a framework for non interactive instance dependent commitment schemes nic zero knowledge protocols are often studied through specific problems like graph isomorphism in many cases this approach prevents an important level of abstraction and leads to limited results whereas in fact the constructions apply to a wide variety of problems we propose to address this issue with a formal framework of non interactive instance dependent commitment schemes nic we define nic in the perfect statistical and computational settings and formally characterize problems admitting nic in all of these settings we also prove other useful lemmas such as closure properties consequently results that previously applied only to specific problems are now strengthened by our framework to apply to classes of problems by providing formal yet intuitive tools our framework facilitates the construction of zero knowledge protocols for a wide variety of problems in various settings without the need to refer to a specific problem our results are unconditional

survey of disjoint np pairs and relations to propositional proof systems we survey recent results on disjoint np pairs in particular we survey the relationship of disjoint np pairs to the theory of proof systems for propositional calculus

optimality conditions for degenerate extremum problems with equality constraints in this paper we consider an optimization problem with equality constraints given in operator form as f x 0 where f x to y is an operator between banach spaces the paper addresses the case when the equality constraints are not regular in the sense that the frechet derivative f x is not onto in the first part of the paper we pursue an approach based on the construction of p regularity for p regular constrained optimization problems we formulate necessary conditions for optimality and derive sufficient conditions for optimality in the second part of the paper we consider a generalization of the concept of p regularity and derive generalized necessary conditions for optimality for an optimization problem that is neither regular nor p regular for this problem we show that the tangent cone to a level surface of f can consist of rays rather than lines this is in contrast to the regular and the p regular cases for which the tangent cone is always two sided we state that if the gradien

implication of clauses is undecidable abstract clause implication a b of two clauses a and b is shown to be undecidable using the undecidability of finitely generated stable transitive relations on free terms clause implication is undecidable even in the case where a consists of four literals the decision problem of clause implication is equivalent to the decision problem of clause sets that consist of one clause and some ground units hence the undecidability results hold also for these clause sets clause implication is an important problem in automated deduction systems as it can be used advantageously to reduce the search space

bounded query classes polynomial time machines having restricted access to an np oracle are investigated restricted access means that the number of queries to the oracle is restricted or the way in which the queries are made is restricted e g queries made during truth table reductions very different kinds of such restrictions result in the same or comparable complexity classes in particular the class p text np o log n can be characterized in very different ways furthermore the boolean hierarchy is generalized in such a way that it is possible to characterize p text np and p text np o log n in terms of the generalization

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

relativized cryptography it appears to be very difficult to give a formal definition of computational security for public key cryptography a slightly different notion called transient key cryptography is defined for which a natural definition of security against chosen plaintext attacks is given the main result presented here is the existence of a relativized model of computation under which there does exist a secure transient key cryptosystem indeed there exists a computable oracle that can be used by cryptographers to efficiently encipher and decipher messages yet it is of no help to the cryptanalyst trying to decode messages not intended for him as a corollary there also exists a length preserving permutation the inverse of which is hard to compute on most elements of its domain even if arbitrary evaluations of the function itself are allowed for free

bulk and surface critical behavior of the three dimensional ising model and conformal invariance using a continuous cluster monte carlo algorithm we investigate the critical three dimensional ising model in its anisotropic limit from the ratio of the magnetic correlations in the strong and the weak coupling directions we determine the length ratio relating the isotropic ising model and the anisotropic limit on this basis we simulate the critical ising model on a spherocylinder s2 x r1 i e a curved geometry obtained from a conformal mapping of the infinite space r3 from correlation lengths along the spherocylinder combined with the prediction of conformal invariance we estimate the magnetic and thermal scaling dimensions as x h 0 5182 6 and x t 1 419 7 respectively the behavior of the binder cumulant is also determined in the limit of an infinitely long spherocylinder next free boundary conditions are imposed on the equators of the spherocylinder and thus the geometry s1 x s x r1 is obtained the surface magnetic scaling dimension is estimated as x s h 1 263 5 the consistency of the aforementioned estimations and existing results confirms that the three dimensional ising model is conformally invariant further the precision of these results reveals that as in two dimensions conformal mappings provide a powerful tool to investigate critical phenomena with the continuous cluster algorithm we also perform simulations of systems inside a conventional solid cylinder the surface magnetic correlation length differs within the estimated error margin by a factor pi 2 from that along a half spherocylinder s1 x s x r1 with the same radius

quantum finite automata we first outline main steps and achievements along bertoni s research path in quantum finite automata theory from the very basic definitions of the models of quantum finite automata throughout the investigation of their computational and descriptional power next we choose to focus on bertoni s studies on quantum finite automata descriptional complexity in particular we expand on a statistical framework for the synthesis of succinct quantum finite automata discussing its adaptation to the case of multiperiodic events and languages we then improve such a framework to obtain even more succinct quantum finite automata for some multiperiodic languages finally we introduce some promise problems for multiperiodic inputs showing that even on this class of problems the descriptional power of quantum finite automata greatly outperforms that of equivalent classical finite automata we build small size monte carlo quantum finite automata for multiperiodic languages we analyze the modular architecture of such monte carlo quantum finite automata we solve promise problems on multiperiodic inputs by small quantum finite automata

probabilistic low rank factorization accelerates tensor network simulations of critical quantum many body ground states we provide evidence that randomized low rank factorization is a powerful tool for the determination of the ground state properties of low dimensional lattice hamiltonians through tensor network techniques in particular we show that randomized matrix factorization outperforms truncated singular value decomposition based on state of the art deterministic routines in time evolving block decimation tebd and density matrix renormalization group dmrg style simulations even when the system under study gets close to a phase transition we report linear speedups in the bond or local dimension of up to 24 times in quasi two dimensional cylindrical systems

more complicated questions about maxima and minima and some closures of np abstract starting from np complete problems defined by questions of the kind max m and min m we consider problems defined by more complicated questions about these maxima and minima as for example max m min m and is max odd this continues a work started by papadimitriou and yannakakis 1982 it is shown that these and other problems are complete in certain subclasses of the boolean closure of np and other classes in the interesting area below the class p 2 of the polynomial time hierarchy special methods are developed to prove such completeness results for this it is necessary to establish some properties of the classes in question which might be interesting in their own right

critical percolation clusters in seven dimensions and on a complete graph we study critical bond percolation on a seven dimensional hypercubic lattice with periodic boundary conditions 7d and on the complete graph cg of finite volume number of vertices v we numerically confirm that for both cases the critical number density n s v of clusters of size s obeys a scaling form n s v s n over s v d f with identical volume fractal dimension d f 2 3 and exponent 1 1 d f 5 2 we then classify occupied bonds into bridge bonds which includes branch and junction bonds and nonbridge bonds a bridge bond is a branch bond if and only if its deletion produces at least one tree deleting branch bonds from percolation configurations produces leaf free configurations whereas deleting all bridge bonds leads to bridge free configurations composed of blobs it is shown that the fraction of nonbridge biconnected bonds vanishes n cg 0 for large cgs but converges to a finite value n 7d 0 0061931 7 for the 7d hypercube further we observe that while the bridge free dimension d bf 1 3 holds for both the cg and 7d cases the volume fractal dimensions of the leaf free clusters are different d lf 7d 0 669 9 2 3 and d lf cg 0 3337 17 1 3 on the cg and in 7d the whole leaf free and bridge free clusters all have the shortest path volume fractal dimension d min 1 3 characterizing their graph diameters we also study the behavior of the number and the size distribution of leaf free and bridge free clusters for the number of clusters we numerically find the number of leaf free and bridge free clusters on the cg scale as lnv while for 7d they scale as v for the size distribution we find the behavior on the cg is governed by a modified fisher exponent 1 while for leaf free clusters in 7d it is governed by fisher exponent 5 2 the size distribution of bridge free clusters in 7d displays two scaling behavior with exponents 4 and 1 the probability distribution p c 1 v dc 1 of the largest cluster of size c 1 for whole percolation configurations is observed to follow a single variable function p over x dx with x c 1 v d f for both cg and 7d up to a rescaling factor for the variable x the probability functions for cg and 7d collapse on top of each other within the entire range of x the analytical expressions in the x 0 and x limits are further confirmed our work demonstrates that the geometric structure of high dimensional percolation clusters cannot be fully accounted for by their complete graph counterparts

compactly representing utility functions using weighted goals and the max aggregator weighted propositional formulas can be used to model preferences over combinatorial domains each formula represents a goal we would like to see satisfied the weight of a formula represents the importance of the goal in question and to assess the desirability of a given alternative we aggregate the weights of the goals satisfied by that alternative one of several options is to aggregate by using the maximum of the weights of the satisfied goals this approach gives rise to a family of preference representation languages one for each of a range of possible restrictions we can impose on either formulas or weights we analyze the properties of these languages and establish results regarding their expressivity and absolute and relative succinctness we also study the computational complexity of the problem of finding the best and the worst alternative for a given set of weighted goals and of finding an alternative that is optimal for a group of agents for a range of different notions of collective optimality proposed in social choice theory and welfare economics

the boolean hierarchy ii applications the boolean hierarchy i structural properties j cai et al siam j comput 17 1988 pp 1232 252 explores the structure of the boolean hierarchy the closure of np with respect to boolean

computing functions with parallel queries to np the class 2p of languages polynomial time truth table reducible to sets in np has a wide range of different characterizations we consider several functional versions of 2p based on these characterizations we show that in this way the three function classes fllognp fplognp and fp np are obtained in contrast to the language case the function classes seem to all be different we give evidence in support of this fact by showing that fllognp coincides with any of the other classes then l p and that the equality of the classes fplognp and fp np would imply that the number of nondeterministic bits needed for the computation of any problem in np can be reduced by a polylogarithmic factor and that the problem can be computed deterministically with a subexponential time bound of order 2no 1 log log n

unambiguous computations and locally definable acceptance types abstract hertrampf s locally definable acceptance types show that many complexity classes can be defined in terms of polynomial time bounded ntms with simple local conditions on the nodes of its computation tree rather than global concepts like number of accepting paths etc we introduce a modification of hertrampf s locally definable acceptance types which allows to get a larger number of characterizable complexity classes among others the newly characterizable classes are up and mod z k p it is shown how different types of oracle access e g guarded access can be characterized by this model this sheds new light on the discussion on how to access unambiguous computation we present simple functions that describe precisely objects of current research as the unambiguous oracle alternation and promise hierarchies we exhibit the new class uap which seems to be an unambiguous analogue of wagner s p uap and thus p contains few and is currently the smallest class known with this property

the boolean hierarchy i structural properties in this paper we study the complexity of sets formed by boolean operations union intersection and complement on np sets these are the sets accepted by trees of hardware with np predicates as leaves and together these form the boolean hierarchy we present many results about the structure of the boolean hierarchy separation and immunity results natural complete languages and structural asymmetries between complementary classes we show that in some relativized worlds the boolean hierarchy is infinite and that for every k there is a relativized world in which the boolean hierarchy extends exactly k levels we prove natural languages variations of vertex cover complete for the various levels of the boolean hierarchy we show the following structural asymmetry though no set in the boolean hierarchy is text d text p immune there is a relativized world in which the boolean hierarchy contains text cod text p immune sets thus this paper explores the structural properties of the

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

graph isomorphism is in spp we show that graph isomorphism is in the complexity class spp and hence it is in p in fact in modkp for each k 2 these inclusions for graph isomorphism were not known prior to membership in spp we derive this result as a corollary of a more general result we show that a generic problem find group has an fpspp algorithm this general result has other consequences for example it follows that the hidden subgroup problem for permutation groups studied in the context of quantum algorithms has an fpspp algorithm also some other algorithmic problems over permutation groups known to be at least as hard as graph isomorphism e g coset intersection are in spp and thus in modkp for each k 2

optimality conditions for irregular inequality constrained problems we consider feasible sets given by conic constraints where the cone defining the constraints is convex with nonempty interior we study the case where the feasible set is not assumed to be regular in the classical sense of robinson and obtain a constructive description of the tangent cone under a certain new second order regularity condition this condition contains classical regularity as a special case while being weaker when constraints are twice differentiable assuming that the cone defining the constraints is finitely generated we also derive a special form of primal dual optimality conditions for the corresponding constrained optimization problem our results subsume optimality conditions for both the classical regular and second order regular cases while still being meaningful in the more general setting in the sense that the multiplier associated with the objective function is nonzero

an envelope solitary wave solution for a generalized nonlinear schrodinger equation we derive an envelope solitary wave solution for the following generalized nonlinear schrodinger equation ut ia2uxx a3uxxx ib mod u mod 2u b1 mod u mod 2u x by gauge transformation

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

cluster monte carlo algorithms abstract the swendsen wang and wolff monte carlo algorithms are described in some detail using the potts model as an example various generalizations are then reviewed and some applications are discussed two complete fortran programs for the algorithms are provided

on the reducibility of sets inside np to sets with low information content this paper studies for various natural problems in np whether they can be reduced to sets with low information content such as branches p selective sets and membership comparable sets the problems that are studied include the satisfiability problem the graph automorphism problem the undirected graph accessibility problem the determinant function and all logspace self reducible languages some of these are complete for complexity classes within np but for others an exact complexity theoretic characterization is not known reducibility of these problems is studied in a general framework introduced in this paper prover verifier protocols with low complexity provers it is shown that all these natural problems indeed have such protocols this fact is used to show for certain reduction types that these problems are not reducible to sets with low information content unless their complexity is much less than what it is currently believed to be the general framework is also used to obtain a new characterization of the complexity class l l is the class of all logspace self reducible sets in ll sel

critical exponents of the n vector model recently the series for two renormalization group functions corresponding to the anomalous dimensions of the fields and of the three dimensional field theory have been extended to next order seven loops by murray and nickel we examine the influence of these additional terms on the estimates of critical exponents of the n vector model using some new ideas in the context of the borel summation techniques the estimates have slightly changed but remain within the errors of the previous evaluation exponents such as related to the field anomalous dimension which were poorly determined in the previous evaluation of le guillou zinn justin have seen their apparent errors significantly decrease more importantly perhaps summation errors are better determined the change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values finally because an error has been discovered in the last order of the published expansions order we have also re analysed the determination of exponents from the expansion the conclusion is that the general agreement between expansion and three dimensional series has improved with respect to le guillou zinn justin

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

conformal invariance and the ising model on a spheroid we formulate conformal mappings between an infinite plane and a spheroid and one between a semi infinite plane and a half spheroid special cases of the spheroid include the surface of an infinitely long cylinder of a sphere and of a flat disc these mappings are applied to the critical ising model for the case of the sphere and the flat disc we derive analytical expressions for the second and the fourth moments of the magnetization density and thus for the binder cumulant next we investigate ising models on spheroids and half spheroids by means of a continuous cluster monte carlo method for simulations in curved geometries fixed and free boundary conditions are imposed for half spheroids the monte carlo data are analyzed by finite size scaling critical values of the binder cumulants and other ratios on the sphere and on the flat disc agree precisely with the exact calculations mentioned above at criticality we also sample two and one point correlation functions on spheroids on half spheroids respectively the magnetic and temperature scaling dimensions as determined from the monte carlo data and the theory of conformal invariance are in good agreement with exact results

the pth order optimality conditions for inequality constrained optimization problems in this paper we present pth order necessary conditions for optimality for an optimization problem with inequality constraints in the finite dimensional spaces models of this type arise as the discretization of optimal control problems calculus of variations problems and other problems the paper addresses the degenerate nonregular case when the active constraint gradients are linearly dependent in this case the classical necessary conditions are either inapplicable or trivially satisfied with the zero multiplier corresponding to the objective function the proposed high order optimality conditions give new and nontrivial conditions for nonregular cases and reduce to the classical conditions for regular cases

promise problems complete for complexity classes abstract a general framework is given to obtain hardness results for promise problems that derive from self reducible decision problems the principal theorem is that if a set a is d p equivalent to a disjunctive self reducible set in np then the natural promise problem associated with a is as hard to solve as it is to recognize a np hardness of the satisfiability promise problem follows and graph isomorphism hardness of a promise problem that derives from the graph isomorphism problem is proved

resource bounded kolmogorov complexity revisited we take a fresh look at cd complexity where cdt x is the size of the smallest program that distinguishes x from all other strings in time t x we also look at cnd complexity a new nondeterministic variant of cd complexity and time bounded kolmogorov complexity denoted by c complexity we show several results relating time bounded c cd and cnd complexity and their applications to a variety of questions in computational complexity theory including the following showing how to approximate the size of a set using cd complexity without using the random string as needed in sipser s earlier proof of a similar result also we give a new simpler proof of this result of sipser s improving these bounds for almost all strings using extractors a proof of the valiant vazirani lemma directly from sipser s earlier cd lemma a relativized lower bound for cnd complexity exact characterizations of equivalences between c cd and cnd complexity showing that satisfying assignments of a satisfiable boolean formula can be enumerated in time polynomial in the size of the output if and only if a unique assignment can be found quickly this answers an open question of papadimitriou a new kolmogorov complexity based proof that bpp subseteq sigma 2 p new kolmogorov complexity based constructions of the following relativized worlds there exists an infinite set in p with no sparse infinite np subsets exp nexp but there exists a nexp machine whose accepting paths cannot be found in exponential time satisfying assignments cannot be found with nonadaptive queries to sat

on truth table reducibility to sat we show that polynomial time truth table reducibility via boolean circuits to sat is the same as logspace truth table reducibility via boolean formulas to sat and the same as logspace turing reducibility to sat in addition we prove that a constant number of rounds of parallel queries to sat is equivalent to one round of parallel queries we give an oracle relative to which 2p is not equal to the class of predicates polynomial time truth table reducible to sat

high order approximations and generalized necessary conditions for optimality in this paper we derive generalized necessary conditions for optimality for an optimization problem with equality and inequality constraints in a banach space the equality constraints are given in operator form as q x in x f x 0 where f x rightarrow y is an operator between banach spaces the inequality constraints are given by smooth functionals or by closed convex sets models of this type are common in the optimal control problem the paper addresses the case when the frechet derivative f x is not onto and hence the classical lyusternik theorem does not apply to describe the tangent space to q in this case the classical euler lagrange type necessary conditions are trivially satisfied generating abnormal cases a high order generalization of the lyusternik theorem derived earlier u ledzewicz and h schattler nonlinear anal 34 1998 pp 793 815 is used to calculate high order tangent cones to the equality constraint at points x in q where f x is not onto combining these with high order approximating cones related to the other constraints of the problem feasible cones respectively cones of decrease a high order generalization of the dubovitskii milyutin theorem is given and then applied to derive generalized necessary conditions for optimality these conditions reduce to classical conditions for normal cases but they give new and nontrivial conditions for abnormal cases

on the complexity of entailment in existential conjunctive first order logic with atomic negation we consider the entailment problem in the fragment of first order logic fol composed of existentially closed conjunctions of literals without functions denoted by fol a this problem can be recast as several fundamental problems in artificial intelligence and databases namely query containment for conjunctive queries with negation clause entailment for clauses without functions and query answering with incomplete information for boolean conjunctive queries with negation over a fact base entailment in fol a is p 2 p complete whereas it is only np complete when the formulas contain no negation we investigate the role of specific literals in this complexity increase these literals have the property of being exchangeable with this notion taking the structure of the formulas into account to focus on the structure of formulas we shall see them as labeled graphs graph homomorphism which provides a sound and complete proof procedure for positive formulas is at the core of this study let entailment k be the following family of problems given two formulas g and h in fol a such that g has at most k pairs of exchangeable literals is g entailed by h the main results are that entailment k is np complete if k is less or equal to 1 and p n p complete for any value of k greater or equal to 3 as a corollary of our proofs we are able to classify exactly entailment k for any value of k 2 when g is decomposable into a tree

reductions between disjoint np pairs disjoint np pairs are pairs a b of nonempty disjoint sets in np we prove that all of the following assertions are equivalent there is a many one complete disjoint np pair there is a strongly many one complete disjoint np pair there is a turing complete disjoint np pair such that all reductions are smart reductions there is a complete disjoint np pair for one to one invertible reductions the class of all disjoint np pairs is uniformly enumerable let a b c and d be nonempty sets belonging to np a smart reduction between the disjoint np pairs a b and c d is a turing reduction with the additional property that if the input belongs to a b then all queries belong to c d we prove under the reasonable assumption that up co up has a p bi immune set that there exist disjoint np pairs a b and c d such that a b is truth table reducible to c d but there is no smart reduction between them this paper contains several additional separations of reductions between disjoint np pairs we exhibit an oracle relative to which distnp has a truth table complete disjoint np pair but has no many one complete disjoint np pair

universal ratio of magnetization moments in two dimensional ising models the authors calculate the universal critical point ratios of the square of the second and the fourth moment of the magnetization for ferromagnetic ising models on the square and on the triangular lattices periodic boundary conditions are used in accordance with the four fold and six fold rotational symmetries of the respective lattices these results which are obtained by means of an analysis of finite size data computed with a transfer matrix technique have an accuracy of the order of one millionth this analysis is also applied to rectangular systems with arbitrary aspect ratios

a hierarchy based on output multiplicity abstract the class np k v consists of those partial multivalued functions that can be computed by a nondeterministic polynomial time bounded transducer that has at most k distinct values on any input we define the output multiplicity hierarchy to consist of the collection of classes np k v for all positive integers k 1 in this paper we investigate the strictness of the output multiplicity hierarchy and establish three main results pertaining to this 1 1 if for any k 1 the class np k v collapses into the class np k 1 v then the polynomial hierarchy collapses to 2 p 2 2 if the converse of the above result is true then any proof of this converse cannot relativize we exhibit an oracle relative to which the polynomial hierarchy collapses to p np but the output multiplicity hierarchy is strict 3 3 relative to a random oracle the output multiplicity hierarchy is strict this result is in contrast to the still open problem of the strictness of the polynomial hierarchy relative to a random oracle in introducing the technique for the third result we prove a related result of interest relative to a random oracle up np

series expansions for the 3d transverse ising model at t 0 both weak coupling and strong coupling series expansions are calculated for the ising model in a transverse field at zero temperature in three dimensions series are obtained for the ground state energy the magnetization the susceptibility and the energy gaps on the simple cubic the body centred cubic and the face centred cubic lattices the analysis of the critical behaviour is consistent with the behaviour predicted by renormalization group theory for the four dimensional simple ising model there is a remarkable degree of universality between all three lattices

the shrinking property for np and conp we study the shrinking and separation properties two notions well known in descriptive set theory for np and conp and show that under reasonable complexity theoretic assumptions both properties do not hold for np and the shrinking property does not hold for conp in particular we obtain the following results 1 np and conp do not have the shrinking property unless ph is finite in general s n p and p n p do not have the shrinking property unless ph is finite this solves an open question posed by selivanov 1994 33 2 the separation property does not hold for np unless email protected conp 3 the shrinking property does not hold for np unless there exist np hard disjoint np pairs existence of such pairs would contradict a conjecture of even et al 1984 6 4 the shrinking property does not hold for np unless there exist complete disjoint np pairs moreover we prove that the assumption np conp is too weak to refute the shrinking property for np in a relativizable way for this we construct an oracle relative to which email protected conp np conp and np has the shrinking property this solves an open question posed by blass and gurevich 1984 3 who explicitly ask for such an oracle

locally testable codes and pcps of almost linear length we initiate a systematic study of locally testable codes that is error correcting codes that admit very efficient membership tests specifically these are codes accompanied with tests that make a constant number of random queries into any given word and reject non codewords with probability proportional to their distance from the code locally testable codes are believed to be the combinatorial core of pcps however the relation is less immediate than commonly believed nevertheless we show that certain pcp systems can be modified to yield locally testable codes on the other hand we adapt techniques that we develop for the construction of the latter to yield new pcps our main results are locally testable codes and pcps of almost linear length specifically we prove the existence of the following constructs locally testable binary linear codes in which k information bits are encoded by a codeword of length k exp o log k this improves over previous results that either yield codewords of exponential length or obtained almost quadratic length codewords for sufficiently large nonbinary alphabet pcp systems of almost linear length for sat the length of the proof is n exp o log n and verification in performed by a constant number i e 19 of queries as opposed to previous results that used proof length n 1 p o 1 q for verification by q queries the novel techniques in use include a random projection of certain codewords and pcp oracles that preserves local testability an adaptation of pcp constructions to obtain linear pcp oracles for proving conjunctions of linear conditions and design of pcps with some new soundness properties a direct construction of locally testable linear codes of subexponential length

cluster monte carlo simulation of the transverse ising model we formulate a cluster monte carlo method for the anisotropic limit of ising models on d 1 dimensional lattices which in effect are equivalent with d dimensional quantum transverse ising models using this technique we investigate the transverse ising models on the square triangular kagome honeycomb and simple cubic lattices the monte carlo data are analyzed by finite size scaling in each case we find as expected that the critical behavior fits well in the d 1 dimensional ising universality class for the transverse ising model on the square lattice we determine the binder cumulant of the classical counterpart for a range of aspect ratios between the system sizes in the third or classical direction and that in the other two directions matching this universal function with the case of the isotropic ising model yields the length ratio relating the isotropic ising model with the anisotropic limit the efficiency of the present algorithm is reflected by the precision of its results which improves significantly on earlier analyses

length scaling in mfrg the mean field renormalisation group mfrg has so far given poor estimates for critical indices it is argued that this can be traced to an unsatisfactory definition of the length scaling factor a new definition that improves the estimates in most cases is proposed

high dimensional lattice gases we investigate the critical behaviour of hard core lattice gases in four five and six dimensions by means of monte carlo simulations in order to suppress critical slowing down we use a geometrical cluster monte carlo algorithm in particular nearest neighbour exclusion lattice gases on simple hypercubic lattices are investigated these models undergo ising like ordering transitions where the majority of the lattice gas particles settle on one of two sublattices a finite size scaling analysis of the simulation data confirms that these lattice gases display classical critical behaviour the results agree with the renormalization predictions at and above the upper critical dimensionality in particular the predicted value of the binder cumulant is confirmed

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

ising universality in three dimensions a monte carlo study we investigate three ising models on the simple cubic lattice by means of monte carlo methods and finite size scaling these models are the spin 1 2 ising model with nearest neighbour interactions a spin 1 2 model with nearest neighbour and third neighbour interactions and a spin 1 model with nearest neighbour interactions the results are in accurate agreement with the hypothesis of universality analysis of the finite size scaling behaviour reveals corrections beyond those caused by the leading irrelevant scaling field we find that the correction to scaling amplitudes are strongly dependent on the introduction of further neighbour interactions or a third spin state in a spin 1 ising model these corrections appear to be very small this is very helpful for the determination of the universal constants of the ising model the renormalization exponents of the ising model are determined as yt 1 587 2 yh 2 4815 15 and yi 0 82 6 the universal ratio q m2 2 m4 is equal to 0 6233 4 for periodic systems with cubic symmetry the critical point of the nearest neighbour spin 1 2 model is kc 0 2216546 10

separating complexity classes with tally oracles abstract long and selman 1986 proved that for most familiar pairs of complexity classes separating the classes with a tally oracle is no easier than truly separating the classes refuting a claim in the literature we prove for the first time that for many familiar pairs of complexity classes separating the classes with a tally oracle is easier than truly separating the classes

computing answers with model elimination abstract we demonstrate that theorem provers using model elimination me can be used as answer complete interpreters for disjunctive logic programming more specifically we introduce a family of restart variants of model elimination and we introduce a mechanism for computing answers building on this we develop a new calculus called ancestry restart me this variant admits a more restrictive regularity restriction than restart me and as a side effect it is in particular attractive for computing definite answers the presented calculi can also be used successfully in the context of automated theorem proving we demonstrate experimentally that it is more difficult to compute nontrivial answers to goals than to prove the existence of answers

an oracle separating conjectures about incompleteness in the finite domain abstract pudlak 19 lists several major complexity theoretic conjectures relevant to proof complexity and asks for oracles that separate pairs of corresponding relativized conjectures among these conjectures are disjnp the class of all disjoint np pairs does not have many one complete problems sat np does not contain many one complete sets that have p optimal proof systems up up does not have many one complete problems np conp np conp does not have many one complete problems as one answer to this question we construct an oracle relative to which among others disjnp sat up and np conp hold hence there is no relativizable proof for the implication disjnp up np conp sat in particular regarding the conjectures by pudlak this extends a result by khaniki 11

revisiting deutsch jozsa algorithm abstract the deutsch jozsa algorithm is essentially faster than any possible deterministic classical algorithm for solving a promise problem that is in fact a symmetric partial boolean function named as the deutsch jozsa problem the deutsch jozsa problem can be equivalently described as a partial function d j n 0 0 1 n 0 1 defined as d j n 0 x 1 for x n 2 d j n 0 x 0 for x 0 n and it is undefined for the remaining cases where n is even and x is the hamming weight of x the deutsch jozsa algorithm needs only one query to compute d j n 0 but the classical deterministic algorithm requires n 2 1 queries to compute it in the worse case we present all symmetric partial boolean functions with degree 1 and 2 we prove the exact quantum query complexity of all symmetric partial boolean functions with degree 1 and 2 we prove deutsch jozsa algorithm can compute any symmetric partial boolean function f with exact quantum 1 query complexity

free bits pcps and nonapproximability towards tight results this paper continues the investigation of the connection between probabilistically checkable proofs pcps and the approximability of np optimization problems the emphasis is on proving tight nonapproximability results via consideration of measures such as the free bit complexity and the amortized free bit complexity of proof systems the first part of the paper presents a collection of new proof systems based on a new error correcting code called the long code we provide a proof system that has amortized free bit complexity of 2 epsilon implying that approximating maxclique within n frac13 e and approximating the chromatic number within n frac15 e are hard assuming np neq corp for any e 0 we also derive the first explicit and reasonable constant hardness factors for min vertex cover msat 2 and max cut and we improve the hardness factor for msat 3 we note that our nonapproximability factors for maxsnp problems are appreciably close to the values known to be achievable by polynomial time algorithms finally we note a general approach to the derivation of strong nonapproximability results under which the problem reduces to the construction of certain gadgets the increasing strength of nonapproximability results obtained via the pcp connection motivates us to ask how far this can go and whether pcps are inherent in any way the second part of the paper addresses this the main result is a reversal of the connection due to feige et al fglss connection j acm 43 1996 pp 268 292 where the latter had shown how to translate proof systems for np into np hardness of approximation results for maxclique we show how any np hardness of approximation result for maxclique yields a proof system for np roughly our result says that for any constant f if maxclique is np hard to approximate within n 1 1 f then np subseteq overline fpcp log f the latter being the class of languages possessing proofs of logarithmic randomness and amortized free bit complexity f this suggests that pcps are inherent to obtaining nonapproximability results furthermore the tight relation suggests that reducing the amortized free bit complexity is necessary for improving the nonapproximability results for maxclique the third part of our paper initiates a systematic investigation of the properties of pcp and fpcp free pcp as a function of the following various parameters randomness query complexity free bit complexity amortized free bit complexity proof size etc we are particularly interested in triviality results which indicate which classes are not powerful enough to capture np we also distill the role of randomized reductions in this area and provide a variety of useful transformations between proof checking complexity classes

removing redundancy from a clause abstract this paper deals with the problem of removing redundant literals from a given clause we first consider condensing a weak type of redundancy elimination a clause is condensed if it does not subsume any proper subset of itself it is often useful and sometimes necessary to replace a non condensed clause c by a condensation i e by a condensed subset of c which is subsumed by c after studying the complexity of an existing clause condensing algorithm we present a more efficient algorithm and provide arguments for the optimality of the new method we prove that testing whether a given clause is condensed is co np complete and show that several problems related to clause condensing belong to complexity classes that are probably slightly harder than np we also consider a stronger version of redundancy elimination a clause c is strongly condensed iff it does not contain any proper subset c such that c logically implies c we show that the problem of testing whether a clause is strongly condensed is undecidable

bounded queries to sat and the boolean hierarchy we study the complexity of decision problems that can be solved by a polynomial time turing machine that makes a bounded number of queries to an np oracle depending on whether we allow some queries to depend on the results of other queries we obtain two probably different hierarchies we present several results relating the bounded np query hierarchies to each other and to the boolean hierarchy we also consider the similarly defined hierarchies of functions that can be computed by a polynomial time turing machine that makes a bounded number of queries to an np oracle we present relations among these two hierarchies and the boolean hierarchy in particular we show for all k that there are functions computable with 2k parallel queries to an np set that are not computable in polynomial time with k serial queries to any oracle unless p np as a corollary k 1 parallel queries to an np set allow us to compute more functions than are computable with only k parallel queries to an np set unless p np the same is true of serial queries similar results hold for all tt self reducible sets using a mind change technique we show that 2k 1 parallel queries to an np set allow us to accept in polynomial time exactly the same sets as can be accepted in polynomial time with k serial queries to an np set in fact the same is true for any class in place of np that is closed under polynomial time positive bounded truth table reductions this contrasts with the expected result for function computations with an np oracle beigel 1988 in addition we show that the boolean hierarchy and the bounded query hierarchies of languages either stand or collapse together finally we show that if the boolean hierarchy collapses to any level but the zeroth deterministic polynomial time then for all k there are functions computable in polynomial time with k parallel queries to an np set that are not computable in polynomial time with k 1 serial queries to any set np complete sets are p superterse

sandpile model on an optimized scale free network on euclidean space deterministic sandpile models are studied on a cost optimized barabasi albert ba scale free network whose nodes are the sites of a square lattice for the optimized ba network the sandpile model has the same critical behaviour as the btw sandpile whereas for the un optimized ba network the critical behaviour is mean field like

computational complexity studies of synchronous boolean finite dynamical systems on directed graphs abstract a finite dynamical system is a system consisting of some finite number of objects that take upon a value from some domain as a state in which after initialization the states of the objects are updated based upon the states of the other objects and themselves according to a certain update schedule this paper studies a subclass of finite dynamical systems the synchronous boolean finite dynamical system synchronous bfds for short where the states are boolean and the state update takes place in discrete time and at the same on all objects the paper is concerned with three problems convergence path intersection and cycle length of the synchronous bfds in which the state update functions or the local state transition functions are chosen from a predetermined finite basis of boolean functions b the paper results characterize their computational complexity