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Omega Automata and its Classes

Natasha Singh, Ajay Kumar
2018 Current Science  
In addition, this paper also summarizes the applicability of omega automata in various interdisciplinary fields.  ...  They applied the concept of PBA in the verification of a Markov chain. Park 39 modelled fair concurrency using the concept of ω-regular languages.  ...  Properties in model checking are explicitly specified using Linear-time Temporal Logic (LTL). Giannakopoulou and Lerda 6 proposed an efficient approach for the conversion of LTL to Büchi automata.  ... 
doi:10.18520/cs/v115/i11/2042-2051 fatcat:byu5hbxpnbaclbp2rkx3qa6uhm

Markov Chain Monte Carlo Methods in Quantum Field Theories [article]

Anosh Joseph
2019 arXiv   pre-print
We review the underlying theoretical foundations of Markov chain Monte Carlo.  ...  We introduce and discuss Monte Carlo methods in quantum field theories.  ...  Properties of Markov chains A Markov chain consists of a sequence of random elements, x 0 , x 1 , x 2 , · · · , of some set.  ... 
arXiv:1912.10997v1 fatcat:63alcxe6xrfolidnj6tql6siie

Quantum Complexity of Testing Group Commutativity [article]

Frederic Magniez, Ashwin Nayak (U. Waterloo and Perimeter Inst.)
2007 arXiv   pre-print
Along the way, we prove the optimality of the algorithm of Pak for the randomized model.  ...  For the lower bound of Omega(k^2/3), we give a reduction from a special case of Element Distinctness to our problem.  ...  The Markov chains we construct in this paper are all random walks on regular graphs.  ... 
arXiv:quant-ph/0506265v4 fatcat:sfknwj2apbdrfpamh2u5iis4mm

Probabilistic Automata over Infinite Words: Expressiveness, Efficiency, and Decidability

Christel Baier, Nathalie Bertrand, Marcus Größer
2009 Electronic Proceedings in Theoretical Computer Science  
Probabilistic omega-automata are variants of nondeterministic automata for infinite words where all choices are resolved by probabilistic distributions.  ...  In this paper, we put the main focus on the probable semantics and provide a summary of the fundamental properties of probabilistic omega-automata concerning expressiveness, efficiency, and decision problems  ...  Pr(σ), as the probability measure of the accepting runs for σ in the Markov chain M σ .  ... 
doi:10.4204/eptcs.3.1 fatcat:5pczusd67jh5jmoqed53ymijcm

Asymptotic Perturbation Bounds for Probabilistic Model Checking with Empirically Determined Probability Parameters

Guoxin Su, Yuan Feng, Taolue Chen, David S. Rosenblum
2016 IEEE Transactions on Software Engineering  
We focus on verification of reachability properties but also address automata-based verification of omega-regular properties.  ...  The formal model that we adopt is a parametric variant of discrete-time Markov chains equipped with a vector norm to measure the perturbation.  ...  We thank the anonymous reviewers for their instructive comments on an earlier version of the paper.  ... 
doi:10.1109/tse.2015.2508444 fatcat:2lgw3vhyqrgatapyd2hrl4u5si

Quantum Büchi Automata [article]

Qisheng Wang, Mingsheng Ying
2018 arXiv   pre-print
This paper defines a notion of quantum Büchi automaton (QBA for short) with two different acceptance conditions for ω-words: non-disturbing and disturbing.  ...  The closure properties of the languages accepted by QBAs are studied in the probable, almost sure and threshold semantics.  ...  Shenggang Ying for valuable discussions.  ... 
arXiv:1804.08982v1 fatcat:6tghxncrazb65m2j6ggk7xyxzi

Quantum Algorithm for Commutativity Testing of a Matrix Set [article]

Yuki Kelly Itakura
2005 arXiv   pre-print
We also present Ambainis's method of lower bounding technique (quant-ph/0002066) to obtain a lower bound for this problem.  ...  This is probably the first problem to be studied on the quantum query complexity using quantum walks that involves more than one parameter, here, k and n.  ...  The author would also like to acknowledge both her quantum and classical friends, especially; Pierre Philipps for "Tempest", Pranab Sen for regular helps, Alex Golynski for feeding her brownies, the Crazy  ... 
arXiv:quant-ph/0509206v1 fatcat:d2vtqjggnrdgtbflzrke6rpmqa

Random Partitions and the Quantum Benjamin-Ono Hierarchy [article]

Alexander Moll
2017 arXiv   pre-print
We derive exact and asymptotic results for random partitions from general results in the semi-classical analysis of coherent states applied to the classical periodic Benjamin-Ono equation at critical regularity  ...  For quantum stationary states, this conserved density is dF_λ(c | ε_2, ε_1) the Rayleigh measure of the profile of a partition λ of anisotropy (ε_2, ε_1) ∈C^2 for ħ = - ε_1 ε_2, ε= ε_1 + ε_2 invariant  ...  We now have a model M Υ( ) (ε, ) of random partitions for every > 0,ε ∈ R, and -dependent quantum state Υ( ).  ... 
arXiv:1508.03063v3 fatcat:agw5xrfmfrcj3kkfjxtn5zzinm

Finite and Algorithmic Model Theory (Dagstuhl Seminar 17361)

Anuj Dawar, Erich Grädel, Phokion G. Kolaitis, Thomas Schwentick, Marc Herbstritt
2018 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 17361 "Finite and Algorithmic Model Theory".  ...  Our main results are conditions that imply an abstraction is sound, and further conditions that imply it preserves the Markov property.  ...  We formalize agent-based models as stochastic processes whose states are metafinite models, and we define a notion of abstraction.  ... 
doi:10.4230/dagrep.7.9.1 dblp:journals/dagstuhl-reports/DawarGKS17 fatcat:teyilwvdgrd6tch2gdb4d4dd5m

QSW_MPI: a framework for parallel simulation of quantum stochastic walks [article]

Edric Matwiejew, Jingbo Wang
2020 arXiv   pre-print
This model allows for the study of Markovian open quantum systems in the Lindblad formalism, including a generalisation of the continuous-time random walk and continuous-time quantum walk.  ...  QSW_MPI is a python package developed for time-series simulation of continuous-time quantum stochastic walks.  ...  This allows for the model to be easily tuned to explore a continuum of mixed quantum and classical dynamics.  ... 
arXiv:2003.02450v2 fatcat:olira4cttjeb3a7gxxwqkqyfwq

Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function [article]

Hiroshi Shinaoka, Naoya Chikano, Emanuel Gull, Jia Li, Takuya Nomoto, Junya Otsuki, Markus Wallerberger, Tianchun Wang, Kazuyoshi Yoshimi
2022 arXiv   pre-print
This lecture note reviews recently proposed sparse-modeling approaches for efficient ab initio many-body calculations based on the data compression of Green's functions.  ...  The sparse-modeling techniques are based on a compact orthogonal basis, an intermediate representation (IR) basis, for imaginary-time and Matsubara Green's functions.  ...  Masayuki Ohzeki, which aims to apply sparse modeling to quantum many-body calculations, led to the discovery of the IR basis.  ... 
arXiv:2106.12685v3 fatcat:5v6q7inm6vhfthnwourltqddjq

Understanding Tools and Techniques in Protein Structure Prediction [chapter]

Geraldine Sandana Mala John, Chellan Rose, Satoru Takeuchi
2011 Systems and Computational Biology - Bioinformatics and Computational Modeling  
For each entry a protein sequence alignment and a hidden Markov model is stored. These hidden Markov models can be used to search sequence databases.  ...  It searches for suitable templates, checks sequence identity with targets, generates models and calculates energy minimization. MODELLER is another program for homology modeling.  ... 
doi:10.5772/18585 fatcat:hxcc7ifyobedba3v7ptqrbzlhi

Technical Program

2021 2020 IEEE Information Theory Workshop (ITW)  
Our proof is based entirely on convex optimization and functional analysis, without resorting to any "quantum" arguments.  ...  The optimal local signal satisfies very favorable properties: it is independent of the time horizon, and the resulting error probability is independent of the measurements.  ...  This model is sufficient for establishing many consistency and liveness properties of longest-chain protocols.  ... 
doi:10.1109/itw46852.2021.9457668 fatcat:j425ygeajrbd5esztbe5zgygty

Interactions of Computational Complexity Theory and Mathematics [article]

Avi Wigderson
2017 arXiv   pre-print
chains ∙ Analysis and Probability: Noise stability ∙ Lattice Theory: Short vectors ∙ Invariant Theory: Actions on matrix tuples  ...  We aim for variety. We give short, simple descriptions (without proofs or much technical detail) of ideas, motivations, results and connections; this will hopefully entice the reader to dig deeper.  ...  While the algorithm only outputs g for which g(r) ≈ 0, it is often easy to check that it actually vanishes.  ... 
arXiv:1710.09780v1 fatcat:js6k4t7gefcutfus6te4vxx6ty

An Introduction to Inductive Statistical Inference: from Parameter Estimation to Decision-Making [article]

Henk van Elst
2020 arXiv   pre-print
Following an exposition of exactly solvable cases of single- and two-parameter estimation problems, the main focus is laid on Markov Chain Monte Carlo (MCMC) simulations on the basis of Hamiltonian Monte  ...  Carlo sampling of posterior joint probability distributions for regression parameters occurring in generalised linear models for a univariate outcome variable.  ...  Acknowledgements: I am grateful to Ariane, Vincent and Audrey for their enduring patience with my continuing absent-mindedness during the intense writing-up process of these lecture notes.  ... 
arXiv:1808.10173v2 fatcat:3nkxeicqrbbbtpaywqtpuieerm
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