wanyu/IteraTeR_v2 huggingface dataset:
Original:  The problem is to determine whether for a given graph and given number of cops the cops are able to prevent the robber from entering the guarded region.
Revised:  The problem is to determine whether for a given graph and given number of cops the cops are able to prevent Robber from entering the guarded region.
Edit intent: fluency
Original:  In this paper we prove that for arbitrary graphs (directed or undirected) the problem is E-complete  .
Revised:  In this paper we prove that the problem is E-complete .
Edit intent: clarity
Original:  This yields a solution to a long-standing open problem in propositional proof complexity, namely, whether there are polynomial-size NC^2-Frege proofs for the determinant identities and the hard matrix identities, as considered, e.g., in Soltys and Cook (2004) (cf., Beame and Pitassi (1998)).
Revised:  This yields a solution to a basic open problem in propositional proof complexity, namely, whether there are polynomial-size NC^2-Frege proofs for the determinant identities and the hard matrix identities, as considered, e.g., in Soltys and Cook (2004) (cf., Beame and Pitassi (1998)).
Edit intent: clarity
Original:  Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic ( CHP-SL ) , with the aim of getting a powerful framework for reasoning explicitly about strategies.
Revised:  Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic ( CHP-SL , with the aim of getting a powerful framework for reasoning explicitly about strategies.
Edit intent: fluency
Original:  CHP-SL is obtained by using first-order quantifications over strategies and it has been investigated in the  setting of two-agents turned-based games, where a non-elementary model-checking algorithm has been provided.
Revised:  CHP-SL is obtained by using first-order quantifications over strategies and has been investigated in the setting of two-agents turned-based games, where a non-elementary model-checking algorithm has been provided.
Edit intent: coherence
Original:  CHP-SL is obtained by using first-order quantifications over strategies and it has been investigated in the  setting of two-agents turned-based games, where a non-elementary model-checking algorithm has been provided.
Revised:  CHP-SL is obtained by using first-order quantifications over strategies and it has been investigated in the very specific setting of two-agents turned-based games, where a non-elementary model-checking algorithm has been provided.
Edit intent: clarity
Original:  This negative result has spurred us to investigate  syntactic fragments of SL, strictly subsuming ATL* , with the aim of obtaining an elementary model-checking problem.
Revised:  This negative result has spurred us to investigate here syntactic fragments of SL, strictly subsuming ATL* , with the aim of obtaining an elementary model-checking problem.
Edit intent: coherence
Original:  This negative result has spurred us to investigate  syntactic fragments of SL, strictly subsuming ATL* , with the aim of obtaining an elementary model-checking problem.
Revised:  This negative result has spurred us to investigate syntactic fragments of SL, strictly subsuming ATL* , with the hope of obtaining an elementary model-checking problem.
Edit intent: clarity
Original:  Among the others, we have introduced and studied the sublogics SL[NG], SL[BG], and SL[1G].
Revised:  Among the others, we study the sublogics SL[NG], SL[BG], and SL[1G].
Edit intent: clarity
Original:  They refer to formulas in a special prenex normal form having, respectively, nested temporal goals, Boolean combinations of goals and, one single goal at a time.
Revised:  They encompass formulas in a special prenex normal form having, respectively, nested temporal goals, Boolean combinations of goals and, one single goal at a time.
Edit intent: clarity
Original:  They refer to formulas in a special prenex normal form having, respectively, nested temporal goals, Boolean combinations of goals and, one single goal at a time.
Revised:  They refer to formulas in a special prenex normal form having, respectively, nested temporal goals, Boolean combinations of goals and, a single goal at a time.
Edit intent: clarity
Original:  On the contrary, for SL NG%DIFDELCMD < ]%%% , it is NonElementarySpace-hard, enforcing the corresponding result for SL .
Revised:  On the contrary, for SL %DIFDELCMD < ]%%% , it is NonElementarySpace-hard, enforcing the corresponding result for SL .
Edit intent: style
Original: We consider chains of random Constraint Satisfaction Problems that are spatially coupled across a finite window along the chain direction.
Revised: We consider chains of random constraint satisfaction models that are spatially coupled across a finite window along the chain direction.
Edit intent: clarity
Original:  We prove that the  phase transition threshold of an infinite chain is identical to the one of the individual (standard ) model and is therefore not affected by spatial coupling.
Revised:  We prove that the phase transition threshold of an infinite chain is identical to the one of the individual standard model, and is therefore not affected by spatial coupling.
Edit intent: clarity
Original:  We compute the  complexity using population dynamics and also large degree approximations, and determine the survey propagation threshold , which marks the onset of clustering of solutions .
Revised:  We compute the survey propagation complexity using population dynamics and also large degree approximations, and determine the survey propagation threshold , which marks the onset of clustering of solutions .
Edit intent: fluency
Original:  We compute the  complexity using population dynamics and also large degree approximations, and determine the survey propagation threshold , which marks the onset of clustering of solutions .
Revised:  We compute the complexity using population dynamics as well as large degree approximations, and determine the survey propagation threshold , which marks the onset of clustering of solutions .
Edit intent: coherence
Original:  We compute the  complexity using population dynamics and also large degree approximations, and determine the survey propagation threshold , which marks the onset of clustering of solutions .
Revised:  We compute the complexity using population dynamics and also large degree approximations, and determine the survey propagation threshold .
Edit intent: clarity
Original:  We find that a clustering phase survives coupling , however, as one increases the range of the coupling window, the survey propagation threshold increases and saturates towards the phase transition threshold.
Revised:  We find that a clustering phase survives coupling . However, as one increases the range of the coupling window, the survey propagation threshold increases and saturates towards the phase transition threshold.
Edit intent: fluency
Original:  The MAXCLIQUE problem, or the problem of finding the size of the maximum clique, for t-interval graphs is known to be NP-complete  when t\geq 3 and is polynomial-time solvable when t=1.
Revised:  The MAXCLIQUE problem, or the problem of finding the size of the maximum clique, is known to be NP-complete when t\geq 3 and is polynomial-time solvable when t=1.
Edit intent: clarity
Original:  The MAXCLIQUE problem, or the problem of finding the size of the maximum clique, for t-interval graphs is known to be NP-complete  when t\geq 3 and is polynomial-time solvable when t=1.
Revised:  The MAXCLIQUE problem, or the problem of finding the size of the maximum clique, for t-interval graphs is known to be NP-complete for t-interval graphs when t\geq 3 and is polynomial-time solvable when t=1.
Edit intent: fluency
Original:  The MAXCLIQUE problem, or the problem of finding the size of the maximum clique, for t-interval graphs is known to be NP-complete  when t\geq 3 and is polynomial-time solvable when t=1.
Revised:  The MAXCLIQUE problem, or the problem of finding the size of the maximum clique, for t-interval graphs is known to be NP-complete when t\geq 3 and polynomial-time solvable when t=1.
Edit intent: fluency
Original: We study subset selection for matrices defined as follows: given a matrix \matX \in \R^{n \times m} (m > n) and an oversampling parameter k (n \le k \le m), select a subset of k columns from \matX such that the pseudo-inverse of the subsampled matrix has as smallest norm as possible.
Revised: We study subset selection for matrices defined as follows: given a matrix \matX \in \R^{n \times m} (m > n) and an oversampling parameter k (n \le k \le m), select a subset of k columns from \matX such that the pseudo-inverse of the subsampled matrix has as smallest norm as possible.
Edit intent: fluency
Original: An atom of a regular language L with n (left) quotients is a non-empty intersection of uncomplemented or complemented quotients of L, where each of the n quotients appears in a term of the intersection , and at least one quotient is uncomplemented .
Revised: An atom of a regular language L with n (left) quotients is a non-empty intersection of uncomplemented or complemented quotients of L, where each of the n quotients appears in a term of the intersection .
Edit intent: clarity
Original:  The quotient complexity of L, which is the same as the state complexity of L, is the number of quotients of L. We prove that, for any language L with quotient complexity n, the quotient complexity of any atom of L with r complemented quotients has an upper bound of 2^n-1 if r=0 , and k=1^r h=k+1 ^{ n-r+ k %DIFDELCMD < \MBLOCKRIGHTBRACE %%% C_h^nC_k^h + 1 ^{n} \cdot C_{k}^{h} } otherwise, where C_j^i is the binomial coefficient.
Revised:  The quotient complexity of L, which is the same as the state complexity of L, is the number of quotients of L. We prove that, for any language L with quotient complexity n, the quotient complexity of any atom of L with r complemented quotients has an upper bound of 2^n-1 if r=0 , and k=1^r h=k+1 ^{ n-r+ k %DIFDELCMD < \MBLOCKRIGHTBRACE %%% C_h^nC_k^h + n-r ^{n} \cdot C_{k}^{h} } otherwise, where C_j^i is the binomial coefficient.
Edit intent: fluency
Original:  The quotient complexity of L, which is the same as the state complexity of L, is the number of quotients of L. We prove that, for any language L with quotient complexity n, the quotient complexity of any atom of L with r complemented quotients has an upper bound of 2^n-1 if r=0 , and k=1^r h=k+1 ^{ n-r+ k %DIFDELCMD < \MBLOCKRIGHTBRACE %%% C_h^nC_k^h + 1 ^{n} \cdot C_{k}^{h} } otherwise, where C_j^i is the binomial coefficient.
Revised:  The quotient complexity of L, which is the same as the state complexity of L, is the number of quotients of L. We prove that, for any language L with quotient complexity n, the quotient complexity of any atom of L with r complemented quotients has an upper bound of 2^n-1 if r=0 , and k=1^r h=k+1 ^{ n-r+ k %DIFDELCMD < \MBLOCKRIGHTBRACE %%% C_h^nC_k^h + 1 C_{h^{n} \cdot C_{k}^{h} } otherwise, where C_j^i is the binomial coefficient.
Edit intent: fluency
Original:  Several improvements are based on specifi?c properties of any formula where each branch of its syntax tree contains at least one eventually operator and at least one always operator.
Revised:  Several improvements are based on specific properties of any formula where each branch of its syntax tree contains at least one eventually operator and at least one always operator.
Edit intent: fluency
Original: The impact of damping effect to the DNA bubble is investigated within the Peyrard-Bishop model.
Revised: The damping effect to the DNA bubble is investigated within the Peyrard-Bishop model.
Edit intent: clarity
Original:  Traveling wave solution showed that when the viscosity is not introduced in the system, solitary wave patterns propagate without vanishing .
Revised:  It is shown that the propagation of solitary wave pattern is not vanishing in a non-viscous system. Inversely, the solitary wave vanishes soon as the viscous force is introduced .
Edit intent: clarity
Original: In this paper, we propose LMEEC, a cluster-based rout- ing protocol with low energy consumption for wireless sensor networks.
Revised: In this paper, we propose LMEEC, a cluster-based routing protocol with low energy consumption for wireless sensor networks.
Edit intent: fluency
Original:  Our protocol is based on a strategy which aims to provide a more equitable exploitation of the selected nodes (cluster-heads) energy.
Revised:  Our protocol is based on a strategy which aims to provide a more reasonable exploitation of the selected nodes (cluster-heads) energy.
Edit intent: clarity
Original:  Simulation results show the effective- ness of LMEEC in decreasing the energy consumption, and in prolonging the network lifetime, compared to LEACH.
Revised:  Simulation results show the effectiveness of LMEEC in decreasing the energy consumption, and in prolonging the network lifetime, compared to LEACH.
Edit intent: fluency
Original: A class of graphs G is \chi-bounded if the chromatic number of the graphs in G is bounded by some function of their clique number.
Revised: A class of graphs G is chi-bounded if the chromatic number of the graphs in G is bounded by some function of their clique number.
Edit intent: fluency
Original:  We show that the class of intersection graphs of simple x-monotone curves in the plane intersecting a vertical line is \chi-bounded .
Revised:  We show that the class of intersection graphs of simple x-monotone curves in the plane intersecting a vertical line is chi-bounded .
Edit intent: coherence
Original:  As a corollary , the class of intersection graphs of rays in the plane is \chi-bounded.
Revised:  As a corollary we show that the class of intersection graphs of rays in the plane is \chi-bounded.
Edit intent: clarity
Original:  Our main result is a common generalization of two classical results in graph theory: the theorem of Kov\'{a}ri, S\'{o}s and Tur\'{a}n on the minimum number of edges in a bipartite graph that has no large independent set, and the theorem of Hansel (also Katona and Szemer\'{e}di and Krichevskii) on the sum of the sizes of bipartite graphs that can be used to construct a graph (non-necessarily bipartite) that has no large independent set.
Revised:  Our main result is a common generalization of two classical results in graph theory: the theorem of Kov\'{a}ri, S\'{o}s and Tur\'{a}n on the minimum number of edges in a bipartite graph that has no large independent set, and the theorem of Hansel (also Katona and Szemer\'{e}di , Krichevskii) on the sum of the sizes of bipartite graphs that can be used to construct a graph (non-necessarily bipartite) that has no large independent set.
Edit intent: fluency
Original:  Our results unify the underlying combinatorial principles developed in the proof of tight lower bounds for depth-two superconcentrators.
Revised:  As an application of our results, we show how they unify the underlying combinatorial principles developed in the proof of tight lower bounds for depth-two superconcentrators.
Edit intent: coherence
Original:  Hagan, Kumar, Leniewski and Woodward have given an approximate solution by means of perturbative techniques.
Revised:  Hagan, Kumar, Leniewski and Woodward have obtained an approximate solution by means of perturbative techniques.
Edit intent: clarity
Original:  A more precise approximation was obtained by Henry-Labord\`ere using the heat kernel expansion method.
Revised:  A more precise approximation was found by Henry-Labord\`ere using the heat kernel expansion method.
Edit intent: clarity
Original:  A more precise approximation was obtained by Henry-Labord\`ere using the heat kernel expansion method.
Revised:  A more precise approximation was obtained by Henry-Labord\`ere with the heat kernel expansion method.
Edit intent: fluency
Original:  The latter relies on deep and hard theorems from Riemannian geometry which are almost totally unknown to people working in finance, who however are those primarily interested in these results.
Revised:  The latter relies on deep and hard theorems from Riemannian geometry which are almost totally unknown to the professionals of finance, who however are those primarily interested in these results.
Edit intent: clarity
Original:  The goal of this report is to fill this gap and makes these topics understandable to people with a basic knowledge of calculus and linear algebra.
Revised:  The goal of this report is to fill this gap and to make these topics understandable to people with a basic knowledge of calculus and linear algebra.
Edit intent: fluency
Original:  The goal of this report is to fill this gap and makes these topics understandable to people with a basic knowledge of calculus and linear algebra.
Revised:  The goal of this report is to fill this gap and makes these topics understandable with a basic knowledge of calculus and linear algebra.
Edit intent: coherence
Original:  In addition to being of interest in their own right, our main results shed light on the relationship between hyperbolicity and navigability  , as well as the relationship between \delta-hyperbolicity and the use of randomness in common random graph constructions }  .
Revised:  In addition to being of interest in their own right, our main results shed light on the relationship between hyperbolicity and navigability of random graphs , as well as the relationship between \delta-hyperbolicity and the use of randomness in common random graph constructions } .
Edit intent: clarity
Original:  Here, we consider Gromov's notion of \delta-hyperbolicity, and we establish several positive and negative results for small-world and tree-like random graph models.
Revised:  We consider Gromov's notion of \delta-hyperbolicity, and we establish several positive and negative results for small-world and tree-like random graph models.
Edit intent: coherence
Original:  Here, we consider Gromov's notion of \delta-hyperbolicity, and we establish several positive and negative results for small-world and tree-like random graph models.
Revised:  Here, we consider Gromov's notion of \delta-hyperbolicity, and establish several results for small-world and tree-like random graph models.
Edit intent: clarity
Original:  On the other hand, for a class of tree-like graphs called ringed trees that have constant hyperbolicity , adding random links among the leaves in a manner similar to the small-world graph constructions may easily destroy the hyperbolicity of the graphs, except for a class of random edges added using an exponentially decaying probability function based on the ring distance among the leaves.
Revised:  Next we study a class of tree-like graphs called ringed trees that have constant hyperbolicity , adding random links among the leaves in a manner similar to the small-world graph constructions may easily destroy the hyperbolicity of the graphs, except for a class of random edges added using an exponentially decaying probability function based on the ring distance among the leaves.
Edit intent: clarity
Original:  On the other hand, for a class of tree-like graphs called ringed trees that have constant hyperbolicity , adding random links among the leaves in a manner similar to the small-world graph constructions may easily destroy the hyperbolicity of the graphs, except for a class of random edges added using an exponentially decaying probability function based on the ring distance among the leaves.
Revised:  On the other hand, for a class of tree-like graphs called ringed trees that have constant hyperbolicity . We show that adding random links among the leaves in a manner similar to the small-world graph constructions may easily destroy the hyperbolicity of the graphs, except for a class of random edges added using an exponentially decaying probability function based on the ring distance among the leaves.
Edit intent: coherence
Original:  On the other hand, for a class of tree-like graphs called ringed trees that have constant hyperbolicity , adding random links among the leaves in a manner similar to the small-world graph constructions may easily destroy the hyperbolicity of the graphs, except for a class of random edges added using an exponentially decaying probability function based on the ring distance among the leaves.
Revised:  On the other hand, for a class of tree-like graphs called ringed trees that have constant hyperbolicity , adding random links among the leaves similar to the small-world graph constructions may easily destroy the hyperbolicity of the graphs, except for a class of random edges added using an exponentially decaying probability function based on the ring distance among the leaves.
Edit intent: clarity
Original:  Our study provides  the first significant analytical results on the hyperbolicity of a rich class of random graphs, which shed light on the relationship between hyperbolicity and navigability of random graphs, as well as on the sensitivity of hyperbolic {\delta} to noises in random graphs.
Revised:  Our study provides one of the first significant analytical results on the hyperbolicity of a rich class of random graphs, which shed light on the relationship between hyperbolicity and navigability of random graphs, as well as on the sensitivity of hyperbolic {\delta} to noises in random graphs.
Edit intent: clarity
Original: The requirement of a language to be conditionally decomposable is placed on a specification language in the coordination supervisory control framework of discrete-event systems.
Revised: The requirement of a language to be conditionally decomposable is imposed on a specification language in the coordination supervisory control framework of discrete-event systems.
Edit intent: clarity
Original:  Conditional decomposability is a weaker condition than decomposability discussed in the literature.
Edit intent: coherence
Original:  A relation of conditional decomposability with nonblockingness of modular discrete-event systems is also discussed in this paper in the general settings.
Revised:  A relationship of conditional decomposability with nonblockingness of modular discrete-event systems is also discussed in this paper in the general settings.
Edit intent: fluency
Original:  A relation of conditional decomposability with nonblockingness of modular discrete-event systems is also discussed in this paper in the general settings.
Revised:  A relation of conditional decomposability to nonblockingness of modular discrete-event systems is also discussed in this paper in the general settings.
Edit intent: fluency
Original:  Even when the exponent is very close to -1, adding an exponential component is able to yield a better fit with regard to a pure power-law to plants, mammals, ray-finned fishes and amphibians.
Revised:  Even when the exponent is very close to -1, adding an exponential component is able to yield a better fit with regard to a pure power-law in plants, mammals, ray-finned fishes and amphibians.
Edit intent: fluency
Original: Multi-currency FX derivatives o?er a challenging playground to the mathematical modelling of correlations.
Revised: Multi-currency FX derivatives offer a challenging playground to the mathematical modelling of correlations.
Edit intent: fluency
Original:  Since all our lower bounds arise from the classical LP relaxations, we also obtain the same new bounds on their integrality gaps .
Revised:  Since our lower bounds arise from the classical LP relaxations, we also obtain the same new bounds on their integrality gaps .
Edit intent: clarity
Original:  Since all our lower bounds arise from the classical LP relaxations, we also obtain the same new bounds on their integrality gaps .
Revised:  Since all our lower bounds arise from LP relaxations, we also obtain the same new bounds on their integrality gaps .
Edit intent: clarity
Original:  Since all our lower bounds arise from the classical LP relaxations, we also obtain the same new bounds on their integrality gaps .
Revised:  Since all our lower bounds arise from the classical LP relaxations, we also obtain the same new bounds on integrality gaps of these .
Edit intent: clarity
Original:  A proof of concept was created to asses applicability of the method in real-life scenarios.
Revised:  A proof of concept was created to assess applicability of the method in real-life scenarios.
Edit intent: fluency