on the consistency of cardinal direction constraints we present a formal model for qualitative spatial reasoning with cardinal directions utilizing a co ordinate system then we study the problem of checking the consistency of a set of cardinal direction constraints we introduce the first algorithm for this problem prove its correctness and analyze its computational complexity utilizing the above algorithm we prove that the consistency checking of a set of basic i e non disjunctive cardinal direction constraints can be performed in o n 5 time we also show that the consistency checking of a set of unrestricted i e disjunctive and non disjunctive cardinal direction constraints is np complete finally we briefly discuss an extension to the basic model and outline an algorithm for the consistency checking problem of this extension

a survey of the physical optics inverse scattering identity the physical optics approximation is applied to the acoustic and electromagnetic direct scattering integral representation yielding an inverse scattering identity which relates the characteristic function of a scatterer to the three dimensional spatial fourier transform of the augmented far field scattering amplitude this identity requires full scattering information for all frequencies and aspect angles an integral equation for incomplete scattering information for this identity is developed this integral equation is for the unknown characteristic function of the scatterer in terms of the known incomplete scattering information the kernel of this integral equation is the three dimensional spatial fourier transform of the known characteristic function of the scattering information aperture a regularized analytic closed form solution to this integral equation is obtained synthesized numerico experimental results verifying this solution are presented the details of some special cases consisting of a priori knowledge about the scatterer or the scattering information aperture are presented

constants and finite unary relations in qualitative constraint reasoning extending qualitative csps with the ability of restricting selected variables to finite sets of possible values has been proposed as an interesting research direction with important applications c

incremental qualitative temporal reasoning algorithms for the point algebra and the ord horn class in many applications of temporal reasoning we are interested in processing temporal information incrementally in particular given a set of temporal constraints a temporal csp and a new constraint we want to maintain certain properties of the extended temporal csp e g a solution rather than recomputing them from scratch the point algebra pa and the interval algebra ia are two well known frameworks for qualitative temporal reasoning the reasoning algorithms for pa and the tractable fragments of ia such as nebel and burckert s maximal tractable class of relations ord horn have originally been designed for static reasoning in this paper we study the incremental version of the fundamental reasoning problems in the context of these tractable classes we propose a collection of new polynomial algorithms that can amortize their complexity when processing a sequence of input constraints to incrementally decide satisfiability to maintain a solution or to update the minimal representation of the csp our incremental algorithms improve the total time complexity of using existing static techniques by a factor of o n or o n2 where n is the number of the variables involved by the temporal csp an experimental analysis focused on constraints over pa confirms the computational advantage of our incremental approach

realizing rcc8 networks using convex regions rcc8 is a popular fragment of the region connection calculus in which qualitative spatial relations between regions such as adjacency overlap and parthood can be expressed while rcc8 is essentially dimensionless most current applications are confined to reasoning about two dimensional or three dimensional physical space in this paper however we are mainly interested in conceptual spaces which typically are high dimensional euclidean spaces in which the meaning of natural language concepts can be represented using convex regions the aim of this paper is to analyze how the restriction to convex regions constrains the realizability of networks of rcc8 relations first we identify all ways in which the set of rcc8 base relations can be restricted to guarantee that consistent networks can be convexly realized in respectively 1d 2d 3d and 4d most surprisingly we find that if the relation partially overlaps is disallowed all consistent atomic rcc8 networks can be convexly realized in 4d if instead refinements of the relation part of are disallowed all consistent atomic rcc8 relations can be convexly realized in 3d we furthermore show among others that any consistent rcc8 network with 2 n 1 variables can be realized using convex regions in the n dimensional euclidean space

the complexity of constraint satisfaction problems for small relation algebras andreka and maddux notre dame j formal logic 35 4 1994 classified the small relation algebras those with at most 8 elements or in other terms at most 3 atomic relations they showed that there are eighteen isomorphism types of small relation algebras all representable for each simple small relation algebra they computed the spectrum of the algebra namely the set of cardinalities of square representations of that relation algebra in this paper we analyze the computational complexity of the problem of deciding the satisfiability of a finite set of constraints built on any small relation algebra we give a complete classification of the complexities of the general constraint satisfaction problem for small relation algebras for three of the small relation algebras the constraint satisfaction problem is np complete for the other fifteen small relation algebras the constraint satisfaction problem has cubic or lower complexity we also classify the complexity of the constraint satisfaction problem over fixed finite representations of any relation algebra if the representation has size two or less then the complexity is cubic or lower but if the representation is square finite and bigger than two then the complexity is np complete

normalized compression distance of multisets with applications pairwise normalized compression distance ncd is a parameter free feature free alignment free similarity metric based on compression we propose an ncd of multisets that is also metric previously attempts to obtain such an ncd failed for classification purposes it is superior to the pairwise ncd in accuracy and implementation complexity we cover the entire trajectory from theoretical underpinning to feasible practice it is applied to biological stem cell organelle transport and ocr classification questions that were earlier treated with the pairwise ncd with the new method we achieved significantly better results the theoretic foundation is kolmogorov complexity

information distance while kolmogorov 1965 complexity is the accepted absolute measure of information content in an individual finite object a similarly absolute notion is needed for the information distance between two individual objects for example two pictures we give several natural definitions of a universal information metric based on length of shortest programs for either ordinary computations or reversible dissipationless computations it turns out that these definitions are equivalent up to an additive logarithmic term we show that the information distance is a universal cognitive similarity distance we investigate the maximal correlation of the shortest programs involved the maximal uncorrelation of programs a generalization of the slepian wolf theorem of classical information theory and the density properties of the discrete metric spaces induced by the information distances a related distance measures the amount of nonreversibility of a computation using the physical theory of reversible computation we give an appropriate universal antisymmetric and transitive measure of the thermodynamic work required to transform one object in another object by the most efficient process information distance between individual objects is needed in pattern recognition where one wants to express effective notions of pattern similarity or cognitive similarity between individual objects and in thermodynamics of computation where one wants to analyze the energy dissipation of a computation from a particular input to a particular output

information distance in multiples information distance is a parameter free similarity measure based on compression used in pattern recognition data mining phylogeny clustering and classification the notion of information distance is extended from pairs to multiples finite lists we study maximal overlap metricity universality minimal overlap additivity and normalized information distance in multiples we use the theoretical notion of kolmogorov complexity which for practical purposes is approximated by the length of the compressed version of the file involved using a real world compression program

querying temporal and spatial constraint networks in ptime we start with the assumption that temporal and spatial knowledge usually captured by constraint networks can be represented and queried more effectively by using the scheme of indefinite constraint databases because query evaluation in this scheme is in general a hard computational problem we seek tractable instances of query evaluation we assume that we have a class of constraints c with some reasonable computational and closure properties the computational properties of interest are that the satisfiability problem and an appropriate version of the variable elimination problem for c should be solvable in ptime under this assumption we exhibit general classes of indefinite constraint databases and first order modal queries for which query evaluation can be done with ptime data complexity we then search for tractable instances of c among the subclasses of horn disjunctive linear constraints over the rationals from previous research we know that the satisfiability problem for horn disjunctive linear constraints is solvable in ptime but not the variable elimination problem thus we try to discover subclasses of horn disjunctive linear constraints with tractable variable elimination problems the class of utvpi constraints is the largest class that we show to have this property finally we restate our general tractability results with c ranging over the newly discovered tractable classes interesting tractable query answering problems for indefinite temporal and spatial constraint databases are identified in this way we close our complexity analysis by precisely outlining the frontier between tractable and possibly intractable query answering problems

computational complexity of relating time points with interval abstract several algebras have been proposed for reasoning about qualitative constraints over the time line one of these algebras is vilain s point interval algebra which can relate time points with time intervals apart from being a stand alone qualitative algebra it is also used as a subalgebra in meiri s approach to temporal reasoning which combines reasoning about metric and qualitative temporal constraints over both time points and time intervals while the satisfiability problem for the full point interval algebra is known to be np complete not much is known about its 4 294 967 296 subclasses this article completely determines the computational complexity of these subclasses and it identifies all of the maximal tractable subalgebras five in total

overview and classification of some regularization techniques for the gauss newton inversion method applied to inverse scattering problems different regularization techniques used in conjunction with the gauss newton inversion method for electromagnetic inverse scattering problems are studied and classified into two main categories the first category attempts to regularize the quadratic form of the nonlinear data misfit cost functional at different iterations of the gauss newton inversion method this can be accomplished by utilizing penalty methods or projection methods the second category tries to regularize the nonlinear data misfit cost functional before applying the gauss newton inversion method this type of regularization may be applied via additive multiplicative or additive multiplicative terms we show that these two regularization strategies can be viewed from a single consistent framework

reasoning about cardinal directions between extended objects the np hardness result the cardinal direction calculus cdc proposed by goyal and egenhofer is a very expressive qualitative calculus for directional information of extended objects early work has shown that consistency checking of complete networks of basic cdc constraints is tractable while reasoning with the cdc in general is np hard this paper shows however that if some constraints are unspecified then consistency checking of incomplete networks of basic cdc constraints is already intractable this draws a sharp boundary between the tractable and intractable subclasses of the cdc the result is achieved by a reduction from the well known 3 sat problem

classifying the complexity of constraints using finite algebras many natural combinatorial problems can be expressed as constraint satisfaction problems this class of problems is known to be np complete in general but certain restrictions on the form of the constraints can ensure tractability here we show that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and we explore how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra hence we completely translate the problem of classifying the complexity of restricted constraint satisfaction problems into the language of universal algebra we introduce a notion of tractable algebra and investigate how the tractability of an algebra relates to the tractability of the smaller algebras which may be derived from it including its subalgebras and homomorphic images this allows us to reduce significantly the types of algebras which need to be classified using our results we also show that if the decision problem associated with a given collection of constraint types can be solved efficiently then so can the corresponding search problem we then classify all finite strictly simple surjective algebras with respect to tractability obtaining a dichotomy theorem which generalizes schaefer s dichotomy for the generalized satisfiability problem finally we suggest a possible general algebraic criterion for distinguishing the tractable and intractable cases of the constraint satisfaction problem

shape reconstruction from po multifrequency scattered fields via the singular value decomposition approach this paper deals with the problem of determining the shape of unknown perfectly conducting infinitely long cylinders starting from the knowledge of the scattered electric far field under the incidence of plane waves with a fixed angle of incidence and varying frequency the problem is formulated as a nonlinear inverse one by searching for a compact support distribution accounting for the objects contour the nonlinear unknown to data mapping is then linearized by means of the kirchhoff approximation which reduces it into a fourier transform relationship then the fourier transform inversion from incomplete data is dealt with by means of the singular value decomposition svd approach and the features of the reconstructable unknowns are investigated finally numerical results confirm the performed analysis

region connection calculus its models and composition table originating in allen s analysis of temporal relations the notion of composition table has become a key technique in providing an efficient inference mechanism for a wide class of theories in the field artificial intelligence this paper is mainly about the consistency based composition table rcc8 ct of the region connection calculus rcc raised by randell cui and cohn first we show each rcc model is a consistent model of the rcc8 ct then after an exhaustive analysis we show that no rcc model can be interpreted extensionally anyway and hence give a negative answer to a conjecture raised by bennett all these results are given in an extensional rcc8 composition table where we attach to each cell entry in the rcc8 ct a superscript to indicate in what circumstances an extensional interpretation is possible

point algebras for temporal reasoning algorithms and complexity we investigate the computational complexity of temporal reasoning in different time models such as totally ordered partially ordered and branching time our main result concerns the satisfiability problem for point algebras and point algebras extended with disjunctions for these problems we identify all tractable subclasses we also provide a number of additional results for instance we present a new time model suitable for reasoning about systems with a bounded number of unsynchronized clocks we investigate connections with spatial reasoning and we present improved algorithms for deciding satisfiability of the tractable point algebras

beyond physical optics svd shape reconstruction of metallic cylinders we consider the problem of reconstructing the shape of perfectly conducting cylinders under the physical optics approximation for direct scattering physical optics provides small model errors when the scatterers are convex smooth have large radii of curvature as compared to the impinging wavelength and are noninteracting in this paper we investigate whether these hypotheses can be relaxed for the inverse problem in particular we consider three classes of scatterers circular cylinder with radius smaller than the wavelength multiple cylinders and a concave cylinder and we show that for them the model error is provided by a multiplicative almost frequency independent factor since this factor can be incorporated within the unknown distribution representing the scatterers illuminated boundaries then we are able to show that successful reconstructions also beyond the physical optics limits can be obtained

localizing thin metallic cylinders by a 2 5 d linear distributional approach experimental results the problem of detecting and localizing thin metallic scatterers from electromagnetic scattered field measurements is addressed the scatterers are assumed to be infinitely long and a 2 5 dimensional mathematical model is adopted according to the distributional approach the problem is cast as the inversion of a linear integral operator acting on 6 distributions whose supports are representative of the scatterers locations in this paper we present the experimental validation of such an approach to this end we perform the reconstructions by exploiting experimental scattered field data collected in controlled conditions at the electromagnetic diagnostics laboratory of the second university of naples the experiments are conducted in an anechoic chamber where the scatterers are embedded in a homogenous and lossless background medium the multistatic single view multifrequency and the multistatic multiview multifrequency configurations are both considered

spatial reasoning with rcc 8 and connectedness constraints in euclidean spaces the language rcc 8 is a widely studied formalism for describing topological arrangements of spatial regions the variables of this language range over the collection of non empty regular closed sets of n dimensional euclidean space here denoted rc r n and its non logical primitives allow us to specify how the interiors exteriors and boundaries of these sets intersect the key question is the satisfiability problem given a finite set of atomic rcc 8 constraints in m variables determine whether there exists an m tuple of elements of rc r n satisfying them these problems are known to coincide for all n 1 so that rcc 8 satisfiability is independent of dimension this common satisfiability problem is nlogspace complete unfortunately rcc 8 lacks the means to say that a spatial region comprises a single piece and the present article investigates what happens when this facility is added we consider two extensions of rcc 8 rcc 8 c in which we can state that a region is connected and rcc 8 c in which we can instead state that a region has a connected interior the satisfiability problems for both these languages are easily seen to depend on the dimension n for n 3 furthermore in the case of rcc 8 c we show that there exist finite sets of constraints that are satisfiable over rc r 2 but only by wild regions having no possible physical meaning this prompts us to consider interpretations over the more restrictive domain of non empty regular closed polyhedral sets rcp r n we show that a the satisfiability problems for rcc 8 c equivalently rcc 8 c over rc r and rcp r are distinct and both np complete b the satisfiability problems for rcc 8 c over rc r 2 and rcp r 2 are identical and np complete c the satisfiability problems for rcc 8 c over rc r 2 and rcp r 2 are distinct and the latter is np complete decidability of the satisfiability problem for rcc 8 c over rc r 2 is open for n 3 rcc 8 c and rcc 8 c are not interestingly different from rcc 8 we finish by answering the following question given that a set of rcc 8 c or rcc 8 c constraints is satisfiable over rc r n or rcp r n how complex is the simplest satisfying assignment in particular we exhibit for both languages a sequence of constraints n satisfiable over rcp r 2 such that the size of n grows polynomially in n while the smallest configuration of polygons satisfying n cuts the plane into a number of pieces that grows exponentially we further show that over rc r 2 rcc 8 c again requires exponentially large satisfying diagrams while rcc 8 c can force regions in satisfying configurations to have infinitely many components

resoning about action in polynomial time abstract although many formalisms for reasoning about action exist surprisingly few approaches have taken computational complexity into consideration the contributions of this article are the following a temporal logic with a restriction for which deciding satisfiability is tractable a tractable extension for reasoning about action and np completeness results for the unrestricted problems many interesting reasoning problems can be modelled involving nondeterminism concurrency and memory of actions the reasoning process is proved to be sound and complete

equalization of the antenna pattern in shape reconstruction of metallic objects we address the problem of reconstructing the shape of perfectly electric conducting cylinders for a two dimensional scalar geometry when the physical optics po model is exploited we are interested in analyzing how the radiation pattern of the source providing the incident field affects the shape reconstruction problem we find that owing to the regularization necessary to deal with the ill posedness of the problem the more weakly illuminated objects are more weakly reconstructed as a consequence these objects can be mistaken for spurious artifacts appearing in the reconstruction and thus can be discarded when a threshold procedure is employed to curtail spurious artifacts in order to overcome such a problem we present a simple equalization strategy based on the knowledge of the incident field to compensate for the differences in amplitude of reconstructed image furthermore we give a criterion which restricts the region over which we apply the procedure which enables us to perform the equalization in a stable way the effectiveness of the equalization procedure is shown by reconstructions obtained with synthetic data and considering the unknown cylinders embedded in both a homogeneous and a half space background medium under single and multi view multi frequency measurement configuration

complexity and algorithms for reasoning about time a graph theoretic approach temporal events are regarded here as intervals on a time line this paper deals with problems in reasoning about such intervals when the precise topological relationship between them is unknown or only partially specified this work unifies notions of interval algebras in artificial intelligence with those of interval orders and interval graphs in combinatorics the satisfiability minimal labeling all solutions and all realizations problems are considered for temporal internal data several versions are investigated by restricting the possible interval relationships yielding different complexity results we show that even when the temporal data comprises of subsets of relations based on intersection and precedence only the satisfiability question is np complete

rcc8 binary constraint network can be consistently extended the rcc8 constraint language developed by randell et al has been popularly adopted by the qualitative spatial reasoning and gis communities the recent observation that rcc8 composition table describes only weak composition instead of composition raises questions about renz and nebel s maximality results about the computational complexity of reasoning with rcc8 this paper shows that any consistent rcc8 binary constraint network rcc8 network for short can be consistently extended given an rcc8 network and z a fresh variable suppose xty and t is contained in the weak composition of r and s this means that we can add two new constraints xrz and zsy to without changing the consistency of the network the result guarantees the applicability to rcc8 of one key technique theorem 5 of j renz b nebel on the complexity of qualitative spatial reasoning a maximal tractable fragment of the region connection calculus artificial intelligence 108 1999 69 123 which allows the transfer of tractability of a set of rcc8 relations to its closure under composition intersection and converse

maximal infinite valued constraint languages we systematically investigate the computational complexity of constraint satisfaction problems for constraint languages over an infinite domain in particular we study a generalization of the well established notion of maximal constraint languages from finite to infinite domains if the constraint language can be defined with an w categorical structure then maximal constraint languages are in one to one correspondence to minimal oligomorphic clones based on this correspondence we derive general tractability and hardness criteria for the corresponding constraint satisfaction problems

boolean connection algebras a new approach to the region connection calculus abstract the region connection calculus rcc is a well established formal system for qualitative spatial reasoning it provides an axiomatization of space which takes regions as primitive rather than as constructions from sets of points the paper introduces boolean connection algebras bcas and proves that these structures are equivalent to models of the rcc axioms bcas permit a wealth of results from the theory of lattices and boolean algebras to be applied to rcc this is demonstrated by two theorems which provide constructions for bcas from suitable distributive lattices it is already well known that regular connected topological spaces yield models of rcc but the theorems in this paper substantially generalize this result additionally the lattice theoretic techniques used provide the first proof of this result which does not depend on the existence of points in regions

spatial reasoning in a fuzzy region connection calculus although the region connection calculus rcc offers an appealing framework for modelling topological relations its application in real world scenarios is hampered when spatial phenomena are affected by vagueness to cope with this we present a generalization of the rcc based on fuzzy set theory and discuss how reasoning tasks such as satisfiability and entailment checking can be cast into linear programming problems we furthermore reveal that reasoning in our fuzzy rcc is np complete thus preserving the computational complexity of reasoning in the rcc and we identify an important tractable subfragment moreover we show how reasoning tasks in our fuzzy rcc can also be reduced to reasoning tasks in the original rcc while this link with the rcc could be exploited in practical reasoning algorithms we mainly focus on the theoretical consequences in particular using this link we establish a close relationship with the egg yolk calculus and we demonstrate that satisfiable knowledge bases can be realized by fuzzy regions in any dimension

reasoning about temporal relations the tractable subalgebras of allen s interval algebra allen s interval algebra is one of the best established formalisms for temporal reasoning this article provides the final step in the classification of complexity for satisfiability problems over constraints expressed in this algebra when the constraints are chosen from the full allen s algebra this form of satisfiability problem is known to be np complete however eighteen tractable subalgebras have previously been identified we show here that these subalgebras include all possible tractable subsets of allen s algebra in other words we show that this algebra contains exactly eighteen maximal tractable subalgebras and reasoning in any fragment not entirely contained in one of these subalgebras is np complete we obtain this dichotomy result by giving a new uniform description of the known maximal tractable subalgebras and then systematically using a general algebraic technique for identifying maximal subalgebras with a given property

combining topological and size information for spatial reasoning information about the size of spatial regions is often easily accessible and when combined with other types of spatial information it can be practically very useful in this paper we introduce four classes of qualitative and metric size constraints and we study their integration with the region connection calculus rcc 8 a well known approach to qualitative spatial reasoning with topological relations we propose a new path consistency algorithm for combining rcc 8 relations and qualitative size relations the algorithm is complete for deciding satisfiability of an input set of topological constraints over one of the three maximal tractable subclasses of rcc 8 containing all the basic relations moreover its time complexity is cubic and is the same as the complexity of the best known method for deciding satisfiability when only these topological relations are considered we also provide results on finding a consistent scenario in cubic time for these combined classes regarding metric size constraints we first study their combination with rcc 8 and we show that deciding satisfiability for the combined sets of constraints is np hard even when only the rcc 8 basic relations are used then we introduce rcc 7 a subalgebra of rcc 8 that can be used for applications where spatial regions cannot partially overlap we show that reasoning with the seven rcc 7 basic relations and the universal relation is intractable but that reasoning with the rcc 7 basic relations combined with metric size information is tractable finally we give a polynomial algorithm for the latter case and a backtracking algorithm for the general case

tractable disjunctions of linear constraints basic results and applications to temporal reasoning we study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and disequations with at most one inequality per disjunction this new class of constraints extends the class of generalized linear constraints originally studied by lassez and mcaloon we show that deciding consistency of a set of constraints in this class can be done in polynomial time we also present a variable elimination algorithm which is similar to fourier s algorithm for linear inequalities finally we use these results to provide new temporal reasoning algorithms for the ord horn subclass of allen s interval formalism we also show that there is no low level of local consistency that can guarantee global consistency for the ord horn subclass this property distinguishes the ord horn subclass from the pointizable subclass for which strong 5 consistency is sufficient to guarantee global consistency and the continuous endpoint subclass for which strong 3 consistency is sufficient to guarantee global consistency copyright 2001 elsevier science b v

a new approach to cyclic ordering of 2d orientations using ternary relation algebras abstract in tarski s formalisation the universe of a relation algebra ra consists of a set of binary relations a first contribution of this work is the introduction of ras whose universe is a set of ternary relations these support rotation as an operation in addition to those present in tarski s formalisation then we propose two particular ras a binary ra cyc b whose universe is a set of binary relations on 2d orientations and a ternary ra cyc t whose universe is a set of ternary relations on 2d orientations the ra cyc t more expressive than cyc b constitutes a new approach to cyclic ordering of 2d orientations an atom of cyc t expresses for triples of orientations whether each of the three orientations is equal to to the left of opposite to or to the right of each of the other two orientations cyc t has 24 atoms and the elements of its universe consist of all possible 2 24 subsets of the set of all atoms amongst other results 1 we provide for cyc t a constraint propagation procedure computing the closure of a problem under the different operations and show that the procedure is polynomial and complete for a subset including all atoms 2 we prove that another subset expressing only information on parallel orientations is np complete 3 we show that provided that a subset s of cyc t includes two specific elements deciding consistency for a problem expressed in the closure of s can be polynomially reduced to deciding consistency for a problem expressed in s and 4 we derive from the previous result that for both ras we jump from tractability to intractability if we add the universal relation to the set of all atoms a comparison to the most closely related work in the literature indicates that the approach is promising

on the complexity of qualitative spatial reasoning a maximal tractable fragment of the region connection calculus the computational properties of qualitative spatial reasoning have been investigated to some degree however the question for the boundary between polynomial and np hard reasoning problems has not been addressed yet in this paper we explore this boundary in the region connection calculus rcc 8 we extend bennett s encoding of rcc 8 in modal logic based on this encoding we prove that reasoning is np complete in general and identify a maximal tractable subset of the relations in rcc 8 that contains all base relations further we show that for this subset path consistency is sufficient for deciding consistency

the similarity metric a new class of distances appropriate for measuring similarity relations between sequences say one type of similarity per distance is studied we propose a new normalized information distance based on the noncomputable notion of kolmogorov complexity and show that it is in this class and it minorizes every computable distance in the class that is it is universal in that it discovers all computable similarities we demonstrate that it is a metric and call it the similarity metric this theory forms the foundation for a new practical tool to evidence generality and robustness we give two distinctive applications in widely divergent areas using standard compression programs like gzip and gencompress first we compare whole mitochondrial genomes and infer their evolutionary history this results in a first completely automatic computed whole mitochondrial phylogeny tree secondly we fully automatically compute the language tree of 52 different languages

reasoning about partially ordered events abstract this paper describes a class of temporal reasoning problems involving events whose order is not completely known we examine the complexity of such problems and show that for all but trivial cases these problems are likely to be intractable as an alternative to a complete but potentially exponential time decision procedure we provide a partial decision procedure that reports useful results and runs in polynomial time

composing cardinal direction relations we study the recent proposal of goyal and egenhofer who presented a model for qualitative spatial reasoning about cardinal directions our approach is formal and complements the presentation of goyal and egerdaofer we focus our efforts on the composition operator for two cardinal direction relations we consider two interpretations of the composition operator consistency based and existential composition we point out that the only published method to compute the consistency based composition does not always work correctly then we consider progressively more expressive classes of cardinal direction relations and give consistency based composition algorithms for these classes our theoretical framework allows us to prove formally that our algorithms are correct when we consider existential composition we demonstrate that the binary relation resulting from the composition of two cardinal direction relations cannot be expressed using the relations defined by goyal and egenhofer finally we discuss some extensions to the basic model and consider the composition problem for these extensions

shape reconstruction by the spectral data of the far field operator analysis and performances the second version of the linear sampling method is considered with reference to perfectly conducting cylinders and its performances analyzed it is pointed out that for nonconvex objects the shape of the object under test is not retrieved whereas in its place the convex hull is recovered we also point out that in the case of aspect limited data neither the convex hull of the object is reconstructed

a unifying approach to temporal constraint reasoning abstract we present a formalism disjunctive linear relations dlrs for reasoning about temporal constraints dlrs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive we also present a restricted type of dlrs horn dlrs which have a polynomial time satisfiability problem we prove that most approaches to tractable temporal constraint reasoning can be encoded as horn dlrs including the ord horn algebra by nebel and burckert and the simple temporal constraints by dechter et al thus dlrs is a suitable unifying formalism for reasoning about temporal constraints

on the combinatorial and algebraic complexity of quantifier elimination in this paper a new algorithm for performing quantifier elimination from first order formulas over real closed fields in given this algorithm improves the complexity of the asymptotically fastest algorithm for this problem known to this data a new feature of this algorithm is that the role of the algebraic part the dependence on the degrees of the imput polynomials and the combinatorial part the dependence on the number of polynomials are sparated another new feature is that the degrees of the polynomials in the equivalent quantifier free formula that is output are independent of the number of input polynomials as special cases of this algorithm new and improved algorithms for deciding a sentence in the first order theory over real closed fields and also for solving the existential problem in the first order theory over real closed fields are obtained

disjunctions independence refinements an important question in constraint satisfaction is how to restrict the problem to ensure tractability since the general problem is np hard the use of disjunctions has proven to be a useful method for constructing tractable constraint classes from existing classes the well known max closed and ord horn constraints are examples of tractable classes that can be constructed this way three sufficient conditions the guaranteed satisfaction property 1 independence and 2 independence that each ensure the tractability of constraints combined by disjunctions have been proposed in the literature we show that these conditions are both necessary and sufficient for tractability in three different natural classes of disjunctive constraints this suggests that deciding this kind of property is a very important task when dealing with disjunctive constraints we provide a simple automatic method for checking the 1 independence property this method is applicable whenever the consistency of the constraints under consideration can be decided by path consistency our method builds on a connection between independence and refinements which is a way of reducing one constraint satisfaction problem to another

reasoning about qualitative temporal information abstract representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks an interval based framework and a point based framework have been proposed for representing such temporal information in this paper we address two fundamental reasoning tasks that arise in applications of these frameworks given possibly indefinite and incomplete knowledge of the relationships between some intervals or points i find a scenario that is consistent with the information provided and ii find the feasible relations between all pairs of intervals or points for the point based framework and a restricted version of the interval based framework we give computationally efficient procedures for finding a consistent scenario and for finding the feasible relations our algorithms are marked improvements over the previously known algorithms in particular we develop an o n2 time algorithm for finding one consistent scenario that is an o n improvement over the previously known algorithm where n is the number of intervals or points and we develop an algorithm for finding all the feasible relations that is of far more practical use than the previously known algorithm for the unrestricted version of the interval based framework finding a consistent scenario and finding the feasible relations have been shown to be np complete we show how the results for the point algebra aid in the design of a backtracking algorithm for finding one consistent scenario that is shown to be useful in practice for planning problems

exp time tableaux for alc abstract the last years have seen two major advances in knowledge representation and reasoning first many interesting problems ranging from semi structured data to linguistics were shown to be expressible in logics whose main deductive problems are exptime complete second experiments in automated reasoning have substantially broadened the meaning of practical tractability instances of realistic size for pspace complete problems are now within reach for implemented systems still there is a gap between the reasoning services needed by the expressive logics mentioned above and those provided by the current systems indeed the algorithms based on tree automata which are used to prove exptime completeness require exponential time and space even in simple cases on the other hand current algorithms based on tableau methods can take advantage of such cases but require double exponential time in the worst case we propose a tableau calculus for the description logic alc for checking the satisfiability of a concept with respect to a tbox with general axioms and transform it into the first simple tableau based decision procedure working in single exponential time to guarantee the ease of implementation we also discuss the effects that optimizations propositional backjumping simplification semantic branching etc might have on our complexity result and introduce a few optimizations ourselves

inverse scattering for conductors by the equivalent source method the inverse scattering for two dimensional conductors is investigated assume that an incident wave is incident upon conducting cylinders of unknown shape and the scattered field is measured outside by properly processing the scattering data the position and shape of the conducting scatterers can then be reconstructed the proposed theory of inverse scattering is a combination of the diffraction tomography and the equivalent source method to overcome the ill posedness the condition of the measured scattered field and the boundary condition on the conductor surfaces are combined and recast into an optimization problem using the least squares concept by comparing the reconstructed and the prescribed results the inversion algorithms are numerically examined note that if a priori information of the shape is sufficient and the equivalent sources are properly placed the algorithms can be flexibly applied to the cases of multiple conductors also the effects of noise contamination and multiple scattering on the reconstruction result are numerically investigated

conditional complexity and codes let x and y be binary strings we prove that there exists a program p of size about k x y that maps y tox and has small complexity when x is known k p x 0 8776 0 having in mind the parallelism between shannon information theory and algorithmic information theory one can say that this result is parallel to wolf slepian and korner csiszar marton theorems see i csiszar and j korner information theory coding theorems for discrete memoryless systems akademiai kiado budapest 1981 we show also that for any three stringsx y z of length at most n the length of the shortest program p that maps both y and z to x i e p y p z x equals max k x y k x z o logn

qualitative constraint satisfaction problems an extended framework with landmarks dealing with spatial and temporal knowledge is an indispensable part of almost all aspects of human activity the qualitative approach to spatial and temporal reasoning known as qualitative spatial and temporal reasoning qstr typically represents spatial temporal knowledge in terms of qualitative relations e g to the east of after and reasons with spatial temporal knowledge by solving qualitative constraints when formulating qualitative constraint satisfaction problems csps it is usually assumed that each variable could be here there and everywhere practical applications such as urban planning however often require a variable to take its value from a certain finite domain i e it is required to be here or there but not everywhere entities in such a finite domain often act as reference objects and are called landmarks in this paper the paper extends the classical framework of qualitative csps by allowing variables to take values from finite domains the computational complexity of the consistency problem in this extended framework is examined for the five most important qualitative calculi viz point algebra interval algebra cardinal relation algebra rcc5 and rcc8 we show that all these consistency problems remain in np and provide under practical assumptions efficient algorithms for solving basic constraints involving landmarks for all these calculi

linear distribution imaging of thin metallic cylinders under mutual scattering in this paper we address the problem of imaging thin metallic cylinders from the knowledge of the electric far field scattered under the incidence of plane waves a scattering model based on a multipole expansion accounting for the mutual scattering is introduced and then simplified under the single and second order scattering hypotheses the locations of the unknown cylinders for the inverse problem are described in terms of support of spl delta functions the performances of a truncated singular value decomposition based linear inversion algorithm in the presence of model errors due to mutual scattering is investigated by both analytical and numerical arguments in three different measurement configurations single frequency multiview multifrequency single view and multifrequency multiview the different effects of the angular and frequency diversities are pointed out

generalized region connection calculus the region connection calculus rcc is one of the most widely referenced system of high level qualitative spatial reasoning rcc assumes a continuous representation of space this contrasts sharply with the fact that spatial information obtained from physical recording devices is nowadays invariably digital in form and therefore implicitly uses a discrete representation of space recently galton developed a theory of discrete space that parallels rcc but question still lies in that can we have a theory of qualitative spatial reasoning admitting models of discrete spaces as well as continuous spaces in this paper we aim at establishing a formal theory which accommodates both discrete and continuous spatial information and a generalization of region connection calculus is introduced grcc the new theory takes two primitives the mereological notion of part and the topological notion of connection rcc and galton s theory for discrete space are both extensions of grcc the relation between continuous models and discrete ones is also clarified by introducing some operations on models of grcc in particular we propose a general approach for constructing countable rcc models as direct limits of collections of finite models compared with standard rcc models given rise from regular connected spaces these countable models have the nice property that each region can be constructed in finite steps from basic regions two interesting countable rcc models are also given one is a minimal rcc model the other is a countable sub model of the continuous space r 2

reasoning about cardinal directions between extended objects direction relations between extended spatial objects are important commonsense knowledge recently goyal and egenhofer proposed a relation model known as the cardinal direction calculus cdc for representing direction relations between connected plane regions the cdc is perhaps the most expressive qualitative calculus for directional information and has attracted increasing interest from areas such as artificial intelligence geographical information science and image retrieval given a network of cdc constraints the consistency problem is deciding if the network is realizable by connected regions in the real plane this paper provides a cubic algorithm for checking the consistency of complete networks of basic cdc constraints and proves that reasoning with the cdc is in general an np complete problem for a consistent complete network of basic cdc constraints our algorithm returns a canonical solution in cubic time this cubic algorithm is also adapted to check the consistency of complete networks of basic cardinal constraints between possibly disconnected regions

on redundant topological constraints redundancy checking is an important task in the research of knowledge representation and reasoning in this paper we consider redundant qualitative constraints for a set of qualitative constraints we say a constraint x r y in is redundant if it is entailed by the rest of a prime subnetwork of is a subset of which contains no redundant constraints and has the same solution set as it is natural to ask how to compute such a prime subnetwork and when it is unique we show that this problem is in general intractable but becomes tractable if is over a tractable subalgebra s of a qualitative calculus furthermore if s is a subalgebra of the region connection calculus rcc8 in which weak composition distributes over nonempty intersections then has a unique prime subnetwork which can be obtained in cubic time by removing all redundant constraints simultaneously from as a by product we show that any path consistent network over such a distributive subalgebra is minimal and globally consistent in a qualitative sense a thorough empirical analysis of the prime subnetwork upon real geographical data sets demonstrates the approach is able to identify significantly more redundant constraints than previously proposed algorithms especially in constraint networks with larger proportions of partial overlap relations

reasoning about temporal relations a maximal tractable subclass of allen s interval algebra we introduce a new subclass of allen s interval algebra we call ord horn subclass which is a strict superset of the pointisable subclass we prove that reasoning in the ord horn subclass is a polynomial time problem and show that the path consistency method is sufficient for deciding satisfiability further using an extensive machine generated case analysis we show that the ord horn subclass is a maximal tractable subclass of the full algebra assuming p np in fact it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations

a fuzzy sets theoretic approach to approximate spatial reasoning relational composition based reasoning has become the most prevalent method for qualitative reasoning since allen s 1983 work on temporal intervals underlying this reasoning technique is the concept of a jointly exhaustive and pairwise disjoint set of relations systems of relations such as rcc5 and rcc8 were originally developed for ideal regions not subject to imperfections such as vagueness or fuzziness which are found in many applications in geographic analysis and image understanding this paper however presents a general method for classifying binary topological relations involving fuzzy regions using the rcc5 or the rcc8 theory our approach is based on fuzzy set theory and the theory of consonant random set some complete classifications of topological relations between fuzzy regions are also given furthermore two composition operators on spatial relations between fuzzy regions are introduced in this paper these composition operators provide reasonable relational composition based reasoning engine for spatial reasoning involving fuzzy regions

solving conflicts in information merging by a flexible interpretation of atomic propositions although many techniques for merging conflicting propositional knowledge bases have already been proposed most existing work is based on the idea that inconsistency results from the presence of incorrect pieces of information which should be identified and removed in contrast we take the view in this paper that conflicts are often caused by statements that are inaccurate rather than completely false suggesting to restore consistency by interpreting certain statements in a flexible way rather than ignoring them completely in accordance with this view we propose a novel approach to merging which exploits extra logical background information about the semantic relatedness of atomic propositions several merging operators are presented which are based on different formalizations of this background knowledge ranging from purely qualitative approaches related to possibilistic logic to quantitative approaches with a probabilistic flavor both syntactic and semantic characterizations are provided for each merging operator and the computational complexity is analyzed