hybrid feedback laws for a class of cascade nonlinear control systems a stabilization problem for a class of nonlinear control systems is considered systems in this class can be viewed as a cascade connection of a linear time invariant subsystem a nonlinear time periodic static subsystem and an integrator hybrid logic based feedback controllers are constructed to globally stabilize these systems to the origin the controllers operate by switching between various time periodic control functions at discrete time instants as specific applications we consider stabilization of nonholonomic control systems in power form to the origin and stabilization of trajectories for a class of nonlinear control systems numerical examples of global stabilization and tracking are reported

on matrices related with fibonacci and lucas numbers in this paper we obtain some new results on matrices related with fibonacci numbers and lucas numbers also we derive the relation between pell numbers and its companion sequence by using our representations

generalized heisenberg algebras and k generalized fibonacci numbers it is shown how some of the recent results of de souza et al 2006 j phys a math gen 39 10415 can be generalized to describe hamiltonians whose eigenvalues are given as k generalized fibonacci numbers here k is an arbitrary integer and the cases considered by de souza et al correspond to k 2

fast block diagonalization of k tridiagonal matrices abstract in the present paper we give a fast algorithm for block diagonalization of k tridiagonalmatrices the block diagonalization provides us with some useful results e g another der ivation of a very recent result on generalized k fibonacci numbers in m e a el mikkawy t sogabe a new family of k fibonacci numbers appl math comput 215 2010 4456 4461 ef cient symbolic algorithm for computing the matrix determinant 2011 elsevier inc all rights reserved 1 introduction and objectiveslet t k n be the k tridiagonal matrix of order n n i e t k n d 1 0 0 a 1 0 00 d 2 0 0 a 2 0 0 00 d n k a n k b k 1 0 00 b k 2 0 0 0 0 d n 1 00 0 b n 0 0 d n 0bbbbbbbbbbbbbbbbbbb 1ccccccccccccccccccca 1 for example t 3 7 is given as follows t 3 7 d 1 00a 1 00 00 d 2 00a 2 0000d 3 00a 3 0b 4 00d 4 00a 4 0 b 5 00d 5 0000b 6 00d 6 0000b 7 00d 7 0bbbbbbbbbbb 1ccccccccccca 2 0096 3003 see front matter 2011 elsevier inc all rights reserved doi 10 1016 j amc 2011 08 014

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

on asymptotic stabilization of driftless systems a simple approach is proposed to investigate the stabilization of driftless systems by taking the control input as a function of system states we can transform the stabilization design into a stability problem the known stability results on the nonlinear autonomous system are then employed to derive the asymptotically stabilizing controllers by solving an algebraic equation existence conditions of the asymptotic stabilizing feedback controller for the driftless systems by employing the stability criteria on linear systems and a class of third order homogeneous systems are obtained to demonstrate the application of the approach

trajectory generation for the n trailer problem using goursat normal form develops the machinery of exterior differential forms more particularly the goursat normal form for a pfaffian system for solving nonholonomic motion planning problems i e motion planning for systems with nonintegrable velocity constraints the authors use this technique to solve the problem of steering a mobile robot with n trailers the authors present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the goursat canonical form two of these transformations are studied in detail the goursat normal form for exterior differential systems is dual to the so called chained form for vector fields that has been studied previously consequently the authors are able to give the state feedback law and change of coordinates to convert the n trailer system into chained form three methods for planning trajectories for chained form systems using sinusoids piecewise constants and polynomials as inputs are presented the motion planning strategy is therefore to first convert the n trailer system into goursat form use this to find the chained form coordinates plan a path for the corresponding chained form system and then transform the resulting trajectory back into the original coordinates simulations and frames of movie animations of the n trailer system for parallel parking and backing into a loading dock using this strategy are included

a note on generalized k horadam sequence in this paper we define generalized k horadam sequence h k n n n after that we study the properties of the generalized k horadam sequence and prove some of these properties by means of determinant also we obtain a generating function for the generalized k horadam sequence

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

on determinants of matrices with general fibonacci numbers entries in this paper we investigate the properties of the determinants of matrices obtained by generalized order k k step fibonacci numbers

the complexity of some polynomial network consistency algorithms for constraint satisfaction problems abstract constraint satisfaction problems play a central role in artificial intelligence a class of network consistency algorithms for eliminating local inconsistencies in such problems has previously been described we analyze the time complexity of several node arc and path consistency algorithms and prove that arc consistency is achievable in time linear in the number of binary constraints the waltz filtering algorithm is a special case of the arc consistency algorithm in the edge labelling computational vision application the constraint graph is planar and so the time complexity is linear in the number of variables

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

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

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

a complete classification of tractability in allen s algebra relative to subsets of basic relations abstract we characterise the set of subalgebras of allen s algebra which have a tractable satisfiability problem and in addition contain certain basic relations the conclusion is that no tractable subalgebra dial is not known in the literature can contain more than the three basic relations b and b where b d o s f this means that concerning algebras for specifying complete knowledge about temporal information there is no hope of finding yet unknown classes with much expressivity we also classify completely some cases where we cannot even express complete information but close to complete showing that there are exactly two maximal tractable algebras containing the relation exactly two containing the relation m m and exactly three containing the relation m the algebras containing can express the notion of sequentiality thus we have a complete characterization of tractable inference using that notion

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

modelling and solving temporal reasoning as propositional satisfiability representing and reasoning about time dependent information is a key research issue in many areas of computer science and artificial intelligence one of the best known and widely used formalisms for representing interval based qualitative temporal information is allen s interval algebra ia the fundamental reasoning task in ia is to find a scenario that is consistent with the given information this problem is in general np complete in this paper we investigate how an interval based representation or ia network can be encoded into a propositional formula of boolean variables and or predicates in decidable theories our task is to discover whether satisfying such a formula can be more efficient than finding a consistent scenario for the original problem there are two basic approaches to modelling an ia network one represents the relations between intervals as variables and the other represents the end points of each interval as variables by combining these two approaches with three different boolean satisfiability sat encoding schemes we produced six encoding schemes for converting ia to sat in addition we also showed how ia networks can be formulated into satisfiability modulo theories smt formulae based on the quantifier free integer difference logic qf idl these encodings were empirically studied using randomly generated ia problems of sizes ranging from 20 to 100 nodes a general conclusion we draw from these experimental results is that encoding ia into sat produces better results than existing approaches more specifically we show that the new point based 1 d support sat encoding of ia produces consistently better results than the other alternatives considered in comparison with the six different sat encodings the smt encoding came fourth after the point based and interval based 1 d support schemes and the point based direct scheme further we observe that the phase transition region maps directly from the ia encoding to each sat or smt encoding but surprisingly the location of the hard region varies according to the encoding scheme our results also show a fixed performance ranking order over the various encoding schemes

on k fibonacci numbers of arithmetic indexes in this paper we study the sums of k fibonacci numbers with indexes in an arithmetic sequence say an r for fixed integers a and r this enables us to give in a straightforward way several formulas for the sums of such numbers

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

on the k generalized fibonacci numbers and high order linear recurrence relations in this paper using elementary symmetric function and complete homogeneous symmetric function we obtain a determinant formula for the k generalized fibonacci sequence the relationship between the k generalized fibonacci sequence and the order k linear homogeneous recurrence relation has been investigated and a general solution for the latter is also derived furthermore we obtain an explicit expression for the elements in the nth power of the companion matrix in terms of k generalized fibonacci numbers

on the order k generalized lucas numbers in this paper we give a new generalization of the lucas numbers in matrix representation also we present a relation between the generalized order k lucas sequences and fibonacci sequences

on the representation of k generalized fibonacci and lucas numbers abstract in this paper we give some determinantal and permanental representations of k generalized fibonacci and lucas numbers we obtain the binet s formula for these sequences by using our representations

twenty one large tractable subclasses of allen s algebra abstract this paper continues nebel and burckert s investigation of allen s interval algebra by presenting nine more maximal tractable subclasses of the algebra provided that p np in addition to their previously reported ord horn subclass furthermore twelve tractable subclasses are identified whose maximality is not decided four of them can express the notion of sequentiality between intervals which is not possible in the ord horn algebra all of the algebras are considerably larger than the ord horn subclass the satisfiability algorithm which is common for all the algebras is shown to be linear furthermore the path consistency algorithm is shown to decide satisfiability of interval networks using any of the algebras

combining interval based temporal reasoning with general tboxes while classical description logics dls concentrate on the representation of static conceptual knowledge recently there is a growing interest in dls that additionally allow to capture the temporal aspects of conceptual knowledge such temporal dls are based either on time points or on time intervals as the temporal primitive whereas point based temporal dls are well investigated this is not the case for interval based temporal dls all known logics either suffer from rather limited expressive power or have undecidable reasoning problems in particular there exists no decidable interval based temporal dl that provides for general tboxes one of the most important expressive means in modern description logics in this paper for the first time we define an interval temporal dl that is equipped with general tboxes and for which reasoning is decidable and more precisely exptime complete

automated complexity analysis based on ordered resolution we define order locality to be a property of clauses relative to a term ordering this property generalizes the subformula property for proofs where the terms appearing in proofs can be bounded under the given ordering by terms appearing in the goal clause we show that when a clause set is order local then the complexity of its ground entailment problem is a function of its structure e g full versus horn clauses and the ordering used we prove that in many cases order locality is equivalent to a clause set being saturated under ordered resolution this provides a means of using standard resolution theorem provers for testing order locality and transforming non local clause sets into local ones we have used the saturate system to automatically establish complexity bounds for a number of nontrival entailment problems relative to complexity classes which include polynomial and exponential time and co np

complexity classification in qualitative temporal constraint reasoning we study the computational complexity of the qualitative algebra which is a temporal constraint formalism that combines the point algebra the point interval algebra and allen s interval algebra we identify all tractable fragments and show that every other fragment is np complete

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

a path following problem for a class of non holonomic control systems with noise this paper deals with a path following problem for a system affected by noise and proposes a dynamic inversion based controller that makes use of the error between the real position and a suitable path location an estimate of such error is given in terms of the noise bounds showing the practical stability of the closed loop system the results presented in this article apply to a subclass of chaplygin control systems which includes several common mechanical systems as an example the developed strategy has been applied to maneuver a kinematic model of a system moving in a 3 dimensional space in such a way that a point located at a positive distance from its center of geometry is driven towards a given path

stabilization of trajectories for systems with nonholonomic constraints a new technique for stabilizing nonholonomic systems to trajectories is presented it is well known that such systems cannot be stabilized to a point using smooth static state feedback in this note we suggest the use of control laws for stabilizing a system about a trajectory instead of a point given a nonlinear system and a desired nominal feasible trajectory the note gives an explicit control law which will locally exponentially stabilize the system to the desired trajectory the theory is applied to several examples including a car like robot

inversion of k tridiagonal matrices with toeplitz structure in this paper we consider an inverse problem with the k tridiagonal toeplitz matrices a theoretical result is obtained that under certain assumptions the explicit inverse of a k tridiagonal toeplitz matrix can be derived immediately two numerical examples are given to demonstrate the validity of our results

k lucas numbers and associated bipartite graphs for a positive integer k 2 the k fibonacci sequence gn k is defined as g1 k gk 2 k 0 gk 1 k gk k 1 and for n k 2 gn k gn 1 k gn 2 k gn k k moreover the k lucas sequence ln k is defined as ln k gn 1 k gn k 1 k for n 1 in this paper we consider the relationship between gn k and ln k and 1 factors of a bipartite graph

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

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

a new approach to generalized fibonacci and lucas numbers with binomial coefficients in this study fibonacci and lucas numbers have been obtained by using generalized fibonacci numbers in addition some new properties of generalized fibonacci numbers with binomial coefficients have been investigated to write generalized fibonacci sequences in a new direct way furthermore it has been given a new formula for some lucas numbers

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

fuzzifying allen s temporal interval relations when the time span of an event is imprecise it can be represented by a fuzzy set called a fuzzy time interval in this paper we propose a framework to represent compute and reason about temporal relationships between such events since our model is based on fuzzy orderings of time points it is not only suitable to express precise relationships between imprecise events ldquoroosevelt died before the beginning of the cold warrdquo but also imprecise relationships ldquoroosevelt died just before the beginning of the cold warrdquo we show that unlike previous models our model is a generalization that preserves many of the properties of the 13 relations allen introduced for crisp time intervals furthermore we show how our model can be used for efficient fuzzy temporal reasoning by means of a transitivity table finally we illustrate its use in the context of question answering systems

on the period of fibonacci sequences in nilpotent groups in this paper we will constitute 2 step fibonacci sequences by the two generating elements of a group of exponent p p is prime and nilpotency class 5 using a improved computer program unless p 2 we show that the period of the fibonacci sequences is pk p in gf p for certain prime numbers

computing the minimal relations in point based qualitative temporal reasoning through metagraph closure computing the minimal representation of a given set of constraints a csp over the point algebra pa is a fundamental temporal reasoning problem the main property of a minimal csp over pa is that the strongest entailed relation between any pair of variables in the csp can be derived in constant time we study some new methods for solving this problem which exploit and extend two prominent graph based representations of a csp over pa the timegraph and the series parallel sp metagraph essentially these are graphs partitioned into sets of chains and series parallel subgraphs respectively on which the search is supported by a metagraph data structure the proposed approach is based on computing the metagraph closure for these representations which can be accomplished by some methods studied in the paper in comparison with the known techniques based on enforcing path consistency under certain conditions about the structure of the input csp and the size of the generated metagraph the proposed metagraph closure approach has better worst case time and space complexity moreover for every sparse csp over the convex pa the time complexity is reduced to o n 2 from o n 3 where n is the number of variables involved in the csp an extensive experimental analysis presented in the paper compares the proposed techniques and other known algorithms these experimental results identify the best performing methods and show that in practice for csps exhibiting chain or sp graph structure and randomly generated both sparse and dense csps the metagraph closure approach is significantly faster than the approach based on enforcing path consistency

temporal reasoning based on semi intervals abstract a generalization of allen s interval based approach to temporal reasoning is presented the notion of conceptual neighborhood of qualitative relations between events is central to the presented approach relations between semi intervals rather than intervals are used as the basic units of knowledge semi intervals correspond to temporal beginnings or endings of events we demonstrate the advantages of reasoning on the basis of semi intervals 1 semi intervals are rather natural entities both from a cognitive and from a computational point of view 2 coarse knowledge can be processed directly computational effort is saved 3 incomplete knowledge about events can be fully exploited 4 incomplete inferences made on the basis of complete knowledge can be used directly for further inference steps 5 there is no trade off in computational strength for the added flexibility and efficiency 6 for a natural subset of allen s algebra global consistency can be guaranteed in polynomial time 7 knowledge about relations between events can be represented much more compactly

a semi dynamical approach for solving qualitative spatial constraint satisfaction problems in this paper we solve the problem of determining a consistent instantiation of any finite path consistent and atomic network of rcc8 base relations we already know that such networks that contain a finite number of variables have a realization in any dimension d 1 the novelty of our work is that given any path consistent and atomic constraint rcc8 network we are able to construct in polynomial time a realization that satisfies it for this purpose we suitably instantiate the variables of such a network by associating to them some regular closed sets of the set of real numbers

temporal reasoning about fuzzy intervals traditional approaches to temporal reasoning assume that time periods and time spans of events can be accurately represented as intervals real world time periods and events on the other hand are often characterized by vague temporal boundaries requiring appropriate generalizations of existing formalisms this paper presents a framework for reasoning about qualitative and metric temporal relations between vague time periods in particular we show how several interesting problems like consistency and entailment checking can be reduced to reasoning tasks in existing temporal reasoning frameworks we furthermore demonstrate that all reasoning tasks of interest are np complete which reveals that adding vagueness to temporal reasoning does not increase its computational complexity to support efficient reasoning a large tractable subfragment is identified among others generalizing the well known ord horn subfragment of the interval algebra extended with metric constraints

building tractable disjunctive constraints many combinatorial search problems can be expressed as constraint satisfaction problems this class of problems is known to be np hard in general but a number of restricted constraint classes have been identified which ensure tractability this paper presents the first general results on combining tractable constraint classes to obtain larger more general tractable classes we give examples to show that many known examples of tractable constraint classes from a wide variety of different contexts can be constructed from simpler tractable classes using a general method we also construct several new tractable classes that have not previously been identified

the algebra ia fuz a framework for qualitative fuzzy temporal reasoning the aim of this work is to integrate the ideas of flexibility and uncertainty into allen s interval based temporal framework defining a new formalism called ia f u z which extends classical interval algebra ia in order to express qualitative fuzzy constraints between intervals we generalize the classical operations between ia relations to ia f u z relations as well as the concepts of minimality and local consistency referring to the framework of fuzzy constraint satisfaction problem we analyze the most interesting reasoning tasks in our framework which generalize the classical problems of checking consistency finding a solution and computing the minimal network in the context of ia in order to solve these tasks we devise two constraint propagation algorithms and a branch bound algorithm since these tasks are np difficult we address the problem of finding tractable sub algebras of ia f u z by extending to our fuzzy framework the classical pointizable sub algebras sa c and sa as well as the maximal tractable subalgebra h introduced by nebel in particular we prove that the fuzzy extension of the latter called h f u z shares with its classical counterpart a maximality property in that it is the unique maximal subalgebra of ia f u z which contains the fuzzy extensions of allen s atomic relations ions

a class of generalized tribonacci sequences applied to counting problems abstract generalized tribonacci numbers with the third order linear recurrence with constant coefficients t k n t k n 1 t k n 2 k t k n 3 for n 2 are investigated for some sets of the initial triples t0 t1 t2 in particular generating functions the binet formula and the limit of ratio of consecutive terms t k n 1 t k n are discussed these numbers are related to numbers of path graphs colorings with k 2 colors or equivalently to counting of q ary sequences of length n for q k 2 satisfying requirements which follow the problem of degeneration in the ising model with the second neighbor interactions it is shown that the results obtained can be considered as the base for considerations of cycle graph colorings cyclic q ary sequences these are counting problems so t0 t1 t2 and k should be natural numbers but these sequences can be considered for any real numbers the special cases k 0 1 lead to the fibonacci and the usual tribonacci numbers respectively so the results can be applied to binary and ternary sequences

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

on binary constraint problems the concepts of binary constraint satisfaction problems can be naturally generalized to the relation algebras of tarski the concept of path consistency plays a central role algorithms for path consistency can be implemented on matrices of relations and on matrices of elements from a relation algebra we give an example of a 4 by 4 matrix of infinite relations on which on iterative local path consistency algorithm terminates we give a class of examples over a fixed finite algebra on which all iterative local algorithms whether parallel or sequential must take quadratic time specific relation algebras arising from interval constraint problems are also studied the interval algebra the point algebra and the containment algebra

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

the complexity of temporal constraint satisfaction problems a temporal constraint language is a set of relations that has a first order definition in q an extended abstract of this article appeared in the proceedings of stoc 08

adaptive tracking control of uncertain nonholonomic dynamic system this note considers the tracking problem of nonholonomic dynamic systems with unknown inertia parameters a new controller is proposed relying on newly defined tracking errors and the passivity property of the nonholonomic dynamic system the proposed controller ensures that the entire state of the system asymptotically tracks the desired trajectory simulation results show effectiveness of the proposed controller

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

towards a general theory of action and time abstract a formalism for reasoning about actions is proposed that is based on a temporal logic it allows a much wider range of actions to be described than with previous approaches such as the situation calculus this formalism is then used to characterize the different types of events processes actions and properties that can be described in simple english sentences in addressing this problem we consider actions that involve non activity as well as actions that can only be defined in terms of the beliefs and intentions of the actors finally a framework for planning in a dynamic world with external events and multiple agents is suggested

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

reasoning about causality between distributed nonatomic events abstract the complex events in distributed applications such as industrial process control avionics navigation planning robotics diagnostics virtual reality and temporal and geographic databases are realistically modeled by nonatomic events this paper derives and studies causality relations between nonatomic distributed events in the execution of a complex distributed application such causality relations are useful because they provide a fine level of discrimination in the specification of the relative timing relations and synchronization conditions between the nonatomic events the paper then proposes a set of axioms on the proposed causality relations the set of axioms provides a mechanism for temporal and spatial reasoning with the set of relations and can be used to derive all possible implications from any valid predicate on the proposed relations

backtracking algorithms for disjunctions of temporal constraints abstract we extend the framework of simple temporal problems studied originally by dechter meiri and pearl to consider constraints of the form x 1 y 1 r 1 x n y n r n where x 1 x n y 1 y n are variables ranging over the real numbers r 1 r n are real constants and n 1 this is a wide class of temporal constraints that can be used to model a variety of problems in temporal reasoning scheduling planning and temporal constraint databases we have implemented several progressively more efficient algorithms for the consistency checking problem for this class of temporal constraints backtracking backjumping three variations of forward checking and forward checking with backjumping we have partially ordered the above algorithms according to the number of visited search nodes and the number of performed consistency checks although our problem is non binary our results agree with the results of kondrak and van beek who consider only binary constraints we have also studied the performance of the above algorithms experimentally using randomly generated sets of data and job shop scheduling problems the experiments with random instances allowed us to locate the hard region for this class of problems the results show that hard problems occur at a critical value of the ratio of disjunctions to variables

determining the consistency of partial tree descriptions we present an efficient algorithm that decides the consistency of partial descriptions of ordered trees the constraint language of these descriptions was introduced by cornell in computational linguistics the constraints specify for pairs of nodes sets of admissible relative positions in an ordered tree cornell asked for an algorithm to find a tree structure satisfying these constraints this computational problem generalizes the common supertree problem studied in phylogenetic analysis and also generalizes the network consistency problem of the so called left linear point algebra we present the first polynomial time algorithm for cornell s problem which runs in time o mn where m is the number of constraints and n the number of variables in the constraint

symbolic algorithms for the inverses of general k tridiagonal matrices two symbolic algorithms for inverting k tridiagonal matrices have been recently found by el mikkawy and atlan 2014 2015 these two algorithms are mainly based on the doolittle lu factorization of the k tridiagonal matrix in the current paper we present a new explicit analytic expression for the inverses of general tridiagonal matrices at first by using a block diagonalization technique we then relate k tridiagonal matrix inversion to tridiagonal matrix inversion meanwhile an efficient algorithm is derived for computing the inverses of nonsingular k tridiagonal matrices with the help of any algorithm for computing the inverses of tridiagonal matrices three examples are given in order to illustrate the performance and efficiency of the proposed algorithms

a note on a fast breakdown free algorithm for computing the determinants and the permanents of k tridiagonal matrices k tridiagonal matrices have attracted much attention in recent years which are a generalization of tridiagonal matrices in this note a breakdown free numerical algorithm of o n is presented for computing the determinants and the permanents of k tridiagonal matrices even though the algorithm is not a symbolic algorithm it never suffers from breakdown furthermore it produces exact values when all entries of the k tridiagonal matrices are given in integer in addition the algorithm can be simplified for a general symmetric toeplitz case and it generates the kth powers of fibonacci pell and jacobsthal numbers for a certain symmetric toeplitz case

global stabilizing near optimal control design for nonholonomic chained systems it is well known that a nonlinear optimal control requires the solution to a two point boundary value problem or to a nonlinear partial differential equation and that such a solution can only be obtained off line by numerical iteration in this paper a new and near optimal control design framework is proposed for controlling any nonholonomic system in the chained form the proposed design is based upon thorough study of uniform complete controllability of the corresponding linear time varying nominal system it is shown that no matter whether the first component u1d t of reference input vector is uniformly nonvanishing or simply nonconvergent to zero or vanishing or identically zero uniform complete controllability of the nominal system can be recovered by employing the proposed time folding unfolding technique upon establishing the common property of uniform complete controllability the proposed framework can be used to design both trajectory tracking control and regulation control in a systematic and unified manner using duality uniform complete observability can also be established a closed form and exponentially convergent observer can be synthesized and the controls designed using the proposed framework can be either state feedback or output feedback the tracking controls are designed using the same three step process that is design of the proposed controls starts with optimal control solutions to two linear nominal subsystems one time invariant and the other time varying the two solutions combined together render a globally stabilizing suboptimal control for the overall system then the optimality condition is invoked to determine the distance between the suboptimal control and the optimal one consequently an improved control can be obtained by introducing a nonlinear additive control term in such a way that the distance aforementioned is minimized as much as possible in closed form an example is used to show that regulation control can be designed similarly all the controls designed are in simple closed forms and hence real time implementable they are time varying and smooth globally and exponentially asymptotically stabilizing and they are near optimal since their closeness to the optimal control attainable only offline can be measured monitored on line and has been minimized

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

brief on controllability and trajectory tracking of a kinematic vehicle model this paper presents some further results concerning the issues of controllability and trajectory tracking regarding a front wheel drive vehicle kinematic model a simple procedure for computing an open loop control strategy that transfers the system between given initial and final states is presented in particular the input function is computed by means of a set of linear algebraic equations the resulting motion planning procedure allows us to present a control scheme for solving the trajectory a time parameterized reference signal tracking problem various applications of the approach in forward and backward motions are considered and simulation results are presented

controllability and stabilizability of a class of systems with higher order nonholonomic constraints a theoretical framework is established for the control of higher order nonholonomic systems defined as systems that satisfy higher order nonintegrable constraints a model for such systems is developed in terms of differential algebraic equations defined on a higher order tangent bundle a number of control theoretic properties such as nonintegrability controllability and stabilizability are presented higher order nonholonomic systems are shown to be strongly accessible and under certain conditions small time locally controllable at any equilibrium the applicability of the theoretical development is illustrated through a third order nonholonomic system example a planar ppr robot manipulator subject to a jerk constraint in particular it is shown that although the system is not asymptotically stabilizable to a given equilibrium configuration using a time invariant continuous feedback it is strongly accessible and small time locally controllable at any equilibrium

on a homogeneous recurrence relation for the determinants of general pentadiagonal toeplitz matrices pentadiagonal toeplitz matrices frequently arise in many application areas and have been attracted much attention in recent years in this paper we present a numerical algorithm of o log n for computing the determinants of general pentadiagonal toeplitz matrices without imposing any restrictive conditions in addition we investigate some special pentadiagonal toeplitz determinants and their relations to well known number sequences and give a few identity formulas for the ordinary fibonacci sequences and the generalized k fibonacci sequences

a new family of k fibonacci numbers in the present paper we give a new family of k fibonacci numbers and establish some properties of the relation to the ordinary fibonacci numbers furthermore we describe the recurrence relations and the generating functions of the new family for k 2 and k 3 and presents a few identity formulas for the family and the ordinary fibonacci numbers