar for every k