Search results for "Time complexity"
showing 10 items of 99 documents
Circular sturmian words and Hopcroft’s algorithm
2009
AbstractIn order to analyze some extremal cases of Hopcroft’s algorithm, we investigate the relationships between the combinatorial properties of a circular sturmian word (x) and the run of the algorithm on the cyclic automaton Ax associated to (x). The combinatorial properties of words taken into account make use of sturmian morphisms and give rise to the notion of reduction tree of a circular sturmian word. We prove that the shape of this tree uniquely characterizes the word itself. The properties of the run of Hopcroft’s algorithm are expressed in terms of the derivation tree of the automaton, which is a tree that represents the refinement process that, in the execution of Hopcroft’s alg…
Efficient algorithm for learning simple regular expressions from noisy examples
1994
We present an efficient algorithm for finding approximate repetitions in a given sequence of characters. First, we define a class of simple regular expressions which are of star-height one and do not contain union operations, and a stochastic mutation process of a given length over a string of characters. Then, assuming that a given string of characters is obtained corrupted by the defined mutation process from some long enough word generated by a simple regular expression, we try to restore the expression. We prove that to within some reasonable accuracy it is always possible if the length of the mutation process is bounded comparing to the length of the example. We provide an algorithm by…
Standard Sturmian words and automata minimization algorithms
2015
The study of some close connections between the combinatorial properties of words and the performance of the automata minimization process constitutes the main focus of this paper. These relationships have been, in fact, the basis of the study of the tightness and the extremal cases of Hopcroft's algorithm, that is, up to now, the most efficient minimization method for deterministic finite state automata. Recently, increasing attention has been paid to another minimization method that, unlike the approach proposed by Hopcroft, is not based on refinement of the set of states of the automaton, but on automata operations such as determinization and reverse, and is also applicable to non-determ…
On Extremal Cases of Hopcroft’s Algorithm
2009
In 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 sequences of refinements of the set of the states that lead to the final partition. We find an infinite family of binary automata for which such a process is unique. Some recent papers (cf. [3,7,1]) have been devoted to find families of automata for which Hopcroft’s algorithm has its worst execution time. They are unary automata associated to circular words. However, automata minimization can be achieved also in linear time when the alphabet has only one letter (cf. [14]), so in …
Uncountable classical and quantum complexity classes
2018
It is known that poly-time constant-space quantum Turing machines (QTMs) and logarithmic-space probabilistic Turing machines (PTMs) recognize uncountably many languages with bounded error (A.C. Cem Say and A. Yakaryılmaz, Magic coins are useful for small-space quantum machines. Quant. Inf. Comput. 17 (2017) 1027–1043). In this paper, we investigate more restricted cases for both models to recognize uncountably many languages with bounded error. We show that double logarithmic space is enough for PTMs on unary languages in sweeping reading mode or logarithmic space for one-way head. On unary languages, for quantum models, we obtain middle logarithmic space for counter machines. For binary la…
Impulsively-controlled systems and reverse dwell time: A linear programming approach
2015
We present a receding horizon algorithm that converges to the exact solution in polynomial time for a class of optimal impulse control problems with uniformly distributed impulse instants and governed by so-called reverse dwell time conditions. The cost has two separate terms, one depending on time and the second monotonically decreasing on the state norm. The obtained results have both theoretical and practical relevance. From a theoretical perspective we prove certain geometrical properties of the discrete set of feasible solutions. From a practical standpoint, such properties reduce the computational burden and speed up the search for the optimum thus making the algorithm suitable for th…
On the use of a metric-space search algorithm (AESA) for fast DTW-based recognition of isolated words
1988
The approximating and eliminating search algorithm (AESA) presented was recently introduced for finding nearest neighbors in metric spaces. Although the AESA was originally developed for reducing the time complexity of dynamic time-warping isolated word recognition (DTW-IWR), only rather limited experiments had been previously carried out to check its performance in this task. A set of experiments aimed at filling this gap is reported. The main results show that the important features reflected in previous simulation experiments are also true for real speech samples. With single-speaker dictionaries of up to 200 words, and for most of the different speech parameterizations, local metrics, a…
A polynomial algorithm solving a special class of hybrid optimal control problems
2006
Hybrid optimal control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions [5]. In this paper, we identify a special class of hybrid optimal control problems which are easy to solve. We do this by using a paradigm borrowed from the Operations Research field. As main result, we present a solution algorithm that converges to the exact solution in polynomial time. Our approach consists in approximating the hybrid optimal control problem via an integer-linear programming reformulation. The integer-linear programming problem is a Set-covering one with a totally unimodular constraint matrix and therefore solving the S…
CUDA-Accelerated Alignment of Subsequences in Streamed Time Series Data
2014
Euclidean Distance (ED) and Dynamic Time Warping (DTW) are cornerstones in the field of time series data mining. Many high-level algorithms like kNN-classification, clustering or anomaly detection make excessive use of these distance measures as subroutines. Furthermore, the vast growth of recorded data produced by automated monitoring systems or integrated sensors establishes the need for efficient implementations. In this paper, we introduce linear memory parallelization schemes for the alignment of a given query Q in a stream of time series data S for both ED and DTW using CUDA-enabled accelerators. The ED parallelization features a log-linear calculation scheme in contrast to the naive …
Inducing the Lyndon Array
2019
In this paper we propose a variant of the induced suffix sorting algorithm by Nong (TOIS, 2013) that computes simultaneously the Lyndon array and the suffix array of a text in $O(n)$ time using $\sigma + O(1)$ words of working space, where $n$ is the length of the text and $\sigma$ is the alphabet size. Our result improves the previous best space requirement for linear time computation of the Lyndon array. In fact, all the known linear algorithms for Lyndon array computation use suffix sorting as a preprocessing step and use $O(n)$ words of working space in addition to the Lyndon array and suffix array. Experimental results with real and synthetic datasets show that our algorithm is not onl…