wanyu/IteraTeR_v2 huggingface dataset:
Original:  we show a complementation construction with upper bound 2^{O(n \lg n+nk \lg k)} for k = O(n) and 2^{O(n^{2} \lg n)} for k = \omega(n) . The upper bound matches exactly the lower bound obtained in CZ11a.
Revised:  we show a complementation construction with upper bound 2^{O(n \lg n+nk \lg k)} for k = O(n) and 2^{O(n^{2} \lg n)} for k = \omega(n) , which matches well the lower bound obtained in CZ11a.
Edit intent: clarity
Original:  We also obtain a tight upper bound 2^{O(n \lg n)} for parity complementation . Combining this with \mbox{ CZ11a .
Revised:  We also obtain a tight upper bound 2^{O(n \lg n)} for parity complementation .
Edit intent: coherence
Original:  In arXiv:1102.2960 we showed a } construction for complementing a Streett automaton with n states and k Streett pairs, is 2^{O(nk\lg nk) bound 2^{ \Omega (n \lg  nk  )}  \lg n)} for k=\omega(n)} . In this paper we improve the lower bound to 2^{\Omega(n \lg n+nk \lg k)} for k = O(n) and to 2^{\Omega(n^{2} \lg n)} for k = \omega(n), which exactly matches the upper bound obtained in \mbox{ CZ11b .
Revised:  In arXiv:1102.2960 we showed a } construction for complementing Streett automata with the upper bound 2^{ \Omega (n \lg nk )} \lg n)} for k=\omega(n)} . In this paper we improve the lower bound to 2^{\Omega(n \lg n+nk \lg k)} for k = O(n) and to 2^{\Omega(n^{2} \lg n)} for k = \omega(n), which exactly matches the upper bound obtained in \mbox{ CZ11b .
Edit intent: clarity
Original:  In arXiv:1102.2960 we showed a } construction for complementing a Streett automaton with n states and k Streett pairs, is 2^{O(nk\lg nk) bound 2^{ \Omega (n \lg  nk  )}  \lg n)} for k=\omega(n)} . In this paper we improve the lower bound to 2^{\Omega(n \lg n+nk \lg k)} for k = O(n) and to 2^{\Omega(n^{2} \lg n)} for k = \omega(n), which exactly matches the upper bound obtained in \mbox{ CZ11b .
Revised:  In arXiv:1102.2960 we showed a } construction for complementing a Streett automaton with n states and k Streett pairs, is 2^{O(nk\lg nk) bound 2^{ O (n \lg nk )} \lg n)} for k=\omega(n)} . In this paper we improve the lower bound to 2^{\Omega(n \lg n+nk \lg k)} for k = O(n) and to 2^{\Omega(n^{2} \lg n)} for k = \omega(n), which exactly matches the upper bound obtained in \mbox{ CZ11b .
Edit intent: fluency
Original:  In arXiv:1102.2960 we showed a } construction for complementing a Streett automaton with n states and k Streett pairs, is 2^{O(nk\lg nk) bound 2^{ \Omega (n \lg  nk  )}  \lg n)} for k=\omega(n)} . In this paper we improve the lower bound to 2^{\Omega(n \lg n+nk \lg k)} for k = O(n) and to 2^{\Omega(n^{2} \lg n)} for k = \omega(n), which exactly matches the upper bound obtained in \mbox{ CZ11b .
Revised:  In arXiv:1102.2960 we showed a } construction for complementing a Streett automaton with n states and k Streett pairs, is 2^{O(nk\lg nk) bound 2^{ \Omega (n \lg n+ nk )} \lg n)} for k=\omega(n)} . In this paper we improve the lower bound to 2^{\Omega(n \lg n+nk \lg k)} for k = O(n) and to 2^{\Omega(n^{2} \lg n)} for k = \omega(n), which exactly matches the upper bound obtained in \mbox{ CZ11b .
Edit intent: fluency
Original:  In arXiv:1102.2960 we showed a } construction for complementing a Streett automaton with n states and k Streett pairs, is 2^{O(nk\lg nk) bound 2^{ \Omega (n \lg  nk  )}  \lg n)} for k=\omega(n)} . In this paper we improve the lower bound to 2^{\Omega(n \lg n+nk \lg k)} for k = O(n) and to 2^{\Omega(n^{2} \lg n)} for k = \omega(n), which exactly matches the upper bound obtained in \mbox{ CZ11b .
Revised:  In arXiv:1102.2960 we showed a } construction for complementing a Streett automaton with n states and k Streett pairs, is 2^{O(nk\lg nk) bound 2^{ \Omega (n \lg nk \lg k )} \lg n)} for k=\omega(n)} . In this paper we improve the lower bound to 2^{\Omega(n \lg n+nk \lg k)} for k = O(n) and to 2^{\Omega(n^{2} \lg n)} for k = \omega(n), which exactly matches the upper bound obtained in \mbox{ CZ11b .
Edit intent: fluency
Original:  In arXiv:1102.2960 we showed a } construction for complementing a Streett automaton with n states and k Streett pairs, is 2^{O(nk\lg nk) bound 2^{ \Omega (n \lg  nk  )}  \lg n)} for k=\omega(n)} . In this paper we improve the lower bound to 2^{\Omega(n \lg n+nk \lg k)} for k = O(n) and to 2^{\Omega(n^{2} \lg n)} for k = \omega(n), which exactly matches the upper bound obtained in \mbox{ CZ11b .
Revised:  In arXiv:1102.2960 we showed a } construction for complementing a Streett automaton with n states and k Streett pairs, is 2^{O(nk\lg nk) bound 2^{ \Omega (n \lg nk )} for k = O(n) and 2^{O(n^{2 \lg n)} for k=\omega(n)} . In this paper we improve the lower bound to 2^{\Omega(n \lg n+nk \lg k)} for k = O(n) and to 2^{\Omega(n^{2} \lg n)} for k = \omega(n), which exactly matches the upper bound obtained in \mbox{ CZ11b .
Edit intent: coherence
Original:  In arXiv:1102.2960 we showed a } construction for complementing a Streett automaton with n states and k Streett pairs, is 2^{O(nk\lg nk) bound 2^{ \Omega (n \lg  nk  )}  \lg n)} for k=\omega(n)} . In this paper we improve the lower bound to 2^{\Omega(n \lg n+nk \lg k)} for k = O(n) and to 2^{\Omega(n^{2} \lg n)} for k = \omega(n), which exactly matches the upper bound obtained in \mbox{ CZ11b .
Revised:  In arXiv:1102.2960 we showed a } construction for complementing a Streett automaton with n states and k Streett pairs, is 2^{O(nk\lg nk) bound 2^{ \Omega (n \lg nk )} \lg n)} for k=\omega(n)} . In this paper we improve the lower bound to 2^{\Omega(n \lg n+nk \lg k)} for k = O(n) and 2^{\Omega(n^{2} \lg n)} for k = \omega(n), which exactly matches the upper bound obtained in \mbox{ CZ11b .
Edit intent: coherence
Original:  Moreover, to our knowledge, there is even no result on QFAs having more than one input head.
Revised:  Moreover, to our knowledge, there is no result related to QFAs having more than one input head.
Edit intent: clarity
Original:  Furthermore, we propose many open problems and conjectures in order to investigate the power of quantumness better.
Revised:  Furthermore, we propose some open problems and conjectures in order to investigate the power of quantumness better.
Edit intent: clarity
Original:  We also give some new results about classical computation.
Revised:  We also give some new results on classical computation.
Edit intent: fluency
Original:  We show that for many commutative semirings K, the rational \Sigma-tree series over A with coefficients in K form the free multi-linear iterative K-\Sigma semialgebra on A.
Revised:  We show that for many commutative semirings K, the rational \Sigma-tree series over A with coefficients in K form the free multi-linear iterative K-\Sigma -semialgebra on A.
Edit intent: fluency
Original: This article is concerned with automated complexity analysis of term rewrite systems (TRSs for short) .
Revised: This article is concerned with automated complexity analysis of term rewrite systems .
Edit intent: clarity
Original: This paper analyzes Least Squares Monte Carlo (LSM) algorithm, which is proposed by Longstaff and Schwartz (2001) for pricing American style securities.
Revised: Consider Least Squares Monte Carlo (LSM) algorithm, which is proposed by Longstaff and Schwartz (2001) for pricing American style securities.
Edit intent: clarity
Original: Wireless sensor networks (WSNs) became one of the high-technology domains during the last  years.
Revised: Wireless sensor networks (WSNs) became one of the high technology domains during the last years.
Edit intent: fluency
Original:  The main contributions of the paper are a service framework and a guaranteed QoS model that are suitable for the WSNs with some characteristics of the distribution, multi-hop, etc .
Revised:  The main contributions of this paper are a service framework and a guaranteed QoS model that are suitable for the WSNs with some characteristics of the distribution, multi-hop, etc .
Edit intent: coherence
Original:  The main contributions of the paper are a service framework and a guaranteed QoS model that are suitable for the WSNs with some characteristics of the distribution, multi-hop, etc .
Revised:  The main contributions of the paper are a system skeleton and a guaranteed QoS model that are suitable for the WSNs with some characteristics of the distribution, multi-hop, etc .
Edit intent: clarity
Original:  The main contributions of the paper are a service framework and a guaranteed QoS model that are suitable for the WSNs with some characteristics of the distribution, multi-hop, etc .
Revised:  The main contributions of the paper are a service framework and a guaranteed QoS model that are suitable for the WSNs .
Edit intent: coherence
Original:  To do it, we develop a sensor node model based on virtual buffer sharing and present a two-layer scheduling model by arrival curves and service curves in the network calculus.
Revised:  To do it, we develop a sensor node model based on virtual buffer sharing and present a two-layer scheduling model using the network calculus.
Edit intent: coherence
Original:  Our proposal leads to buffer dimensioning, guaranteed QoS support and control in  WSNs.
Revised:  Our proposal leads to buffer dimensioning, guaranteed QoS support and control in the WSNs.
Edit intent: fluency
Original:  In this work we show the problem to be NP-Hard for k=1.
Revised:  We show the problem to be NP-Hard for k=1.
Edit intent: clarity
Original:  The the problem being easy for k=n-1, where n is the length of the permutation (the unbounded case).
Revised:  The problem is easy for k=n-1, where n is the length of the permutation (the unbounded case).
Edit intent: coherence
Original:  Sorting by Block Interchanges is a very important and widely studied problem motivated by its applications in comparative genomics.
Revised:  Sorting by Block Interchanges is a very important and widely studied problem with applications in comparative genomics.
Edit intent: clarity
Original:  That is, the behavior of the individuals in our new model and in the model of LHN can be interpreted as an ``aggregation'' vs. an `` all-or-nothing '' strategy, respectively.
Revised:  That is, the behavior of the individuals in our new model and in the model of LHN can be interpreted as an "aggregation" vs. an `` all-or-nothing '' strategy, respectively.
Edit intent: fluency
Original:  That is, the behavior of the individuals in our new model and in the model of LHN can be interpreted as an ``aggregation'' vs. an `` all-or-nothing '' strategy, respectively.
Revised:  That is, the behavior of the individuals in our new model and in the model of LHN can be interpreted as an ``aggregation'' vs. an " all-or-nothing '' strategy, respectively.
Edit intent: fluency
Original:  That is, the behavior of the individuals in our new model and in the model of LHN can be interpreted as an ``aggregation'' vs. an `` all-or-nothing '' strategy, respectively.
Revised:  That is, the behavior of the individuals in our new model and in the model of LHN can be interpreted as an ``aggregation'' vs. an `` all-or-nothing " strategy, respectively.
Edit intent: fluency
Original:  We demonstrate this by introducing and analyzing two different antibiotic scenarios , for which we bound the time needed to return to the healthy state .
Revised:  We demonstrate this by introducing and analyzing two alternative control approaches , for which we bound the time needed to return to the healthy state .
Edit intent: clarity
Original:  We demonstrate this by introducing and analyzing two different antibiotic scenarios , for which we bound the time needed to return to the healthy state .
Revised:  We demonstrate this by introducing and analyzing two different antibiotic scenarios , for which we bound the time needed to stabilize to the "healthy" state of the system .
Edit intent: clarity
Original:  Both the computing the Pfaffian and a related problem, computing the canonical form of a skew-symmetric matrix under unitary congruence, can be solved easily once the skew-symmetric matrix has been reduced to skew-symmetric tridiagonal form.
Revised:  Both computing the Pfaffian and a related problem, computing the canonical form of a skew-symmetric matrix under unitary congruence, can be solved easily once the skew-symmetric matrix has been reduced to skew-symmetric tridiagonal form.
Edit intent: fluency
Original:  We also give a complete and fully optimized implementation of these algorithms in FORTRAN , and also provide python and Mathematica implementations for convenience.
Revised:  We also give a complete and fully optimized implementation of these algorithms in Fortran , and also provide python and Mathematica implementations for convenience.
Edit intent: fluency
Original: Hairpin completion and its restricted variant called bounded hairpin completion are operations on formal languages, inspired by a hairpin formation in molecular biology.
Revised: Hairpin completion and its variant called bounded hairpin completion are operations on formal languages, inspired by a hairpin formation in molecular biology.
Edit intent: clarity
Original:  We introduce a new operation of this kind, called %DIFDELCMD < {\it %DIFDELCMD < %%% hairpin incompletion which is in fact an extension of bounded hairpin completion  .
Revised:  We introduce a new operation of this kind, called %DIFDELCMD < {\it %DIFDELCMD < %%% which is in fact an extension of bounded hairpin completion .
Edit intent: fluency
Original:  We introduce a new operation of this kind, called %DIFDELCMD < {\it %DIFDELCMD < %%% hairpin incompletion which is in fact an extension of bounded hairpin completion  .
Revised:  We introduce a new operation of this kind, called %DIFDELCMD < {\it %DIFDELCMD < %%% hairpin incompletion hairpin incompletion which is not only an extension of bounded hairpin completion .
Edit intent: clarity
Original:  This measure allows comparing different products and models (pricing hypothesis) under a homogeneous framework and conclude which one is the best.
Revised:  This measure allows comparing products valued with different models (pricing hypothesis) under a homogeneous framework and conclude which one is the best.
Edit intent: clarity
Original:  The model risk measure is defined in terms of the expected value and standard deviation of the loss given by the hedging strategy at a given time horizon .
Revised:  The model risk measure is defined as the expected shortfall of the hedging strategy at a given time horizon .
Edit intent: clarity
Original:  The method is applied to estimate and compare model risk under volga-vanna and Black-Scholes models for double-no-touch options and a porfolio of forward fader options.
Revised:  The method is applied to estimate and compare model risk under volga-vanna and Black-Scholes models for double-no-touch options and a portfolio of forward fader options.
Edit intent: fluency
Original: The problem of consciousness faced several challenges for a few reasons: (a) a lack of necessary and sufficient conditions, without which we would not know how close we are to the solution, (b) a lack of a synthesis framework to build conscious systems , i.e., beyond analysis and (c) a lack of mechanisms transitioning between the low-level chemical dynamics and the high-level abstractionsbased on, say, language .
Revised: The problem of consciousness faced several challenges for a few reasons: (a) a lack of necessary and sufficient conditions, without which we would not know how close we are to the solution, (b) a lack of a synthesis framework to build conscious systems and (c) a lack of mechanisms transitioning between the low-level chemical dynamics and the high-level abstractionsbased on, say, language .
Edit intent: coherence
Original: The problem of consciousness faced several challenges for a few reasons: (a) a lack of necessary and sufficient conditions, without which we would not know how close we are to the solution, (b) a lack of a synthesis framework to build conscious systems , i.e., beyond analysis and (c) a lack of mechanisms transitioning between the low-level chemical dynamics and the high-level abstractionsbased on, say, language .
Revised: The problem of consciousness faced several challenges for a few reasons: (a) a lack of necessary and sufficient conditions, without which we would not know how close we are to the solution, (b) a lack of a synthesis framework to build conscious systems , i.e., beyond analysis and (c) a lack of mechanisms explaining the transition between the lower-level chemical dynamics and the high-level abstractionsbased on, say, language .
Edit intent: clarity
Original:  This necessary and sufficient condition lets us move away from the vagueness surrounding consciousness and instead allows us to focus equivalently on: (i) what truths are and how our brain represents/relates them to each other and (ii) how we attain a feeling of knowing for anything, not just a truth.
Revised:  This lets us move away from the vagueness surrounding consciousness and instead allows us to focus equivalently on: (i) what truths are and how our brain represents/relates them to each other and (ii) how we attain a feeling of knowing for anything, not just a truth.
Edit intent: clarity
Original:  This necessary and sufficient condition lets us move away from the vagueness surrounding consciousness and instead allows us to focus equivalently on: (i) what truths are and how our brain represents/relates them to each other and (ii) how we attain a feeling of knowing for anything, not just a truth.
Revised:  This necessary and sufficient condition lets us move away from the vagueness surrounding consciousness and instead focus equivalently on: (i) what truths are and how our brain represents/relates them to each other and (ii) how we attain a feeling of knowing for anything, not just a truth.
Edit intent: clarity
Original:  This necessary and sufficient condition lets us move away from the vagueness surrounding consciousness and instead allows us to focus equivalently on: (i) what truths are and how our brain represents/relates them to each other and (ii) how we attain a feeling of knowing for anything, not just a truth.
Revised:  This necessary and sufficient condition lets us move away from the vagueness surrounding consciousness and instead allows us to focus equivalently on: (i) what truths are and how our brain represents/relates them to each other and (ii) how we attain a feeling of knowing for a truth.
Edit intent: clarity
Original:  For the former problem, since truths are things that do not change (i.e., fixed), I replace the abstract notion with a dynamical one called fixed sets.
Revised:  For the former problem, since truths are things that do not change , I replace the abstract notion with a dynamical one called fixed sets.
Edit intent: coherence
Original:  These sets are guaranteed to exist for our brain and all other stable parallel looped systems.
Revised:  These sets are guaranteed to exist for our brain and other stable parallel looped systems.
Edit intent: clarity
Original:  The relationships between everyday events are now built using relationships between fixed sets, until our brain culminates in creating a unique dynamical state called the self-sustaining threshold 'membrane' of fixed sets.
Revised:  The relationships between everyday events are now built using relationships between fixed sets, until our brain creates a unique dynamical state called the self-sustaining threshold 'membrane' of fixed sets.
Edit intent: clarity
Original:  For the latter problem of knowing , I present necessary and sufficient conditions for attaining a feeling of knowing using a definition of continuity applied to abstractions represented on the membrane . Combining these results, I now say that a person is minimally conscious if and only if his brain has a self-sustaining dynamical membrane with abstract continuous paths.
Revised:  For the latter problem , I present necessary and sufficient conditions for attaining a feeling of knowing using a definition of continuity applied to abstractions represented on the membrane . Combining these results, I now say that a person is minimally conscious if and only if his brain has a self-sustaining dynamical membrane with abstract continuous paths.
Edit intent: clarity
Original:  For the latter problem of knowing , I present necessary and sufficient conditions for attaining a feeling of knowing using a definition of continuity applied to abstractions represented on the membrane . Combining these results, I now say that a person is minimally conscious if and only if his brain has a self-sustaining dynamical membrane with abstract continuous paths.
Revised:  For the latter problem of knowing , I present necessary and sufficient conditions for attaining a feeling of knowing using a definition of continuity applied to abstractions . Combining these results, I now say that a person is minimally conscious if and only if his brain has a self-sustaining dynamical membrane with abstract continuous paths.
Edit intent: clarity
Original: We show that various aspects of k-automatic sequences - such as having an unbordered factor of length n - are both decidable and effectively enumerable.
Revised: We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n - are both decidable and effectively enumerable.
Edit intent: fluency
Original: We show that various aspects of k-automatic sequences - such as having an unbordered factor of length n - are both decidable and effectively enumerable.
Revised: We show that various aspects of k-automatic sequences - such as having an unbordered factor of length n -- are both decidable and effectively enumerable.
Edit intent: fluency
Original:  We describe methods of constructing the atomaton , and prove that it is isomorphic to the normal automaton of Sengoku, and to an automaton of Matz and Potthoff .
Revised:  We describe methods of constructing the \'atomaton , and prove that it is isomorphic to the normal automaton of Sengoku, and to an automaton of Matz and Potthoff .
Edit intent: fluency
Original:  We study "atomic" NFA's in which the right language of every state is a union of atoms.
Revised:  We study "atomic" NFAs in which the right language of every state is a union of atoms.
Edit intent: fluency
Original:  A simple strategy adopted by the salesman might resemble strategies chosen by some foraging and hunting animals, for which anomalous diffusive behaviour has recently been reported but interpreted in terms of Levy flights.
Revised:  A simple strategy adopted by the salesman might resemble strategies chosen by some foraging and hunting animals, for which anomalous diffusive behavior has recently been reported but interpreted in terms of Levy flights.
Edit intent: fluency
Original:  A simple strategy adopted by the salesman might resemble strategies chosen by some foraging and hunting animals, for which anomalous diffusive behaviour has recently been reported but interpreted in terms of Levy flights.
Revised:  A simple strategy adopted by the salesman might resemble strategies chosen by some foraging and hunting animals, for which anomalous diffusive behaviour has recently been reported and interpreted in terms of Levy flights.
Edit intent: coherence
Original:  Our results suggest that anomalous diffusive behaviour in such systems might appear due to the dimension-dependent properties of a search space.
Revised:  Our results suggest that broad and Levy-like distributions in such systems might appear due to the dimension-dependent properties of a search space.
Edit intent: clarity
Original:  Our results suggest that anomalous diffusive behaviour in such systems might appear due to the dimension-dependent properties of a search space.
Revised:  Our results suggest that anomalous diffusive behaviour in such systems might appear due to dimension-dependent properties of a search space.
Edit intent: fluency
Original:  We apply it to analyze two complex bio-medical datasets : multispectral retinal images and microarray gene expressions .
Revised:  We apply it to analyze two complex bio-medical datasets : multispectral retinal images .
Edit intent: clarity