Search results for "A* algorithm"
showing 10 items of 2538 documents
Nondeterministic operations on finite relational structures
1998
Abstract This article builds on a tutorial introduction to universal algebra for language theory (Courcelle, Theoret. Comput. Sci. 163 (1996) 1–54) and extends it in two directions. First, nondeterministic operations are considered, i.e., operations which give a set of results instead of a single one. Most of their properties concerning recognizability and equational definability carry over from the ordinary case with minor modifications. Second, inductive sets of evaluations are studied in greater detail. It seems that they are handled most naturally in the framework presented here. We consider the analogues of top-down and bottom-up tree transducers. Again, most of their closure propertie…
On extremal cases of Hopcroft’s algorithm
2010
AbstractIn this paper we consider the problem of minimization of deterministic finite automata (DFA) with reference to Hopcroft’s algorithm. Hopcroft’s algorithm has several degrees of freedom, so there can exist different executions that can lead to different sequences of refinements of the set of the states up to the final partition. We find an infinite family of binary automata for which such a process is unique, whatever strategy is chosen. Some recent papers (cf. Berstel and Carton (2004) [3], Castiglione et al. (2008) [6] and Berstel et al. (2009) [1]) have been devoted to find families of automata for which Hopcroft’s algorithm has its worst execution time. They are unary automata as…
Superiority Of One-Way And Realtime Quantum Machines
2012
In automata theory, quantum computation has been widely examined for finite state machines, known as quantum finite automata (QFAs), and less attention has been given to QFAs augmented with counters or stacks. In this paper, we focus on such generalizations of QFAs where the input head operates in one-way or realtime mode, and present some new results regarding their superiority over their classical counterparts. Our first result is about the nondeterministic acceptance mode: Each quantum model architecturally intermediate between realtime finite state automaton and one-way pushdown automaton (one-way finite automaton, realtime and one-way finite automata with one-counter, and realtime push…
A Graph Based Algorithm For Intersection Of Subdivision Surfaces
2003
Computing surface intersections is a fundamental problem in geometric modeling. Any boolean operation can be seen as an intersection calculation followed by a selection of the parts necessary for building the surface of the resulting object. A robust and efficient algorithm to compute intersection on subdivision surfaces (surfaces generated by the Loop scheme) is proposed here. This algorithm relies on the concept of a bipartite graph which allows the reduction of the number of faces intersection tests. Intersection computations are accelerated by the use of the bipartite graph and the neighborhood of intersecting faces at a given level of subdivision to deduce intersecting faces at the fol…
Machine-Independent Characterizations and Complete Problems for Deterministic Linear Time
2002
This article presents two algebraic characterizations and two related complete problems for the complexity class DLIN that was introduced in [E. Grandjean, Ann. Math. Artif. Intell., 16 (1996), pp. 183--236]. DLIN is essentially the class of all functions that can be computed in linear time on a Random Access Machine which uses only numbers of linear value during its computations. The algebraic characterizations are in terms of recursion schemes that define unary functions. One of these schemes defines several functions simultaneously, while the other one defines only one function. From the algebraic characterizations, we derive two complete problems for DLIN under new, very strict, and mac…
On the hardness of optimization in power-law graphs
2008
Our motivation for this work is the remarkable discovery that many large-scale real-world graphs ranging from Internet and World Wide Web to social and biological networks appear to exhibit a power-law distribution: the number of nodes y"i of a given degree i is proportional to i^-^@b where @b>0 is a constant that depends on the application domain. There is practical evidence that combinatorial optimization in power-law graphs is easier than in general graphs, prompting the basic theoretical question: Is combinatorial optimization in power-law graphs easy? Does the answer depend on the power-law exponent @b? Our main result is the proof that many classical NP-hard graph-theoretic optimizati…
Bounds for minimum feedback vertex sets in distance graphs and circulant graphs
2008
Graphs and Algorithms
Computing the Probability for Data Loss in Two-Dimensional Parity RAIDs
2017
Parity RAIDs are used to protect storage systems against disk failures. The idea is to add redundancy to the system by storing the parity of subsets of disks on extra parity disks. A simple two-dimensional scheme is the one in which the data disks are arranged in a rectangular grid, and every row and column is extended by one disk which stores the parity of it.In this paper we describe several two-dimensional parity RAIDs and analyse, for each of them, the probability for dataloss given that f random disks fail. This probability can be used to determine the overall probability using the model of Hafner and Rao. We reduce subsets of the forest counting problem to the different cases and show…
Nondeterministic Unitary OBDDs
2017
We investigate the width complexity of nondeterministic unitary OBDDs (NUOBDDs). Firstly, we present a generic lower bound on their widths based on the size of strong 1-fooling sets. Then, we present classically “cheap” functions that are “expensive” for NUOBDDs and vice versa by improving the previous gap. We also present a function for which neither classical nor unitary nondeterminism does help. Moreover, based on our results, we present a width hierarchy for NUOBDDs. Lastly, we provide the bounds on the widths of NUOBDDs for the basic Boolean operations negation, union, and intersection.
Very Narrow Quantum OBDDs and Width Hierarchies for Classical OBDDs
2014
In the paper we investigate a model for computing of Boolean functions – Ordered Binary Decision Diagrams (OBDDs), which is a restricted version of Branching Programs. We present several results on the comparative complexity for several variants of OBDD models. We present some results on the comparative complexity of classical and quantum OBDDs. We consider a partial function depending on a parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2, but any classical OBDD (deterministic or stable bounded-error probabilistic) needs width 2 k + 1. We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient …