Search results for "Automaton"
showing 10 items of 257 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…
Improved Constructions of Quantum Automata
2008
We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use $\frac{4}{\epsilon} \log 2p + O(1)$ states to recognize a language that requires p states classically. The construction is both substantially simpler and achieves a better constant in the front of logp than the previously known construction of [2]. Similarly to [2], our construction is by a probabilistic argument. We consider the possibility to derandomize it and present some preliminary results in this direction.
The Minimum Amount of Useful Space: New Results and New Directions
2014
We consider minimal space requirements when using memory with restricted access policy (pushdown - hence giving pushdown automata (PDAs), and counter - hence giving counter automata (CAs)) in connection with two-way and realtime head motion. The main results are that: (i) loglogn is a tight space lower bound for accepting general nonregular languages on weak realtime PDAs, (ii) there exist unary nonregular languages accepted by realtime alternating CAs within weak logn space, (iii) there exist nonregular languages accepted by two-way DPADs within strong loglogn space, and, (iv) there exist unary nonregular languages accepted by two-way CAs with quantum and classical states within middle log…
Running time to recognize nonregular languages by 2-way probabilistic automata
1991
R. Freivalds proved that the language {0m1m} can be recognized by 2-way probabilistic finite automata (2pfa) with arbitrarily high probability 1-ɛ. A.G.Greenberg and A.Weiss proved that no 2pfa can recognize this language in expected time \(T(n) = c^\circ{(n)}\). For arbitrary languages C.Dwork and L.Stockmeyer showed somewhat less: if a language L is recognized by a 2pfa in expected time \(T(n) = c^{n^\circ{(1)} }\), then L is regular. First, we improve this theorem replacing the expected time by the time with probability 1-ɛ. On the other hand, time bound by C.Dwork and L.Stockmeyer cannot be improved: for arbitrary k≥2 we exhibit a specific nonregular language that can be recognized by 2…
A generalization of Sardinas and Patterson's algorithm to z-codes
1993
Abstract This paper concerns the framework of z-codes theory. The main contribution consists in an extension of the algorithm of Sardinas and Patterson for deciding whether a finite set of words X is a z-code. To improve the efficiency of this test we have found a tight upper bound on the length of the shortest words that might have a double z-factorization over X. Some remarks on the complexity of the algorithm are also given. Moreover, a slight modification of this algorithm allows us to compute the z-deciphering delay of X.
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…
Codification schemes and finite automata
2000
This paper is a note on how Information Theory and Codification Theory are helpful in the computational design both of communication protocols and strategy sets in the framework of finitely repeated games played by boundedly rational agents. More precisely, we show the usefulness of both theories to improve the existing automata bounds of Neyman¿s (1998) work on finitely repeated games played by finite automata.
Learning Automata-based Misinformation Mitigation via Hawkes Processes
2021
AbstractMitigating misinformation on social media is an unresolved challenge, particularly because of the complexity of information dissemination. To this end, Multivariate Hawkes Processes (MHP) have become a fundamental tool because they model social network dynamics, which facilitates execution and evaluation of mitigation policies. In this paper, we propose a novel light-weight intervention-based misinformation mitigation framework using decentralized Learning Automata (LA) to control the MHP. Each automaton is associated with a single user and learns to what degree that user should be involved in the mitigation strategy by interacting with a corresponding MHP, and performing a joint ra…
Representation of NURBS surfaces by Controlled Iterated Functions System automata
2019
Iterated Function Systems (IFS) are a standard tool to generate fractal shapes. In a more general way, they can represent most of standard surfaces like Bézier or B-Spline surfaces known as self-similar surfaces. Controlled Iterated Function Systems (CIFS) are an extension of IFS based on automata. CIFS are basically multi-states IFS, they can handle all IFS shapes but can also manage multi self-similar shapes. For example CIFS can describe subdivision surfaces around extraordinary vertices whereas IFS cannot. Having a common CIFS formalism facilitates the development of generic methods to manage interactions (junctions, differences...) between objects of different natures.This work focuses…
A Fast Algorithm Finding the Shortest Reset Words
2013
In this paper we present a new fast algorithm for finding minimal reset words for finite synchronizing automata, which is a problem appearing in many practical applications. The problem is known to be computationally hard, so our algorithm is exponential in the worst case, but it is faster than the algorithms used so far and it performs well on average. The main idea is to use a bidirectional BFS and radix (Patricia) tries to store and compare subsets. Also a number of heuristics are applied. We give both theoretical and practical arguments showing that the effective branching factor is considerably reduced. As a practical test we perform an experimental study of the length of the shortest …