wanyu/IteraTeR_v2 huggingface dataset:
Original:  We numerically demonstrate for linear systems that PSD-SMG converges nearly identical to flexible PCG-SMG  if SMG post-smoothing is off  .
Revised:  We numerically demonstrate for linear systems that PSD-SMG and flexible PCG-SMG if SMG post-smoothing is off .
Edit intent: clarity
Original:    A series of experiments to validate the Coding theorem method to evaluate Kolmogorov complexity based on approximations to Levin's Universal Distribution are presented, showing that the measure is stable in the face of  changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms .
Revised:  Turmite A series of experiments to validate the Coding theorem method to evaluate Kolmogorov complexity based on approximations to Levin's Universal Distribution are presented, showing that the measure is stable in the face of changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms .
Edit intent: fluency
Original:    A series of experiments to validate the Coding theorem method to evaluate Kolmogorov complexity based on approximations to Levin's Universal Distribution are presented, showing that the measure is stable in the face of  changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms .
Revised:  . A series of experiments to validate the Coding theorem method to evaluate Kolmogorov complexity based on approximations to Levin's Universal Distribution are presented, showing that the measure is stable in the face of changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms .
Edit intent: fluency
Original:    A series of experiments to validate the Coding theorem method to evaluate Kolmogorov complexity based on approximations to Levin's Universal Distribution are presented, showing that the measure is stable in the face of  changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms .
Revised:  A series of experiments to validate estimations of Kolmogorov complexity based on approximations to Levin's Universal Distribution are presented, showing that the measure is stable in the face of changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms .
Edit intent: clarity
Original:    A series of experiments to validate the Coding theorem method to evaluate Kolmogorov complexity based on approximations to Levin's Universal Distribution are presented, showing that the measure is stable in the face of  changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms .
Revised:  A series of experiments to validate the Coding theorem method to evaluate Kolmogorov complexity based on these concepts is presented, showing that the measure is stable in the face of changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms .
Edit intent: clarity
Original:    A series of experiments to validate the Coding theorem method to evaluate Kolmogorov complexity based on approximations to Levin's Universal Distribution are presented, showing that the measure is stable in the face of  changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms .
Revised:  A series of experiments to validate the Coding theorem method to evaluate Kolmogorov complexity based on approximations to Levin's Universal Distribution are presented, showing that the measure is stable in the face of some changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms .
Edit intent: clarity
Original:  We also introduce a Block Matrix Decomposition technique with an  application to classification of  space-time evolutions of cellular automata, providing further evidence of the soundness and readiness of the Coding theorem method as an alternative and complementation to compression algorithms for approximating Kolmogorov complexity, specially for small objects (e. g. short strings and small images) where lossless compression algorithms fail .
Revised:  We also introduce a Block Matrix Decomposition technique with an application to classification of space-time evolutions of discrete systems, providing evidence of the soundness and readiness of the Coding theorem method as an alternative and complementation to compression algorithms for approximating Kolmogorov complexity, specially for small objects (e. g. short strings and small images) where lossless compression algorithms fail .
Edit intent: clarity
Original:  We also introduce a Block Matrix Decomposition technique with an  application to classification of  space-time evolutions of cellular automata, providing further evidence of the soundness and readiness of the Coding theorem method as an alternative and complementation to compression algorithms for approximating Kolmogorov complexity, specially for small objects (e. g. short strings and small images) where lossless compression algorithms fail .
Revised:  We also introduce a Block Matrix Decomposition technique with an application to classification of space-time evolutions of cellular automata, providing further evidence of the soundness of the method as a complementary alternative to compression algorithms for approximating Kolmogorov complexity, specially for small objects (e. g. short strings and small images) where lossless compression algorithms fail .
Edit intent: coherence
Original:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to  n-dimensional algorithmic complexity by using an n-dimensional deterministic Turing machine , popularized under the term ofTurmites for n=2, from which the so-calledLangton's ant is an example of a Turing universalTurmite .
Revised:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to the problem of evaluating n-dimensional algorithmic complexity by using an n-dimensional deterministic Turing machine , popularized under the term ofTurmites for n=2, from which the so-calledLangton's ant is an example of a Turing universalTurmite .
Edit intent: clarity
Original:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to  n-dimensional algorithmic complexity by using an n-dimensional deterministic Turing machine , popularized under the term ofTurmites for n=2, from which the so-calledLangton's ant is an example of a Turing universalTurmite .
Revised:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to n-dimensional complexity by using an n-dimensional deterministic Turing machine , popularized under the term ofTurmites for n=2, from which the so-calledLangton's ant is an example of a Turing universalTurmite .
Edit intent: fluency
Original:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to  n-dimensional algorithmic complexity by using an n-dimensional deterministic Turing machine , popularized under the term ofTurmites for n=2, from which the so-calledLangton's ant is an example of a Turing universalTurmite .
Revised:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to n-dimensional algorithmic complexity by using an n-dimensional deterministic Turing machine Turmites for n=2, from which the so-calledLangton's ant is an example of a Turing universalTurmite .
Edit intent: coherence
Original:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to  n-dimensional algorithmic complexity by using an n-dimensional deterministic Turing machine , popularized under the term ofTurmites for n=2, from which the so-calledLangton's ant is an example of a Turing universalTurmite .
Revised:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to n-dimensional algorithmic complexity by using an n-dimensional deterministic Turing machine , popularized under the term of for n=2, from which the so-calledLangton's ant is an example of a Turing universalTurmite .
Edit intent: fluency
Original:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to  n-dimensional algorithmic complexity by using an n-dimensional deterministic Turing machine , popularized under the term ofTurmites for n=2, from which the so-calledLangton's ant is an example of a Turing universalTurmite .
Revised:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to n-dimensional algorithmic complexity by using an n-dimensional deterministic Turing machine , popularized under the term ofTurmites Langton's ant is an example of a Turing universalTurmite .
Edit intent: coherence
Original:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to  n-dimensional algorithmic complexity by using an n-dimensional deterministic Turing machine , popularized under the term ofTurmites for n=2, from which the so-calledLangton's ant is an example of a Turing universalTurmite .
Revised:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to n-dimensional algorithmic complexity by using an n-dimensional deterministic Turing machine , popularized under the term ofTurmites for n=2, from which the so-calledLangton's ant Turmite .
Edit intent: clarity
Original:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to  n-dimensional algorithmic complexity by using an n-dimensional deterministic Turing machine , popularized under the term ofTurmites for n=2, from which the so-calledLangton's ant is an example of a Turing universalTurmite .
Revised:  Here we provide a measure based upon the concept of Algorithmic Probability that elegantly connects to Kolmogorov complexity that provides a natural approach to n-dimensional algorithmic complexity by using an n-dimensional deterministic Turing machine , popularized under the term ofTurmites for n=2, from which the so-calledLangton's ant is an example of a Turing universal .
Edit intent: clarity
Original:  A series of experiments to validate estimations of Kolmogorov complexity based on these concepts is presented, showing that the measure is stable in the face of some changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms when both methods overlap in their range of applicability.
Revised:  A series of experiments to validate estimations of algorithmic complexity based on these concepts is presented, showing that the measure is stable in the face of some changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms when both methods overlap in their range of applicability.
Edit intent: clarity
Original:  A series of experiments to validate estimations of Kolmogorov complexity based on these concepts is presented, showing that the measure is stable in the face of some changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms when both methods overlap in their range of applicability.
Revised:  A series of experiments to validate estimations of Kolmogorov complexity based on these concepts are presented, showing that the measure is stable in the face of some changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms when both methods overlap in their range of applicability.
Edit intent: fluency
Original:  We also present aBlock Decomposition Method (BDM) application to classification of images and space-time evolutions of discrete systems, providing evidence of the soundness of the method as a complementary alternative to compression algorithms for the evaluation of algorithmic complexity .
Revised:  We Block Decomposition Method (BDM) application to classification of images and space-time evolutions of discrete systems, providing evidence of the soundness of the method as a complementary alternative to compression algorithms for the evaluation of algorithmic complexity .
Edit intent: clarity
Original:  We also present aBlock Decomposition Method (BDM) application to classification of images and space-time evolutions of discrete systems, providing evidence of the soundness of the method as a complementary alternative to compression algorithms for the evaluation of algorithmic complexity .
Revised:  We also present a (BDM) application to classification of images and space-time evolutions of discrete systems, providing evidence of the soundness of the method as a complementary alternative to compression algorithms for the evaluation of algorithmic complexity .
Edit intent: coherence
Original:  CSM-2-Matroids has a (2+epsilon)-approximation algorithm---called LSV2.
Revised:  CSM-2-Matroids has a (2+epsilon)-approximation algorithm - called LSV2.
Edit intent: fluency
Original:  Before our result, it was known that these problems require Omega(n^2) space in one pass, but no n^(1+Omega(1)) lower bound was known for any p>=2.
Revised:  Prior to our result, it was known that these problems require Omega(n^2) space in one pass, but no n^(1+Omega(1)) lower bound was known for any p>=2.
Edit intent: clarity
Original:  Prior to our result, it was known that these problems require Omega (n^2) space in one pass, but no n ^(1+Omega(1)) lower bound was known for any p >= \ge 2.
Revised:  Prior to our result, it was known that these problems require \Omega (n^2) space in one pass, but no n ^(1+Omega(1)) lower bound was known for any p >= \ge 2.
Edit intent: fluency
Original:  Prior to our result, it was known that these problems require Omega (n^2) space in one pass, but no n ^(1+Omega(1)) lower bound was known for any p >= \ge 2.
Revised:  Prior to our result, it was known that these problems require Omega (n^2) space in one pass, but no n ^{1+\Omega(1) lower bound was known for any p >= \ge 2.
Edit intent: fluency
Original:  Prior to our result, it was known that these problems require Omega (n^2) space in one pass, but no n ^(1+Omega(1)) lower bound was known for any p >= \ge 2.
Revised:  Prior to our result, it was known that these problems require Omega (n^2) space in one pass, but no n ^(1+Omega(1)) lower bound was known for any p \ge 2.
Edit intent: clarity
Original:  The task of the players is to find out whether the sets of vertices reachable from a specific vertex in exactly p+1 steps intersect.
Revised:  The task of the players is to find out whether the sets of vertices at distance exactly p+1 steps intersect.
Edit intent: clarity
Original:  The task of the players is to find out whether the sets of vertices reachable from a specific vertex in exactly p+1 steps intersect.
Revised:  The task of the players is to find out whether the sets of vertices reachable from a specific vertex in exactly p+1 from a specific vertex intersect.
Edit intent: clarity
Original:  In addition to meeting the known logarithmic lower bounds on the number of gates required to approximate a unitary by a quantum circuit, we give computational evidence that a very close to the best, or the best existing approximation for unitaries of the type diag 1, exp(i*phi)%DIFDELCMD < } %%% were indeed found.
Revised:  1, exp(i*phi)%DIFDELCMD < } %%% were indeed found.
Edit intent: coherence
Original: The 1-perfect code obtained by Vasil' ev-Schonheim construction from linear base code and  quadratic switching function is transitive and, moreover, propelinear.
Revised: The 1-perfect code obtained by Vasil' ev--Schonheim construction from a linear base code and quadratic switching function is transitive and, moreover, propelinear.
Edit intent: fluency
Original: The 1-perfect code obtained by Vasil' ev-Schonheim construction from linear base code and  quadratic switching function is transitive and, moreover, propelinear.
Revised: The 1-perfect code obtained by Vasil' ev-Schonheim construction from linear base code and a quadratic switching function is transitive and, moreover, propelinear.
Edit intent: fluency
Original: The 1-perfect code obtained by Vasil'ev--Schonheim construction from a linear base code and a quadratic switching function is transitive and, moreover, propelinear.
Revised: Perfect codes obtained by the Vasil'ev--Sch\"onheim construction from a linear base code and a quadratic switching function is transitive and, moreover, propelinear.
Edit intent: clarity
Original: The 1-perfect code obtained by Vasil'ev--Schonheim construction from a linear base code and a quadratic switching function is transitive and, moreover, propelinear.
Revised: The 1-perfect code obtained by Vasil'ev--Schonheim construction from a linear base code and quadratic switching functions are transitive and, moreover, propelinear.
Edit intent: fluency
Original:  This gives at least \exp(cN^2) propelinear 1-perfect codes of length N over an arbitrary finite field, while an upper bound on the number of transitive codes is \exp( c (N\ln N)^2).
Revised:  This gives at least \exp(cN^2) propelinear 1-perfect codes of length N over an arbitrary finite field, while an upper bound on the number of transitive codes is \exp( C (N\ln N)^2).
Edit intent: fluency
Original: Thapper and Zivny obtained in a recent paper [ arXiv:1210.2987 ] a complexity classification of the finite-valued VCSP , i.e. for the case where the constraint-language contains only finite-valued cost functions.
Revised: Thapper and Zivny [ arXiv:1210.2987 ] a complexity classification of the finite-valued VCSP , i.e. for the case where the constraint-language contains only finite-valued cost functions.
Edit intent: clarity
Original: Thapper and Zivny obtained in a recent paper [ arXiv:1210.2987 ] a complexity classification of the finite-valued VCSP , i.e. for the case where the constraint-language contains only finite-valued cost functions.
Revised: Thapper and Zivny obtained in a recent paper [ arXiv:1210.2987 ] recently classified the complexity of VCSP for all finite-valued cost functions.
Edit intent: clarity
Original:  In this paper we study the complexity of two such restrictions of VCSP , namely Min-Cost-Hom and Min-Sol.
Revised:  In this paper we study the complexity of two such VCSPs , namely Min-Cost-Hom and Min-Sol.
Edit intent: clarity
Original:  We obtain a full classification of the complexity of Min-Sol on domains that contain at most three elements .
Revised:  We obtain a full classification for the complexity of Min-Sol on domains that contain at most three elements .
Edit intent: fluency
Original:  Our results answer a question raised by Takhanov in [STACS'10 and COCOON'10].
Revised:  Our results answer a question raised by Takhanov [STACS'10 and COCOON'10].
Edit intent: fluency
Original:  Our results answer a question raised by Takhanov in [STACS'10 and COCOON'10].
Revised:  Our results answer a question raised by Takhanov in [STACS'10 , COCOON'10].
Edit intent: fluency
Original: In this paper we study the parameterized complexity of two well-known permutation group problems which are NP-complete. o Given a permutation group G=< S%DIFDELCMD < }\le %%% S_n and a parameter k, find a permutation \pi \in G such that |{i\in [n]\mid \pi(i)\ne i}| %DIFDELCMD < \ge %%%  k. This generalizes the %DIFDELCMD < \NP%%% -complete problem of finding a fixed-point free permutation in G CW10,Lub81 (this is the case when k=n).
Revised: In this paper we study the parameterized complexity of two well-known permutation group problems which are NP-complete. 1. Given a permutation group G=< S%DIFDELCMD < }\le %%% S_n and a parameter k, find a permutation \pi \in G such that |{i\in [n]\mid \pi(i)\ne i}| %DIFDELCMD < \ge %%% k. This generalizes the %DIFDELCMD < \NP%%% -complete problem of finding a fixed-point free permutation in G CW10,Lub81 (this is the case when k=n).
Edit intent: fluency
Original: In this paper we study the parameterized complexity of two well-known permutation group problems which are NP-complete. o Given a permutation group G=< S%DIFDELCMD < }\le %%% S_n and a parameter k, find a permutation \pi \in G such that |{i\in [n]\mid \pi(i)\ne i}| %DIFDELCMD < \ge %%%  k. This generalizes the %DIFDELCMD < \NP%%% -complete problem of finding a fixed-point free permutation in G CW10,Lub81 (this is the case when k=n).
Revised: In this paper we study the parameterized complexity of two well-known permutation group problems which are NP-complete. o Given a permutation group G=< %DIFDELCMD < }\le %%% S_n and a parameter k, find a permutation \pi \in G such that |{i\in [n]\mid \pi(i)\ne i}| %DIFDELCMD < \ge %%% k. This generalizes the %DIFDELCMD < \NP%%% -complete problem of finding a fixed-point free permutation in G CW10,Lub81 (this is the case when k=n).
Edit intent: clarity
Original: In this paper we study the parameterized complexity of two well-known permutation group problems which are NP-complete. o Given a permutation group G=< S%DIFDELCMD < }\le %%% S_n and a parameter k, find a permutation \pi \in G such that |{i\in [n]\mid \pi(i)\ne i}| %DIFDELCMD < \ge %%%  k. This generalizes the %DIFDELCMD < \NP%%% -complete problem of finding a fixed-point free permutation in G CW10,Lub81 (this is the case when k=n).
Revised: In this paper we study the parameterized complexity of two well-known permutation group problems which are NP-complete. o Given a permutation group G=< S%DIFDELCMD < }\le %%% S_n and a parameter k, find a permutation \pi in G such that |{i\in [n]\mid \pi(i)\ne i}| %DIFDELCMD < \ge %%% k. This generalizes the %DIFDELCMD < \NP%%% -complete problem of finding a fixed-point free permutation in G CW10,Lub81 (this is the case when k=n).
Edit intent: fluency
Original: In this paper we study the parameterized complexity of two well-known permutation group problems which are NP-complete. o Given a permutation group G=< S%DIFDELCMD < }\le %%% S_n and a parameter k, find a permutation \pi \in G such that |{i\in [n]\mid \pi(i)\ne i}| %DIFDELCMD < \ge %%%  k. This generalizes the %DIFDELCMD < \NP%%% -complete problem of finding a fixed-point free permutation in G CW10,Lub81 (this is the case when k=n).
Revised: In this paper we study the parameterized complexity of two well-known permutation group problems which are NP-complete. o Given a permutation group G=< S%DIFDELCMD < }\le %%% S_n and a parameter k, find a permutation \pi \in G such that |{i\in [n]\mid \pi(i)\ne i}| %DIFDELCMD < \ge %%% is at least k. This generalizes the %DIFDELCMD < \NP%%% -complete problem of finding a fixed-point free permutation in G CW10,Lub81 (this is the case when k=n).
Edit intent: clarity