共查询到20条相似文献,搜索用时 62 毫秒
1.
We study the state complexity of certain simple languages. If A is an alphabet of k letters, then a k-language is a nonempty set of words of length k, that is, a uniform language of length k. We show that the minimal state complexity of a k-language is k+2, and the maximal, (kk−1−1)/(k−1)+2k+1. We prove constructively that, for every i between the minimal and maximal bounds, there is a language of state complexity i. We introduce a class of automata accepting sets of words that are permutations of A; these languages define a complete hierarchy of complexities between k2−k+3 and 2k+1. The languages of another class of automata, based on k-ary trees, define a complete hierarchy of complexities between 2k+1 and (kk−1−1)/(k−1)+2k+1. This provides new examples of uniform languages of maximal complexity. 相似文献
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We show how to support efficient back traversal in a unidirectional list, using small memory and with essentially no slowdown in forward steps. Using O(lgn) memory for a list of size n, the i’th back-step from the farthest point reached so far takes O(lgi) time in the worst case, while the overhead per forward step is at most ? for arbitrary small constant ?>0. An arbitrary sequence of forward and back steps is allowed. A full trade-off between memory usage and time per back-step is presented: k vs. kn1/k and vice versa. Our algorithms are based on a novel pebbling technique which moves pebbles on a virtual binary, or n1/k-ary, tree that can only be traversed in a pre-order fashion. 相似文献
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This work is concerned with simulating nondeterministic one-reversal multicounter automata (NCMs) by nondeterministic partially blind multihead finite automata (NFAs). We show that any one-reversal NCM with k counters can be simulated by a partially blind NFA with k blind heads. This provides a nearly complete categorization of the computational power of partially blind automata, showing that the power of a (k+1)-NFA lies between that of a k-NCM and a (k+1)-NCM. 相似文献
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A. Abouelaoualim K.Ch. Das L. Faria Y. Manoussakis C. Martinhon R. Saad 《Theoretical computer science》2008
This paper deals with the existence and search for properly edge-colored paths/trails between two, not necessarily distinct, vertices s and t in an edge-colored graph from an algorithmic perspective. First we show that several versions of the s−t path/trail problem have polynomial solutions including the shortest path/trail case. We give polynomial algorithms for finding a longest properly edge-colored path/trail between s and t for a particular class of graphs and characterize edge-colored graphs without properly edge-colored closed trails. Next, we prove that deciding whether there exist k pairwise vertex/edge disjoint properly edge-colored s−t paths/trails in a c-edge-colored graph Gc is NP-complete even for k=2 and c=Ω(n2), where n denotes the number of vertices in Gc. Moreover, we prove that these problems remain NP-complete for c-edge-colored graphs containing no properly edge-colored cycles and c=Ω(n). We obtain some approximation results for those maximization problems together with polynomial results for some particular classes of edge-colored graphs. 相似文献
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The claw finding problem has been studied in terms of query complexity as one of the problems closely connected to cryptography. Given two functions, f and g, with domain sizes N and M(N≤M), respectively, and the same range, the goal of the problem is to find x and y such that f(x)=g(y). This problem has been considered in both quantum and classical settings in terms of query complexity. This paper describes an optimal algorithm that uses quantum walk to solve this problem. Our algorithm can be slightly modified to solve the more general problem of finding a tuple consisting of elements in the two function domains that has a prespecified property. It can also be generalized to find a claw of k functions for any constant integer k>1, where the domain sizes of the functions may be different. 相似文献
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Given a digraph D, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in D an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree 0. We prove that MinLOB is polynomial-time solvable for acyclic digraphs. In general, MinLOB is NP-hard and we consider three parameterizations of MinLOB. We prove that two of them are NP-complete for every value of the parameter, but the third one is fixed-parameter tractable (FPT). The FPT parameterization is as follows: given a digraph D of order n and a positive integral parameter k, check whether D contains an out-branching with at most n−k leaves (and find such an out-branching if it exists). We find a problem kernel of order O(k2) and construct an algorithm of running time O(2O(klogk)+n6), which is an ‘additive’ FPT algorithm. We also consider transformations from two related problems, the minimum path covering and the maximum internal out-tree problems into MinLOB, which imply that some parameterizations of the two problems are FPT as well. 相似文献
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This paper concerns construction of additive stretched spanners with few edges for n-vertex graphs having a tree-decomposition into bags of diameter at most δ, i.e., the tree-length δ graphs. For such graphs we construct additive 2δ-spanners with O(δn+nlogn) edges, and additive 4δ-spanners with O(δn) edges. This provides new upper bounds for chordal graphs for which δ=1. We also show a lower bound, and prove that there are graphs of tree-length δ for which every multiplicative δ-spanner (and thus every additive (δ−1)-spanner) requires Ω(n1+1/Θ(δ)) edges. 相似文献
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Matroid theory gives us powerful techniques for understanding combinatorial optimization problems and for designing polynomial-time algorithms. However, several natural matroid problems, such as 3-matroid intersection, are NP-hard. Here we investigate these problems from the parameterized complexity point of view: instead of the trivial nO(k) time brute force algorithm for finding a k-element solution, we try to give algorithms with uniformly polynomial (i.e., f(k)⋅nO(1)) running time. The main result is that if the ground set of a represented linear matroid is partitioned into blocks of size ?, then we can determine in randomized time f(k,?)⋅nO(1) whether there is an independent set that is the union of k blocks. As a consequence, algorithms with similar running time are obtained for other problems such as finding a k-element set in the intersection of ? matroids, or finding k terminals in a network such that each of them can be connected simultaneously to the source by ? disjoint paths. 相似文献
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Let F(x,y) be a polynomial over a field K and m a nonnegative integer. We call a polynomial g over K an m-near solution of F(x,y) if there exists a c∈K such that F(x,g)=cxm, and the number c is called an m-value of F(x,y) corresponding to g. In particular, c can be 0. Hence, by viewing F(x,y)=0 as a polynomial equation over K[x] with variable y, every solution of the equation F(x,y)=0 in K[x] is also an m-near solution. We provide an algorithm that gives all m-near solutions of a given polynomial F(x,y) over K, and this algorithm is polynomial time reducible to solving one variable equations over K. We introduce approximate solutions to analyze the algorithm. We also give some interesting properties of approximate solutions. 相似文献
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We investigate the group key management problem for broadcasting applications. Previous work showed that, in handling key updates, batch rekeying can be more cost effective than individual rekeying. One model for batch rekeying is to assume that every user has probability p of being replaced by a new user during a batch period with the total number of users unchanged. Under this model, it was recently shown that an optimal key tree can be constructed in linear time when p is a constant and in O(n4) time when p→0. In this paper, we investigate more efficient algorithms for the case p→0, i.e., when membership changes are sparse. We design an O(n) heuristic algorithm for the sparse case and show that it produces a nearly 2-approximation to the optimal key tree. Simulation results show that its performance is even better in practice. We also design a refined heuristic algorithm and show that it achieves an approximation ratio of 1+? for any fixed ?>0 and n, as p→0. Finally, we give another approximation algorithm for any p∈(0,0.693) which is shown to be quite good by our simulations. 相似文献
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A real x is called h-bounded computable , for some function h:N→N, if there is a computable sequence (xs) of rational numbers which converges to x such that, for any n∈N, at most h(n) non-overlapping pairs of its members are separated by a distance larger than 2-n. In this paper we discuss properties of h-bounded computable reals for various functions h. We will show a simple sufficient condition for a class of functions h such that the corresponding h-bounded computable reals form an algebraic field. A hierarchy theorem for h-bounded computable reals is also shown. Besides we compare semi-computability and weak computability with the h-bounded computability for special functions h. 相似文献
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We prove an explicit bound on the radius of a ball centered at the origin which is guaranteed to contain all bounded connected components of a semi-algebraic set S⊂Rk defined by a weak sign condition involving s polynomials in Z[X1,…,Xk] having degrees at most d, and whose coefficients have bitsizes at most τ. Our bound is an explicit function of s,d,k and τ, and does not contain any undetermined constants. We also prove a similar bound on the radius of a ball guaranteed to intersect every connected component of S (including the unbounded components). While asymptotic bounds of the form 2τdO(k) on these quantities were known before, some applications require bounds which are explicit and which hold for all values of s,d,k and τ. The bounds proved in this paper are of this nature. 相似文献
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The focus of the present paper is on providing a local deterministic algorithm for colouring the edges of Yao-like subgraphs of Unit Disk Graphs. These are geometric graphs such that for some positive integers l,k the following property holds at each node v: if we partition the unit circle centered at v into 2k equally sized wedges then each wedge can contain at most l points different from v. We assume that the nodes are location aware, i.e. they know their Cartesian coordinates in the plane. The algorithm presented is local in the sense that each node can receive information emanating only from nodes which are at most a constant (depending on k and l, but not on the size of the graph) number of hops (measured in the original underlying Unit Disk Graph) away from it, and hence the algorithm terminates in a constant number of steps. The number of colours used is 2kl+1 and this is optimal for local algorithms (since the maximal degree is 2kl and a colouring with 2kl colours can only be constructed by a global algorithm), thus showing that in this class of graphs the price for locality is only one additional colour. 相似文献
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We present algorithmic lower bounds on the size sd of the largest independent sets of vertices in random d-regular graphs, for each fixed d≥3. For instance, for d=3 we prove that, for graphs on n vertices, sd≥0.43475n with probability approaching one as n tends to infinity. 相似文献
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The replication number of a branching program is the minimum number R such that along every accepting computation at most R variables are tested more than once; the sets of variables re-tested along different computations may be different. For every branching program, this number lies between 0 (read-once programs) and the total number n of variables (general branching programs). The best results so far were exponential lower bounds on the size of branching programs with R=o(n/logn). We improve this to R≤?n for a constant ?>0. This also gives an alternative and simpler proof of an exponential lower bound for (1+?)n time branching programs for a constant ?>0. We prove these lower bounds for quadratic functions of Ramanujan graphs. 相似文献
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We define a self-map Pal:F2→F2 of the free group on two generators a,b, using automorphisms of F2 that form a group isomorphic to the braid group B3. The map Pal restricts to de Luca’s right iterated palindromic closure on the submonoid generated by a,b. We show that Pal is continuous for the profinite topology on F2; it is the unique continuous extension of de Luca’s right iterated palindromic closure to F2. The values of Pal are palindromes and coincide with the elements g∈F2 such that abg and bag are conjugate. 相似文献
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We prove that a polynomial f∈R[x,y] with t non-zero terms, restricted to a real line y=ax+b, either has at most 6t−4 zeros or vanishes over the whole line. As a consequence, we derive an alternative algorithm for deciding whether a linear polynomial y−ax−b∈K[x,y] divides a lacunary polynomial f∈K[x,y], where K is a real number field. The number of bit operations performed by the algorithm is polynomial in the number of non-zero terms of f, in the logarithm of the degree of f, in the degree of the extension K/Q and in the logarithmic height of a, b and f. 相似文献