wanyu/IteraTeR_full_sent huggingface dataset:
Original:  In this work, we  introduce the first fully polynomial time randomized approximation scheme (FPRAS) for counting the number of trees of size n accepted by a tree automaton, where n is given in unary , and the first polynomial time algorithm for sampling uniformly from this set of trees.
Revised:  In this work, we introduce the first fully polynomial time randomized approximation scheme (FPRAS) for counting answers to a query in C , and the first polynomial time algorithm for sampling uniformly from this set of trees.
Edit intent: meaning-changed
Original:  In this work, we  introduce the first fully polynomial time randomized approximation scheme (FPRAS) for counting the number of trees of size n accepted by a tree automaton, where n is given in unary , and the first polynomial time algorithm for sampling uniformly from this set of trees.
Revised:  In this work, we introduce the first fully polynomial time randomized approximation scheme (FPRAS) for counting the number of trees of size n accepted by a tree automaton, where n is given in unary , and the first polynomial-time algorithm for sampling uniformly from this set of trees.
Edit intent: fluency
Original:  In this work, we  introduce the first fully polynomial time randomized approximation scheme (FPRAS) for counting the number of trees of size n accepted by a tree automaton, where n is given in unary , and the first polynomial time algorithm for sampling uniformly from this set of trees. Our results improve over the prior quasi-polynomial time randomized approximation scheme (QPRAS)and sampling algorithm of Gore, Jerrum, Kannan, Sweedyk, and Mahaney 97'. At the heart of our algorithm is a reduction to the problem of estimating the number of strings of length\neqP n accepted by a succinct non-deterministic finite automaton(NFA), which is an NFA where the transitions are labeled by succinctly encoded sets of symbols, whose sizes can be exponential in the encoding length.
Revised:  In this work, we introduce the first fully polynomial time randomized approximation scheme (FPRAS) for counting the number of trees of size n accepted by a tree automaton, where n is given in unary , and the first polynomial time algorithm for sampling answers uniformly from a query in C. As a corollary, it follows that a class of conjunctive queries over graphs admits an FPRAS if and only if it has bounded treewidth (unless BPP\neqP n accepted by a succinct non-deterministic finite automaton(NFA), which is an NFA where the transitions are labeled by succinctly encoded sets of symbols, whose sizes can be exponential in the encoding length.
Edit intent: meaning-changed
Original:  At the heart of our algorithm is a reduction to the problem of estimating the number of strings of length\neqP n accepted by a succinct non-deterministic finite automaton(NFA), which is an NFA where the transitions are labeled by succinctly encoded sets of symbols, whose sizes can be exponential in the encoding length.
Revised:  At the heart of our algorithm is a reduction to the problem of estimating the number of strings of length\neqP). In fact, our FPRAS is more general, and also applies to conjunctive queries with bounded hypertree width, as well as unions of such queries. The key ingredient in our proof is the resolution of a fundamental counting problem from automata theory. Specifically, we demonstrate the first FPRAS and polynomial time sampler for the set of trees of size n accepted by a succinct non-deterministic finite automaton(NFA), which is an NFA where the transitions are labeled by succinctly encoded sets of symbols, whose sizes can be exponential in the encoding length.
Edit intent: meaning-changed
Original:  At the heart of our algorithm is a reduction to the problem of estimating the number of strings of length\neqP n accepted by a succinct non-deterministic finite automaton(NFA), which is an NFA where the transitions are labeled by succinctly encoded sets of symbols, whose sizes can be exponential in the encoding length. Assuming these sets of symbols can be efficiently sampled from, and their sizes approximated, we show that there is an FPRAS and polynomial time almost uniform sampler for succinct NFAs, which may be of independent interest. We demonstrate that, by applying our FPRAS for tree automata, we can obtain an FPRAS for many hitherto open problems in the fields of constraint satisfaction problems ( CSPs) , database systems, software verification, and knowledge compilation.
Revised:  At the heart of our algorithm is a reduction to the problem of estimating the number of strings of length\neqP n accepted by a tree automaton, which improves the prior quasi-polynomial time randomized approximation scheme (QPRAS) and sampling algorithm of Gore, Jerrum, Kannan, Sweedyk, and Mahaney '97. We demonstrate how this algorithm can be used to obtain an FPRAS for many hitherto open problems in the fields of constraint satisfaction problems ( CSPs) , database systems, software verification, and knowledge compilation.
Edit intent: meaning-changed
Original:  We demonstrate that, by applying our FPRAS for tree automata, we can obtain an FPRAS for many hitherto open problems in the fields of constraint satisfaction problems ( CSPs) , database systems, software verification, and knowledge compilation.
Revised:  We demonstrate that, by applying our FPRAS for tree automata, we can obtain an FPRAS for many hitherto open problems , such as counting solutions to constraint satisfaction problems ( CSPs) , database systems, software verification, and knowledge compilation.
Edit intent: meaning-changed
Original:  We demonstrate that, by applying our FPRAS for tree automata, we can obtain an FPRAS for many hitherto open problems in the fields of constraint satisfaction problems ( CSPs) , database systems, software verification, and knowledge compilation. Specifically, we obtain an FPRAS for counting solutions for CSPs that are acyclic or, more generally, that have bounded hypertree-width, which results in an FPRAS for counting the number of answers to conjunctive queries that are acyclic or which have bounded hypertree-width. Moreover, these results can be extended to unions of acyclic conjunctive queries, and to the more general class of unions of conjunctive queries with bounded hypertree-width . Finally, we also obtain FPRAS for the problems of counting the number of error threads in programs with nested call subroutines, and counting valid assignments to structured DNNF circuits.
Revised:  We demonstrate that, by applying our FPRAS for tree automata, we can obtain an FPRAS for many hitherto open problems in the fields of constraint satisfaction problems ( CSP) with bounded hypertree-width . Finally, we also obtain FPRAS for the problems of counting the number of error threads in programs with nested call subroutines, and counting valid assignments to structured DNNF circuits.
Edit intent: clarity
Original:  Moreover, these results can be extended to unions of acyclic conjunctive queries, and to the more general class of unions of conjunctive queries with bounded hypertree-width . Finally, we also obtain FPRAS for the problems of counting the number of error threads in programs with nested call subroutines, and counting valid assignments to structured DNNF circuits.
Revised:  Moreover, these results can be extended to unions of acyclic conjunctive queries, and to the more general class of unions of conjunctive queries with bounded hypertree-width , counting the number of error threads in programs with nested call subroutines, and counting valid assignments to structured DNNF circuits.
Edit intent: coherence
Original:  A seminal result of Grohe, Schwentick, and Segoufin (STOC 2004 ) demonstrates that when restricted to graphs, a class of conjunctive queries can be evaluated in polynomial time if and only if it has bounded treewidth.
Revised:  A seminal result of Grohe, Schwentick, and Segoufin (STOC 2001 ) demonstrates that when restricted to graphs, a class of conjunctive queries can be evaluated in polynomial time if and only if it has bounded treewidth.
Edit intent: meaning-changed
Original:  A seminal result of Grohe, Schwentick, and Segoufin (STOC 2004 ) demonstrates that when restricted to graphs, a class of conjunctive queries can be evaluated in polynomial time if and only if it has bounded treewidth.
Revised:  A seminal result of Grohe, Schwentick, and Segoufin (STOC 2004 ) demonstrates that for every class G of graphs, the evaluation of all conjunctive queries whose underlying graph is in G is tractable if, and only if it has bounded treewidth.
Edit intent: clarity
Original:  A seminal result of Grohe, Schwentick, and Segoufin (STOC 2004 ) demonstrates that when restricted to graphs, a class of conjunctive queries can be evaluated in polynomial time if and only if it has bounded treewidth.
Revised:  A seminal result of Grohe, Schwentick, and Segoufin (STOC 2004 ) demonstrates that when restricted to graphs, a class of conjunctive queries can be evaluated in polynomial time if and only if , G has bounded treewidth.
Edit intent: meaning-changed
Original:  As a corollary, it follows that a class of conjunctive queries over graphs admits an FPRAS if  and only if it has bounded treewidth (unless BPP%DIFDELCMD < \neqP%%% ) \neq \text{P})}} . In fact, our FPRAS is more general, and also applies to conjunctive queries with bounded hypertree width, as well as unions of such queries.
Revised:  As a corollary, it follows that for every class G of graphs, the counting problem for conjunctive queries whose underlying graph is in G admits an FPRAS if and only if it has bounded treewidth (unless BPP%DIFDELCMD < \neqP%%% ) \neq \text{P})}} . In fact, our FPRAS is more general, and also applies to conjunctive queries with bounded hypertree width, as well as unions of such queries.
Edit intent: meaning-changed
Original:  As a corollary, it follows that a class of conjunctive queries over graphs admits an FPRAS if  and only if it has bounded treewidth (unless BPP%DIFDELCMD < \neqP%%% ) \neq \text{P})}} . In fact, our FPRAS is more general, and also applies to conjunctive queries with bounded hypertree width, as well as unions of such queries.
Revised:  As a corollary, it follows that a class of conjunctive queries over graphs admits an FPRAS if , and only if it has bounded treewidth (unless BPP%DIFDELCMD < \neqP%%% ) \neq \text{P})}} . In fact, our FPRAS is more general, and also applies to conjunctive queries with bounded hypertree width, as well as unions of such queries.
Edit intent: fluency
Original:  As a corollary, it follows that a class of conjunctive queries over graphs admits an FPRAS if  and only if it has bounded treewidth (unless BPP%DIFDELCMD < \neqP%%% ) \neq \text{P})}} . In fact, our FPRAS is more general, and also applies to conjunctive queries with bounded hypertree width, as well as unions of such queries.
Revised:  As a corollary, it follows that a class of conjunctive queries over graphs admits an FPRAS if and only if , G has bounded treewidth (unless BPP%DIFDELCMD < \neqP%%% ) \neq \text{P})}} . In fact, our FPRAS is more general, and also applies to conjunctive queries with bounded hypertree width, as well as unions of such queries.
Edit intent: meaning-changed
Original:  As a corollary, it follows that a class of conjunctive queries over graphs admits an FPRAS if  and only if it has bounded treewidth (unless BPP%DIFDELCMD < \neqP%%% ) \neq \text{P})}} . In fact, our FPRAS is more general, and also applies to conjunctive queries with bounded hypertree width, as well as unions of such queries.
Revised:  As a corollary, it follows that a class of conjunctive queries over graphs admits an FPRAS if and only if it has bounded treewidth (unless %DIFDELCMD < \neqP%%% ) \neq \text{P})}} . In fact, our FPRAS is more general, and also applies to conjunctive queries with bounded hypertree width, as well as unions of such queries.
Edit intent: coherence
Original:  As a corollary, it follows that a class of conjunctive queries over graphs admits an FPRAS if  and only if it has bounded treewidth (unless BPP%DIFDELCMD < \neqP%%% ) \neq \text{P})}} . In fact, our FPRAS is more general, and also applies to conjunctive queries with bounded hypertree width, as well as unions of such queries.
Revised:  As a corollary, it follows that a class of conjunctive queries over graphs admits an FPRAS if and only if it has bounded treewidth (unless BPP%DIFDELCMD < \neqP%%% \text{BPP \neq \text{P})}} . In fact, our FPRAS is more general, and also applies to conjunctive queries with bounded hypertree width, as well as unions of such queries.
Edit intent: coherence
Original:  For example, two of the most widely used algorithms, the k-cores decomposition and the classic two-block model of URLatti and Everett, extract fundamentally different structures: the former partitions a network into a binary hub-and-spoke layout, while the latter divides it into a layered hierarchy.
Revised:  For example, two of the most widely used algorithms, the k-cores decomposition and the classic two-block model of URLatti and Everett, extract fundamentally different structures: the latter partitions a network into a binary hub-and-spoke layout, while the latter divides it into a layered hierarchy.
Edit intent: clarity
Original:  For example, two of the most widely used algorithms, the k-cores decomposition and the classic two-block model of URLatti and Everett, extract fundamentally different structures: the former partitions a network into a binary hub-and-spoke layout, while the latter divides it into a layered hierarchy.
Revised:  For example, two of the most widely used algorithms, the k-cores decomposition and the classic two-block model of URLatti and Everett, extract fundamentally different structures: the former partitions a network into a binary hub-and-spoke layout, while the former divides it into a layered hierarchy.
Edit intent: fluency
Original:  The ability of the proposed technique to successfully compute complex equilibrium paths in static structural mechanics problems is demonstrated using five numerical examples involving truss and beam models .
Revised:  The ability of the proposed technique to successfully compute complex equilibrium paths in static structural mechanics problems is demonstrated using five numerical examples involving truss , beam-column and shell models. The computed numerical results are in excellent agreement with the reference solutions. The present approach does not require prohibitively small increments for its success .
Edit intent: meaning-changed
Original:  Our BERTweet is trained using the RoBERTa pre-training procedure (Liu et al., 2019), with the same model configuration as BERT-base (Devlin et al., 2019).
Revised:  Our BERTweet , having the same architecture as BERT-base (Devlin et al., 2019), with the same model configuration as BERT-base (Devlin et al., 2019).
Edit intent: meaning-changed
Original:  Our BERTweet is trained using the RoBERTa pre-training procedure (Liu et al., 2019), with the same model configuration as BERT-base (Devlin et al., 2019).
Revised:  Our BERTweet is trained using the RoBERTa pre-training procedure (Liu et al., 2019), is trained using the RoBERTa pre-training procedure (Liu et al., 2019).
Edit intent: clarity
Original:  Upon discretization, the model inherits several desirable attributes from this infinite-dimensional , function space viewpoint, including mesh-invariant approximation error with respect to the true PDE solution map and the capability to be trained at one mesh resolution and then deployed at different mesh resolutions.
Revised:  Upon discretization, the model inherits several desirable attributes from this infinite-dimensional viewpoint, including mesh-invariant approximation error with respect to the true PDE solution map and the capability to be trained at one mesh resolution and then deployed at different mesh resolutions.
Edit intent: clarity
Original:  In this work, we criticise NMT models probabilistically showing that stochastic samples following the model's own generative story do reproduce various statistics of the training data well, but that it is beam search that strays from such statistics.
Revised:  In this work, we criticise NMT models probabilistically showing that stochastic samples following the model's own generative story do reproduce various statistics of the data well, but that it is beam search that strays from such statistics.
Edit intent: clarity
Original:  In this work, we criticise NMT models probabilistically showing that stochastic samples following the model's own generative story do reproduce various statistics of the training data well, but that it is beam search that strays from such statistics.
Revised:  In this work, we criticise NMT models probabilistically showing that stochastic samples following the model's own generative story do reproduce various statistics of the training data well, but that beam search strays from such statistics.
Edit intent: coherence
Original:  As a proof of concept we show that a straightforward implementation of minimum Bayes risk decoding gives good results outperforming beam search using as little as 30 samples, confirming that MLE-trained NMT models do capture important aspects of translation well in expectation.
Revised:  We show that an approximation to minimum Bayes risk decoding gives good results outperforming beam search using as little as 30 samples, confirming that MLE-trained NMT models do capture important aspects of translation well in expectation.
Edit intent: clarity
Original:  As a proof of concept we show that a straightforward implementation of minimum Bayes risk decoding gives good results outperforming beam search using as little as 30 samples, confirming that MLE-trained NMT models do capture important aspects of translation well in expectation.
Revised:  As a proof of concept we show that a straightforward implementation of minimum Bayes risk decoding gives competitive results confirming that NMT models do capture important aspects of translation well in expectation.
Edit intent: clarity
Original: A new class of measurement operators for structured compressed sensing problems, termed `hierarchical ' measurement operators, is introduced. Standard Kronecker measurement operators are block-oriented treating each block equally whereas the hierarchical measurement operator allows for processing each block with a different matrix, e.g. mixtures of FFT and Gaussian matrices of different column space size and different pilot frequencies each, which are received over multiple antennas. We prove that such hierarchical measurement operators exhibit a hierarchical RIP (HiRIP) property provided the involved matriceshave a suitable standard RIP, implying recovery guarantees for a class of algorithm involving hierarchical thresholding operations. Thereby, we generalize prior work on the recovery of hierarchically sparse signals from Kronecker-structured linear measurements.
Revised: A new class of measurement operators for structured compressed sensing problems, termed `hierarchical ' measurement operators, and prove results guaranteeing the efficient, stable and robust recovery of hierarchically structured signals from such measurements. We derive bounds on their hierarchical restricted isometry properties based on the restricted isometry constants of their constituent matrices, generalizing and extending prior work on the recovery of hierarchically sparse signals from Kronecker-structured linear measurements.
Edit intent: clarity
Original:  Thereby, we generalize prior work on the recovery of hierarchically sparse signals from Kronecker-structured linear measurements. This structure arises in a variety of communication scenariosin the context of massive internet of things. We numerical demonstrate that the fast and scalable HiHTP algorithm is  suitable for solving these types of problems and evaluate its performance in terms of sparse signal recovery and block detection capability.
Revised:  Thereby, we generalize prior work on Kronecker-product measurements. As an exemplary application, we apply the theory to two communication scenarios. The fast and scalable HiHTP algorithm is suitable for solving these types of problems and evaluate its performance in terms of sparse signal recovery and block detection capability.
Edit intent: meaning-changed
Original:  We apply the workflow to a set of four applications (NAS CG and BT-MZ, CORAL-2 AMG, and CORAL LULESH), twelve mapping algorithms (communication \& topology oblivious/aware) , and three direct network topologies (3-D mesh, 3-D torus, and a novel highly adaptive energy-efficient 3-D topology, called the HAEC Box) .
Revised:  We apply the workflow to a set of four applications , twelve mapping algorithms (communication \& topology oblivious/aware) , and three direct network topologies (3-D mesh, 3-D torus, and a novel highly adaptive energy-efficient 3-D topology, called the HAEC Box) .
Edit intent: coherence
Original:  We apply the workflow to a set of four applications (NAS CG and BT-MZ, CORAL-2 AMG, and CORAL LULESH), twelve mapping algorithms (communication \& topology oblivious/aware) , and three direct network topologies (3-D mesh, 3-D torus, and a novel highly adaptive energy-efficient 3-D topology, called the HAEC Box) .
Revised:  We apply the workflow to a set of four applications (NAS CG and BT-MZ, CORAL-2 AMG, and CORAL LULESH), twelve mapping algorithms , and three direct network topologies (3-D mesh, 3-D torus, and a novel highly adaptive energy-efficient 3-D topology, called the HAEC Box) .
Edit intent: coherence
Original:  We apply the workflow to a set of four applications (NAS CG and BT-MZ, CORAL-2 AMG, and CORAL LULESH), twelve mapping algorithms (communication \& topology oblivious/aware) , and three direct network topologies (3-D mesh, 3-D torus, and a novel highly adaptive energy-efficient 3-D topology, called the HAEC Box) .
Revised:  We apply the workflow to a set of four applications (NAS CG and BT-MZ, CORAL-2 AMG, and CORAL LULESH), twelve mapping algorithms (communication \& topology oblivious/aware) , and three direct network topologies .
Edit intent: meaning-changed
Original:  It is found that energy plays a central role in the system that aims to achieve minimum error fractions and maximum  specificity with the fastest speed under our kinetic scheme  , but such an optimal condition is accomplished at significant amount cost of energy and sensitivity .
Revised:  It is found that energy plays a central role in the system that aims to achieve minimum error fractions and maximum sensitivity and specificity with the fastest speed under our kinetic scheme , but such an optimal condition is accomplished at significant amount cost of energy and sensitivity .
Edit intent: clarity
Original:  It is found that energy plays a central role in the system that aims to achieve minimum error fractions and maximum  specificity with the fastest speed under our kinetic scheme  , but such an optimal condition is accomplished at significant amount cost of energy and sensitivity .
Revised:  It is found that energy plays a central role in the system that aims to achieve minimum error fractions and maximum specificity with the fastest speed under our kinetic scheme for which numerical values of kinetic parameters are specially chosen , but such an optimal condition is accomplished at significant amount cost of energy and sensitivity .
Edit intent: meaning-changed
Original:  It is found that energy plays a central role in the system that aims to achieve minimum error fractions and maximum  specificity with the fastest speed under our kinetic scheme  , but such an optimal condition is accomplished at significant amount cost of energy and sensitivity .
Revised:  It is found that energy plays a central role in the system that aims to achieve minimum error fractions and maximum specificity with the fastest speed under our kinetic scheme , but such a condition can be broken with varying data .
Edit intent: clarity