Search results for " automata"
showing 10 items of 436 documents
Ambainis-Freivalds’ Algorithm for Measure-Once Automata
2001
An algorithm given by Ambainis and Freivalds [1] constructs a quantum finite automaton (QFA) with O(log p) states recognizing the language Lp = {ai| i is divisible by p} with probability 1 - Ɛ , for any Ɛ > 0 and arbitrary prime p. In [4] we gave examples showing that the algorithm is applicable also to quantum automata of very limited size. However, the Ambainis-Freivalds algoritm is tailored to constructing a measure-many QFA (defined by Kondacs andWatrous [2]), which cannot be implemented on existing quantum computers. In this paper we modify the algorithm to construct a measure-once QFA of Moore and Crutchfield [3] and give examples of parameters for this automaton. We show for the lang…
The Average State Complexity of the Star of a Finite Set of Words Is Linear
2008
We prove that, for the uniform distribution over all sets Xof m(that is a fixed integer) non-empty words whose sum of lengths is n, $\mathcal{D}_X$, one of the usual deterministic automata recognizing X*, has on average $\mathcal{O}(n)$ states and that the average state complexity of X*is i¾?(n). We also show that the average time complexity of the computation of the automaton $\mathcal{D}_X$ is $\mathcal{O}(n\log n)$, when the alphabet is of size at least three.
Achieving Intelligent Traffic-aware Consolidation of Virtual Machines in a Data Center Using Learning Automata
2016
Cloud Computing (CC) is becoming increasingly pertinent and popular. A natural consequence of this is that many modern-day data centers experience very high internal traffic within the data centers themselves. The VMs with high mutual traffic often end up being far apart in the data center network, forcing them to communicate over unnecessarily long distances. The consequent traffic bottlenecks negatively affect both the performance of the application and the network in its entirety, posing nontrivial challenges for the administrators of these cloudbased data centers. The problem can, quite naturally, be compartmentalized into two phases which follow each other. First of all, the VMs are co…
Suffix Automata and Standard Sturmian Words
2007
Blumer et al. showed (cf. [3,2]) that the suffix automaton of a word w must have at least |w|+1 states and at most 2|w|-1 states. In this paper we characterize the language L of all binary words w whose minimal suffix automaton S(w) has exactly |w| + 1 states; they are precisely all prefixes of standard Sturmian words. In particular, we give an explicit construction of suffix automaton of words that are palindromic prefixes of standard words. Moreover, we establish a necessary and sufficient condition on S(w) which ensures that if w ∈ L and a ∈ {0, 1} then wa ∈ L. By using such a condition, we show how to construct the automaton S(wa) from S(w). More generally, we provide a simple construct…
One Alternation Can Be More Powerful Than Randomization in Small and Fast Two-Way Finite Automata
2013
We show a family of languages that can be recognized by a family of linear-size alternating one-way finite automata with one alternation but cannot be recognized by any family of polynomial-size bounded-error two-way probabilistic finite automata with the expected runtime bounded by a polynomial. In terms of finite automata complexity theory this means that neither 1Σ2 nor 1Π2 is contained in 2P2.
On achieving intelligent traffic-aware consolidation of virtual machines in a data center using Learning Automata
2018
Unlike the computational mechanisms of the past many decades, that involved individual (extremely powerful) computers or clusters of machines, cloud computing (CC) is becoming increasingly pertinent and popular. Computing resources such as CPU and storage are becoming cheaper, and the servers themselves are becoming more powerful. This enables clouds to host more virtual machines (VMs). A natural consequence ofthis is that many modern-day data centers experience very high internaltraffic within the data centers themselves. This is, of course, due to the occurrence of servers that belong to the same tenant, communicating between themselves. The problem is accentuated when the VM deployment t…
Alignment-free sequence comparison using absent words
2018
Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realised by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free techniques, which are based on measures referring to the composition of sequences in terms of their constituent patterns. These measures, such as $q$-gram distance, are usually computed in time linear with respect to the length of the sequences. In this paper, we focus on the complementary idea: how two sequences can be efficiently compared based on information that does not occur in the sequences. A word is an {\em absent word} of some sequence if it does not oc…
Probabilities to Accept Languages by Quantum Finite Automata
1999
We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the hierarchy. These probabilities converge to 1/2.
Higher-Fidelity Frugal and Accurate Quantile Estimation Using a Novel Incremental <italic>Discretized</italic> Paradigm
2018
Traditional pattern classification works with the moments of the distributions of the features and involves the estimation of the means and variances. As opposed to this, more recently, research has indicated the power of using the quantiles of the distributions because they are more robust and applicable for non-parametric methods. The estimation of the quantiles is even more pertinent when one is mining data streams. However, the complexity of quantile estimation is much higher than the corresponding estimation of the mean and variance, and this increased complexity is more relevant as the size of the data increases. Clearly, in the context of infinite data streams, a computational and sp…
ON-LINE CONSTRUCTION OF A SMALL AUTOMATON FOR A FINITE SET OF WORDS
2012
In this paper we describe a "light" algorithm for the on-line construction of a small automaton recognising a finite set of words. The algorithm runs in linear time. We carried out good experimental results on real dictionaries, on biological sequences and on the sets of suffixes (resp. factors) of a set of words that shows how our automaton is near to the minimal one. For the suffixes of a text, we propose a modified construction that leads to an even smaller automaton. We moreover construct linear algorithms for the insertion and deletion of a word in a finite set, directly from the constructed automaton.