constructing symmetric boolean functions with maximum algebraic immunity symmetric boolean functions with even variables 2k and maximum algebraic immunity ai f k have been constructed in braeken s thesis 2006 in this paper we show more constructions of such boolean functions including the generalization of a result and prove a conjecture raised in braeken s thesis 2006

cyclic codes and sequences from generalized coulter matthews function in this paper we will study the exponential sum sigmaxisinfq x alphax pk 1 2 betax that is related to the generalized coulter matthews function x pk 1 2 with k gcd as applications we obtain the following the correlation distribution of a p ary m sequence and a decimated m sequence of degree pk 1 2 the weight distribution of the cyclic code whose dual has two zeros pi 1 and pi pk 1 2

characterization of m sequences of lengths 2 2k 1 and 2 k 1 with three valued cross correlation considered is the distribution of the cross correlation between in sequences of length 22k 1 where m 2k and m sequences of shorter length 2k 1 new pairs of m sequences with three valued cross correlation are found and the complete correlation distribution is determined finally we conjecture that there are no more cases with a three valued cross correlation apart from the ones proven here

temporal constraint networks abstract this paper extends network based methods of constraint satisfaction to include continuous variables thus providing a framework for processing temporal constraints in this framework called temporal constraint satisfaction problem tcsp variables represent time points and temporal information is represented by a set of unary and binary constraints each specifying a set of permitted intervals the unique feature of this framework lies in permitting the processing of metric information namely assessments of time differences between events we present algorithms for performing the following reasoning tasks finding all feasible times that a given event can occur finding all possible relationships between two given events and generating one or more scenarios consistent with the information provided we distinguish between simple temporal problems stps and general temporal problems the former admitting at most one interval constraint on any pair of time points we show that the stp which subsumes the major part of vilain and kautz s point algebra can be solved in polynomial time for general tcsps we present a decomposition scheme that performs the three reasoning tasks considered and introduce a variety of techniques for improving its efficiency we also study the applicability of path consistency algorithms as preprocessing of temporal problems demonstrate their termination and bound their complexities

planning as constraint satisfaction solving the planning graph by compiling it into csp the idea of synthesizing bounded length plans by compiling planning problems into a combinatorial substrate and solving the resulting encodings has become quite popular in recent years most work to date has however concentrated on compilation to satisfiability sat theories and integer linear programming ilp in this paper we will show that csp is a better substrate for the compilation approach compared to both sat and ilp we describe gp csp a system that does planning by automatically converting graphplan s planning graph into a csp encoding and solving it using standard csp solvers our comprehensive empirical evaluation of gp csp demonstrates that it is superior to both the blackbox system which compiles planning graphs into sat encodings and an ilp based planner in a wide range of planning domains our results show that csp encodings outperform sat encodings in terms of both space and time requirements in various problems the space reduction is particularly important as it makes gp csp less susceptible to the memory blow up associated with sat compilation methods the paper also discusses various techniques in setting up the csp encodings planning specific improvements to csp solvers and strategies for variable and value selection heuristics for solving the csp encodings of different types of planning problems copyright 2001 elsevier science b v

the weight distribution of a class of linear codes from perfect nonlinear functions in this correspondence the weight distribution of a class of linear codes based on perfect nonlinear functions also called planar functions is determined the class of linear codes under study are either optimal or among the best codes known and have nice applications in cryptography

constructions of balanced odd variable rotation symmetric boolean functions with optimal algebraic immunity and high nonlinearity abstract rotation symmetric boolean functions have been used as components of different cryptosystems in this paper two classes of balanced rotation symmetric boolean functions having optimal algebraic immunity on odd number of variables are constructed we give a lower bound on the algebraic degree of the first class of functions and prove that the n variable functions in the second class has optimal algebraic degree if n 2 m 1 for m 2 moreover it is shown that both classes of functions have much better nonlinearity than all the previously obtained rotation symmetric boolean functions with optimal algebraic immunity and have good behavior against fast algebraic attacks at least for small numbers of input variables

planning graph as the basis for deriving heuristics for plan synthesis by state space and csp search most recent strides in scaling up planning have centered around two competing themesdisjunctive planners exemplified by graphplan and heuristic state search planners exemplified by unpop hsp and hsp r in this paper we present a novel approach for successfully harnessing the advantages of the two competing paradigms to develop planners that are significantly more powerful than either of the approaches specifically we show that the polynomial time planning graph structure that the graphplan builds provides a rich substrate for deriving a family of highly effective heuristics for guiding state space search as well as csp style search the main leverage provided by the planning graph structure is a systematic and graded way to take subgoal interactions into account in designing state space heuristics for state space search we develop several families of heuristics some aimed at search speed and others at optimality of solutions and analyze many approaches for improving the cost quality tradeoffs offered by these heuristics our normalized empirical comparisons show that our heuristics handily outperform the existing state space heuristics for csp style search we describe a novel way of using the planning graph structure to derive highly effective variable and value ordering heuristics we show that these heuristics can be used to improve graphplan s own backward search significantly to demonstrate the effectiveness of our approach vis a vis the state of the art in plan synthesis we present altalt a planner literally cobbled together from the implementations of graphplan and state search style planners using our theory we evaluate altalt on the suite of problems used in the recent aips 2000 planning competition the results place altalt in the top tier of the competition plannersoutperforming both graphplan based and heuristic search based planners

the weight enumerator of three families of cyclic codes cyclic codes are a subclass of linear codes and have wide applications in consumer electronics data storage systems and communication systems due to their efficient encoding and decoding algorithms cyclic codes with many zeros and their dual codes have been a subject of study for many years however their weight distributions are known only for a very small number of cases in general the calculation of the weight distribution of cyclic codes is heavily based on the evaluation of some exponential sums over finite fields very recently li studied a class of p ary cyclic codes of length p2m 1 where p is a prime and m is odd they determined the weight distribution of this class of cyclic codes by establishing a connection between the involved exponential sums with the spectrum of hermitian forms graphs in this paper this class of p ary cyclic codes is generalized and the weight distribution of the generalized cyclic codes is settled for both even m and odd m along with the idea of li the weight distributions of two related families of cyclic codes are also determined

on the complexity of planning for agent teams and its implications for single agent planning if the complexity of planning for a single agent is described by some function f of the input how much more difficult is it to plan for a team of n cooperating agents if these agents are completely independent we can simply solve n single agent problems scaling linearly with the number of agents but if all the agents interact tightly we really need to solve a single problem that is n times larger which could be exponentially in n harder to solve is a more general characterization possible to formulate this question precisely we minimally extend the standard strips model to describe multi agent planning problems then we identify two problem parameters that help us answer our question the first parameter is independent of the precise task the multi agent system should plan for and it captures the structure of the possible direct interactions between the agents via the tree width of a graph induced by the team the second parameter is task dependent and it captures the minimal number of interactions by the most interacting agent in the team that is needed to solve the problem we show that multi agent planning problems can be solved in time exponential only in these parameters thus when these parameters are bounded the complexity scales only polynomially in the size of the agent team these results also have direct implications for the single agent case by casting single agent planning tasks as multi agent planning tasks we can devise novel methods for decomposition based planning for single agents we analyze one such method and use the techniques developed to provide some of the strongest tractability results for classical single agent planning to date

weight distributions of some binary primitive cyclic codes let s and k be integers such that s is a divisor of 2 sup k 1 let g x be a divisor of x sup s 1 over f sub 2 and let spl pi x be a primitive polynomial of degree k over f sub 2 we consider the binary cyclic code c of length n 2 sup k 1 generated by x sup n 1 g x spl pi x for special cases we determine the weight distribution of c by using the weights of the cyclic code of length s generated by x sup s 1 g x

the moments of a kloosterman sum and the weight distribution of a zetterberg type binary cyclic code in this correspondence we give the moments of a kloosterman sum over fq in terms of the frequencies of weights in the binary zetterberg code of length q 1 which are known by the work of schoof and van der vlugt the method is illustrated by giving explicit formulae for the moments up to the tenth moment as a corollary the weight distribution of a zetterberg type binary cyclic code is obtained

generalized kasami sequences the large set in this correspondence new binary sequence families fk of period 2n 1 are constructed for even n and any k with gcd k n 2 if n 2 is odd or gcd k n 1 if n 2 is even the distribution of their correlation values is completely determined these families have maximum correlation 2n 2 1 and family size 23n 2 2n 2 for odd n 2 or 23n 2 2n 2 1 for even n 2 the proposed families include the large set of kasami sequences where the k is taken as k n 2 1

a new binary sequence family with low correlation and large size for odd n 2l 1 and an integer spl rho with 1 spl les spl rho spl les l a new family s sub o spl rho of binary sequences of period 2 sup n 1 is constructed for a given spl rho s sub o spl rho has maximum correlation 1 2 sup n 2 spl rho 1 2 family size 2 sup n spl rho and maximum linear span n n 1 2 similarly a new family of s sub e spl rho of binary sequences of period 2 sup n 1 is also presented for even n 2l and an integer spl rho with 1 spl les spl rho l where maximum correlation family size and maximum linear span are 1 2 sup n 2 spl rho 2 sup n spl rho and n n 1 2 respectively the new family s sub o spl rho or s sub e spl rho contains boztas and kumar s construction or udaya s as a subset if m sequences are excluded from both constructions as a good candidate with low correlation and large family size the family s sub o 2 is discussed in detail by analyzing its distribution of correlation values

two remarks on a paper by moreno and kumar binary reed muller codes o moreno and p v kumar ieee trans inform theory vol 39 no 5 september 1993 showed how deligne s theorem can be applied to coding theory they studied certain subcodes of binary reed muller codes and estimated the associated character sums over a field of q sup 2 elements they obtained bounds of the order spl oscr q the present paper shows that in one case one can improve the coefficient of q in the estimates the author also shows that there is an error in moreno and kumar s argument and in some cases one needs need to replace a bound of the order spl oscr q by a weaker bound of the order spl oscr q sup 3 2

on the relations between intelligent backtracking and failure driven explanation based learning in constraint satisfaction and planning abstract the ideas of intelligent backtracking ib and explanation based learning ebl have developed independently in the constraint satisfaction planning machine learning and problem solving communities the variety of approaches developed for ib and ebl in the various communities have hither to been incomparable in this paper i formalize and unify these ideas under the task independent framework of refinement search which can model the search strategies used in both planning and constraint satisfaction problems csps i show that both ib and ebl depend upon the common theory of explanation analysis which involves explaining search failures and regressing them to higher levels of the search tree my comprehensive analysis shows that most of the differences between the csp and planning approaches to ebl and ib revolve around different solutions to a how the failure explanations are computed b how they are contextualized contextualization involves deciding whether or not to keep the flaw description and the description of the violated problem constraints and c how the storage of explanations is managed the differences themselves can be understood in terms of the differences between planning and csp problems as instantiations of refinement search this unified understanding is expected to support a greater cross fertilization of ideas among csp planning and ebl communities

several classes of binary sequences with three level autocorrelation in this correspondence we describe several classes of binary sequences with three level autocorrelation those classes of binary sequences are based on cyclic almost difference sets some classes of binary sequences have optimum autocorrelation

a new family of four valued cross correlation between m sequences of different lengths the cross correlation function between m sequences of period 2m 1 where m 6k and m sequences of shorter period 2m 2 1 is investigated the first infinite family of pairs of m sequences with four valued cross correlation is constructed and the complete correlation distribution of this family is determined

the weight distribution of a class of cyclic codes related to hermitian forms graphs the determination of weight distribution of cyclic codes involves the evaluation of gauss sums and exponential sums despite some cases where a neat expression is available the computation is generally rather complicated in this note we determine the weight distribution of a class of reducible cyclic codes whose dual codes may have arbitrarily many zeros this goal is achieved by building an unexpected connection between the corresponding exponential sums and the spectra of hermitian forms graphs

optimal cyclic codes with generalized niho type zeros and the weight distribution in this paper we extend two earlier works further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions it is interesting to note that many cyclic codes in the family are optimal and have only a few non zero weights besides using similar ideas we carry out some subtle manipulation of certain exponential sums

new binary sequences with optimal autocorrelation magnitude new binary sequences of period n 4 2m 1 for even m ges 4 are found where the sequences are described by a 4 x 2m 1 array structure the new sequences are almost balanced and have four valued autocorrelation i e n 0 plusmn4 which is optimal with respect to autocorrelation magnitude the complete autocorrelation distribution and the exact linear complexity of the sequences are mathematically derived finally it is shown that the sequences are implemented by a combination of linear feedback shift registers and a simple logic

on the weight distribution of cyclic codes with niho exponents recently there has been intensive research on the weight distributions of cyclic codes in this paper we compute the weight distributions of three classes of cyclic codes with niho exponents more specifically we obtain two classes of binary three weight and four weight cyclic codes and a class of nonbinary four weight cyclic codes the weight distributions follow from the determination of value distributions of certain exponential sums several examples are presented to show that some of our codes are optimal and some have the best known parameters

value distributions of exponential sums from perfect nonlinear functions and their applications in this paper we present a unified way to determine the values and their multiplicities of the exponential sums sigmaxisinf q zetap tr af x bx a bisinfq q pm pges3 for all perfect nonlinear functions f which is a dembowski ostrom polynomial or p 3 f x 3 k 1 2 where k is odd and k m 1 as applications we determine 1 the correlation distribution of the m sequence alambda tr gammalambda lambda 0 1 and the sequence blambda tr f gammalambda lambda 0 1 over fp where gamma is a primitive element of fq and 2 the weight distributions of the linear codes over fp defined by f

on the optimum cyclic subcode chains of cal rm 2 m ast for increasing message length the distance profiles of linear block codes can be employed to design variational coding scheme for encoding message with variational length and getting lower decoding error probability by large minimum hamming distance where one example is in the design of transport format combination indicators tfcis in cdma considering convenience for encoding we focus on the distance profiles with respect to cyclic subcode chains dpcs of cyclic codes over gf q with length n such that gcd n q 1 in this paper the optimum dpcs and the corresponding optimum cyclic subcode chains are investigated on the punctured second order reed muller code rm 2 m for increasing message length where two standards on the optimums are studied according to the rhythm of increase ignoring the dimension profile the device will coincide with that of tfci

surfaces and the weight distribution of a family of codes we derive the weight distribution of the binary trace codes with words tr ax sup q 1 bx sup 3 cx sub x spl isin f q2 where a b c spl isin f q sup 2 and tr is the trace map from f q sup 2 to f sub 2 the weights of these words determine the exponential sums which were considered earlier by moreno and kumar 1994 and lahtonen 1995 results from the theory of quadratic forms play a role but the decisive argument is of an algebraic geometric nature namely from the theory of surfaces

cyclic codes and sequences the generalized kasami case in this paper the large family of generalized kasami sequences has been studied in particular the cross correlation distribution among these sequences has been explicitly calculated meanwhile the weight distributions of two classes of cyclic codes could also be determined this paper generalizes the results from several previous papers

hamming weights of the duals of cyclic codes with two zeros cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms in this paper let bbb f r be a finite field with r q m suppose that g 1 g 2 in bbb f r are not conjugates over bbb f q operatorname ord g 1 n 1 operatorname ord g 2 n 2 d gcd n 1 n 2 and n n 1n 2 d let bbb f q g 1 bbb f q m 1 bbb f q g 2 bbb f q m 2 and text t i denote the trace function from bbb f q m i to bbb f q for i 1 2 we define a cyclic code mathcal c q m n 1 n 2 c a b a in bbb f q m 1 b in bbb f q m 2 where c a b text t 1 ag 1 0 text t 2 bg 2 0 text t 1 ag 1 1 text t 2 bg 2 1 ldots text t 1 ag 1 n 1 text t 2 bg 2 n 1 we mainly use gauss periods to present the weight distribution of the cyclic code mathcal c q m n 1 n 2 as applications we determine the weight distribution of cyclic code mathcal c q m q m 1 1 q m 2 1 with gcd m 1 m 2 1 in particular it is a three weight cyclic code if gcd q 1 m 1 m 2 1 we also explicitly determine the weight distributions of some classes of cyclic codes including several classes of four weight cyclic codes

fast algebraic attacks and decomposition of symmetric boolean functions in this correspondence first we give a decomposition of symmetric boolean functions then we show that almost all symmetric boolean functions including these functions with good algebraic immunity behave badly against fast algebraic attacks besides we improve the relations between algebraic degree and algebraic immunity of symmetric boolean functions

weight distributions of two classes of cyclic codes with respect to two distinct order elements cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms cyclic codes have been studied for many years but their weight distributions are known only for a few cases in this paper let fr be an extension of a finite field fq and r qm we determine the weight distributions of the cyclic codes c c a b a b fr c a b trr q ag10 bg20 trr q ag1n 1 bg2n 1 g1 g2 fr in the following two cases 1 ord g1 n n r 1 and g2 1 and 2 ord g1 n g2 g12 ord g2 n 2 m 2 and 2 r 1 n q 1

constructions of quadratic and cubic rotation symmetric bent functions in this paper we consider constructions of rotation symmetric bent functions which are of the forms fc x i 1m 1 ci j 0n 1 xjxi j cm j 0m 1 xjxm j and ft x i 0n 1 xixt ixm i xixt i i 0m 1 xixm i where n 2m ci 0 1 the subscript u of xu in the previous expressions is taken as u modulo n for each case a necessary and sufficient condition is obtained to the best of our knowledge this class of cubic rotation symmetric bent functions is the first example of an infinite class of nonquadratic rotation symmetric bent functions

planning as satisfiability parallel plans and algorithms for plan search we address two aspects of constructing plans efficiently by means of satisfiability testing efficient encoding of the problem of existence of plans of a given number t of time points in the propositional logic and strategies for finding plans given these formulae for different values of t for the first problem we consider three semantics for plans with parallel operator application in order to make the search for plans more efficient the standard semantics requires that parallel operators are independent and can therefore be executed in any order we consider a more relaxed definition of parallel plans which was first proposed by dimopoulos et al as well as a normal form for parallel plans that requires every operator to be executed as early as possible we formalize the semantics of parallel plans emerging in this setting and present translations of these semantics into the propositional logic the sizes of the translations are asymptotically optimal each of the semantics is constructed in such a way that there is a plan following the semantics exactly when there is a sequential plan and moreover the existence of a parallel plan implies the existence of a sequential plan with as many operators as in the parallel one for the second problem we consider strategies based on testing the satisfiability of several formulae representing plans of n time steps for several values of n concurrently by several processes we show that big efficiency gains can be obtained in comparison to the standard strategy of sequentially testing the satisfiability of formulae for an increasing number of time steps

algebraic immunity for cryptographically significant boolean functions analysis and construction recently algebraic attacks have received a lot of attention in the cryptographic literature it has been observed that a boolean function f used as a cryptographic primitive and interpreted as a multivariate polynomial over f sub 2 should not have low degree multiples obtained by multiplication with low degree nonzero functions in this paper we show that a boolean function having low nonlinearity is also weak against algebraic attacks and we extend this result to higher order nonlinearities next we present enumeration results on linearly independent annihilators we also study certain classes of highly nonlinear resilient boolean functions for their algebraic immunity we identify that functions having low degree subfunctions are weak in terms of algebraic immunity and we analyze some existing constructions from this viewpoint further we present a construction method to generate boolean functions on n variables with highest possible algebraic immunity spl lceil n 2 spl rceil this construction first presented at the 2005 workshop on fast software encryption fse 2005 has been the first one producing such functions these functions are obtained through a doubly indexed recursive relation we calculate their hamming weights and deduce their nonlinearities we show that they have very high algebraic degrees we express them as the sums of two functions which can be obtained from simple symmetric functions by a transformation which can be implemented with an algorithm whose complexity is linear in the number of variables we deduce a very fast way of computing the output to these functions given their input

on the weight distributions of two classes of cyclic codes let q pm where p is an odd prime mges2 and 1lesklesm 1 let tr be the trace mapping from fq to fp and zetap e2pii p be a primitive pth root of unity in this paper we determine the value distribution of the following exponential sums sigmaxisinf qchi alphaxp k 1 betax2 alpha betaisinfq where chi x zetap tr x is the canonical additive character of fq as applications we have the following 1 we determine the weight distribution of the cyclic codes c1 and c2 over fpt with parity check polynomial h2 x h3 x and h1 x h2 x h3 x respectively where t is a divisor of d gcd m k and h1 x h2 x and h3 x are the minimal polynomials of pi 1 pi 2 and pi p k 1 over fpt respectively for a primitive element pi of fq 2 we determine the correlation distribution between two m sequences of period q 1 moreover we find a new class of p ary bent functions this paper extends the results in feng and luo 2008