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Finite-state independence [article]

Verónica Becher and Olivier Carton and Pablo Ariel Heiber
2017 arXiv   pre-print
In this work we introduce a notion of independence based on finite-state automata: two infinite words are independent if no one helps to compress the other using one-to-one finite-state transducers with  ...  We prove that, as expected, the set of independent pairs of infinite words has Lebesgue measure 1. We show that the join of two independent normal words is normal.  ...  Introduction In this work we introduce a notion of independence for pairs of infinite words, based on finite-state automata. We call it finite-state independence.  ... 
arXiv:1611.03921v2 fatcat:wiq24fiwuzarbk7jtt7mg4slfa

Finite-state Independence and Normal Sequences [article]

Nicolás Álvarez, Verónica Becher, Olivier Carton
2018 arXiv   pre-print
We consider the previously defined notion of finite-state independence and we focus specifically on normal words.  ...  Based on one of the characterizations we give an algorithm to construct a pair of finite-state independent normal words.  ...  We show that if x and y ′ are not finite-state independent, then x and y are also not finite-state independent. We suppose that x and y ′ are not finite-state independent.  ... 
arXiv:1702.00320v2 fatcat:4poybtxii5bljpexg4xpy7jylq

Language Independent Text Correction using Finite State Automata

Ahmed Hassan Awadallah, Sara Noeman, Hany Hassan
2008 International Joint Conference on Natural Language Processing  
In this work, we introduce a novel approach for automatic correction of spelling mistakes by deploying finite state automata to propose candidates corrections within a specified edit distance from the  ...  The proposed approach is language independent and requires only a dictionary and text data for building a language model.  ...  All the words are represented by a finite state machine automaton.  ... 
dblp:conf/ijcnlp/HassanNH08 fatcat:i5pk6a5w4valvazulucklyy4hm

Independence of work and entropy for equal energetic finite quantum systems: Passive state energy as an entanglement quantifier [article]

Mir Alimuddin, Tamal Guha, Preeti Parashar
2019 arXiv   pre-print
However, for the finite quantum systems, the relation is not so linear and requires detail investigation.  ...  So ergotropy (work extraction from a closed system by unitary), min free energy F_0 (single shot work extraction in the presence of bath) and entropy, all become independent monotones under this process  ...  Example2: Order of single shot work and entropy Let ρ ≡ ( Figure 2 . 2 Independence of work and entropy on the finite EE states: Let ρ → σ under EP O (i.e., ρ σ).  ... 
arXiv:1912.09780v1 fatcat:ruavos4tlnebdkkrwc2niipr6e

An effected process on finite statistical fluctuation analysis for decoy-state measurement device-independent quantum key distribution [article]

Su-Tong Shi, Fen-Zhuo Guo
2016 arXiv   pre-print
In this paper, we consider the decoy-state Measurement-Device-Independent Quantum key distribution (MDI-QKD) with four intensities.  ...  The average value of successful events and bit errors among the pulse pair set be used to investigate the successful events of different pulses under the statistical fluctuation caused by the finite condition  ...  All elements in L i are independent and identical. Single-photon detection In any real experimental setup, the total pulses sent by both sides are finite.  ... 
arXiv:1610.04311v2 fatcat:bedlmh56pjfg5exs7n4kf5jj44

Testing from semi-independent communicating finite state machines with a slow environment

R.M. Hierons
1997 IEE Proceedings - Software Engineering  
doi:10.1049/ip-sen:19971789 fatcat:gtnw4ycz5fa5hgdngqiptgzsim

Biased decoy-state measurement-device-independent quantum key distribution with finite resources

Chun Zhou, Wan-Su Bao, Hai-long Zhang, Hong-Wei Li, Yang Wang, Yuan Li, Xiang Wang
2015 Physical Review A. Atomic, Molecular, and Optical Physics  
or 1) stands for the encoding of the state.  ...  Interestingly, partial noise-tolerance property is achieved with an acceptable loss of justice correctness when N is set finite.  ... 
doi:10.1103/physreva.91.022313 fatcat:6uab2cbjnbbkdntz6tkdw5tq3i

On Finite Groups With Two Independent Generators: I

J. Douglas
1951 Proceedings of the National Academy of Sciences of the United States of America  
"Independent" means that AXBY = A"B" implies AX ' AU,BY-= B", i.e., x u (mod m), y = v (mod n).  ...  Using the cancellatiQn law of groups, and the independence of A and B, we can prove that 0(x) =-0(y) (mod m) only of xy (mod m).  ... 
doi:10.1073/pnas.37.9.604 pmid:16589020 pmcid:PMC1063428 fatcat:xabq2p4lq5cxfkbrqqu6qrohpu

Sets of Independent Generators of a Finite Group

G. A. Miller
1937 Proceedings of the National Academy of Sciences of the United States of America  
The number of operators in a set of independent generators of G can obviously not exceed the number of the distinct prime factors which divide the order of G and when G has a set of independent generators  ...  A set of independent generators of a group G is a set of operators of G such that they generate G but that no subset of these operators generates G.  ...  SETS OF INDEPENDENT GENERATORS OF A FINITE GROUP A set of independent generators of a group G is a set of operators of G such that they generate G but that no subset of these operators generates G.  ... 
doi:10.1073/pnas.23.9.494 pmid:16577802 pmcid:PMC1076973 fatcat:adtnokca7jbnhokvyq5mdgu5lu

On Finite Groups with Two Independent Generators: II

J. Douglas
1951 Proceedings of the National Academy of Sciences of the United States of America  
Resolution of r: r, rF, r2, r3, with defining substitutions as stated.  ...  Also, A1, B1 are independent, From these formulas we infer THEOREM XXVII.  ... 
doi:10.1073/pnas.37.10.677 pmid:16578401 pmcid:PMC1063445 fatcat:tbgflipsc5bbhnf5p6p4nzzupi

On Finite Groups with Two Independent Generators: IV. Conjugate Substitutions

J. Douglas
1951 Proceedings of the National Academy of Sciences of the United States of America  
A paper, covering some aspects of this work, with the title "On Finite Groups with Two Independent Generators," was read before the Academy, November 7, 1951. 1 See Note I, §2.  ...  This state of affairs applies generally [see (20.4, 8)], so that the first row, corresponding to 0 _ x < s, determines the entire table.  ... 
doi:10.1073/pnas.37.12.808 pmid:16589033 pmcid:PMC1063476 fatcat:nsrjqzvfk5ewdhxx5yiqvqyaqa

On Finite Groups With Two Independent Generators: III. Exponential Substitutions

J. Douglas
1951 Proceedings of the National Academy of Sciences of the United States of America  
As has been stated, in order that (P = 01, r must be equal to n.  ...  Values of A congruent mod pEK give values of a that are congruent mod dEK = dB = u; this is the reason that, as stated, M may be restricted to the values 0 _ M < pE.  ... 
doi:10.1073/pnas.37.11.749 pmid:16578415 pmcid:PMC1063463 fatcat:f64bhbcuozg3bhqsnu3b7haub4

Number-Right, Item-Response, and Finite-State Scoring: Robustness with Respect to Lack of Equally Classifiable Options and Item Option Independence

W. Todd Rogers, Joyce Ndalichako
2000 Educational and Psychological Measurement  
Comparing 12 finite state models of examinee performance on multiple-choice tests. Dissertation Abstracts International, 53(4), 1137. (Doctoral dissertation, Virginia Polytechnic and State University)  ...  Finite state polynomic item characteristic curves. British Journal of Mathematical and Statistical Psychology, 44, 45-75. Glass, G. V, & Hopkins, K. D. (1996).  ... 
doi:10.1177/00131640021970330 fatcat:mhacbw25gjho7oh7bmlleb767m

Independent Unbiased Coin Flips From A Correlated Biased Source: A Finite State Markov Chain

M. Blum
25th Annual Symposium onFoundations of Computer Science, 1984.  
Two algorithms A and B use the simple von Neumann trick on every state of the Markov chain. They differ in the time they choose to announce the coin flip. This timing is crucial.  ...  gives an algorithm to generate an independent unbiased sequence of Hs and Ts that nearly achieves the Entropy of the one-coin source.  ...  The output of B is an independent unbiased (possibly finite) sequence of Hs and Ts 2.  ... 
doi:10.1109/sfcs.1984.715944 dblp:conf/focs/Blum84 fatcat:6n3kruk7czezhnwjf6kuqaqjbi

Zero-one laws in finite W∗-algebras

Elliot C Gootman, D Kannan
1976 Journal of Mathematical Analysis and Applications  
(iv) if p E YP and, for each i, Xi is a normal state on 0& with Xi = TV 1"; except for at most a finite number of indices, then there exists a normal state A E& such that A ldi = hi for all i.  ...  Note that T jl, is a trace on &'a , and is clearly a product state with respect to the independent subalgebras (QZi}iBF of 3s . If there is a normal state X on 6?  ... 
doi:10.1016/0022-247x(76)90078-0 fatcat:qukcayfujzch3hiacjnmwavpwq
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