Search results for "complexi"
showing 10 items of 1116 documents
Pattern Matching and Pattern Discovery Algorithms for Protein Topologies
2001
We describe algorithms for pattern-matching and pattern-learning in TOPS diagrams (formal descriptions of protein topologies). These problems can be reduced to checking for subgraph isomorphism and finding maximal common subgraphs in a restricted class of ordered graphs. We have developed a subgraph isomorphism algorithm for ordered graphs, which performs well on the given set of data. The maximal common subgraph problem then is solved by repeated subgraph extension and checking for isomorphisms. Despite its apparent inefficiency, this approach yields an algorithm with time complexity proportional to the number of graphs in the input set and is still practical on the given set of data. As a…
On the decision problem for the guarded fragment with transitivity
2002
The guarded fragment with transitive guards, [GF+TG], is an extension of GF in which certain relations are required to be transitive, transitive predicate letters appear only in guards of the quantifiers and the equality symbol may appear everywhere. We prove that the decision problem for [GF+TG] is decidable. This answers the question posed in (Ganzinger et al., 1999). Moreover, we show that the problem is 2EXPTIME-complete. This result is optimal since the satisfiability problem for GF is 2EXPTIME-complete (Gradel, 1999). We also show that the satisfiability problem for two-variable [GF+TG] is NEXPTIME-hard in contrast to GF with bounded number of variables for which the satisfiability pr…
On the Finite Satisfiability Problem for the Guarded Fragment with Transitivity
2005
We study the finite satisfiability problem for the guarded fragment with transitivity. We prove that in case of one transitive predicate the problem is decidable and its complexity is the same as the general satisfiability problem, i.e. 2Exptime-complete. We also show that finite models for sentences of GF with more transitive predicate letters used only in guards have essentially different properties than infinite ones.
Words and forbidden factors
2002
AbstractGiven a finite or infinite word v, we consider the set M(v) of minimal forbidden factors of v. We show that the set M(v) is of fundamental importance in determining the structure of the word v. In the case of a finite word w we consider two parameters that are related to the size of M(w): the first counts the minimal forbidden factors of w and the second gives the length of the longest minimal forbidden factor of w. We derive sharp upper and lower bounds for both parameters. We prove also that the second parameter is related to the minimal period of the word w. We are further interested to the algorithmic point of view. Indeed, we design linear time algorithm for the following two p…
Two shortest path metrics on well-formed parentheses strings
1996
We present an analysis of two transformations on well-formed parentheses strings. Using a lattice approach, the corresponding least-move distances are computable, the first in linear time and the second in quadratic time.
Quantum Query Complexity for Some Graph Problems
2004
The paper [4] by H. Buhrman and R. de Wolf contains an impressive survey of solved and open problems in quantum query complexity, including many graph problems. We use recent results by A.Ambainis [1] to prove higher lower bounds for some of these problems. Some of our new lower bounds do not close the gap between the best upper and lower bounds. We prove in these cases that it is impossible to provide a better application of Ambainis’ technique for these problems.
Forbidden Factors and Fragment Assembly
2001
In this paper methods and results related to the notion of minimal forbidden words are applied to the fragment assembly problem. The fragment assembly problem can be formulated, in its simplest form, as follows: reconstruct a word w from a given set I of substrings (fragments ) of a word w . We introduce an hypothesis involving the set of fragments I and the maximal length m(w) of the minimal forbidden factors of w . Such hypothesis allows us to reconstruct uniquely the word w from the set I in linear time. We prove also that, if w is a word randomly generated by a memoryless source with identical symbol probabilities, m(w) is logarithmic with respect to the size of w . This result shows th…
O(n 2 log n) Time On-Line Construction of Two-Dimensional Suffix Trees
2005
The two-dimensional suffix tree of an n × n square matrix A is a compacted trie that represents all square submatrices of Ai¾?[9]. For the off-line case, i.e., A is given in advance to the algorithm, it is known how to build it in optimal time, for any type of alphabet sizei¾?[9,15]. Motivated by applications in Image Compressioni¾?[18], Giancarlo and Guaianai¾?[12] considered the on-line version of the two-dimensional suffix tree and presented an On2log2n-time algorithm, which we refer to as GG. That algorithm is a non-trivial generalization of Ukkonen's on-line algorithm for standard suffix trees [19]. The main contribution in this paper is an Olog n factor improvement in the time complex…
Entropic Profiles, Maximal Motifs and the Discovery of Significant Repetitions in Genomic Sequences
2014
The degree of predictability of a sequence can be measured by its entropy and it is closely related to its repetitiveness and compressibility. Entropic profiles are useful tools to study the under- and over-representation of subsequences, providing also information about the scale of each conserved DNA region. On the other hand, compact classes of repetitive motifs, such as maximal motifs, have been proved to be useful for the identification of significant repetitions and for the compression of biological sequences. In this paper we show that there is a relationship between entropic profiles and maximal motifs, and in particular we prove that the former are a subset of the latter. As a furt…
Quantum Identification of Boolean Oracles
2004
The oracle identification problem (OIP) is, given a set S of M Boolean oracles out of 2 N ones, to determine which oracle in S is the current black-box oracle. We can exploit the information that candidates of the current oracle is restricted to S. The OIP contains several concrete problems such as the original Grover search and the Bernstein-Vazirani problem. Our interest is in the quantum query complexity, for which we present several upper bounds. They are quite general and mostly optimal: (i) The query complexity of OIP is \(O(\sqrt{N {\rm log} M {\rm log} N}{\rm log log} M)\) for anyS such that M = |S| > N, which is better than the obvious bound N if M \(< 2^{N/log^3 N}\). (ii) It is \…