wanyu/IteraTeR_v2 huggingface dataset:
Original:  However , error handling techniques that are often applied to top-down parsers are not directly applicable to PEGs.
Revised:  Unfortunately , error handling techniques that are often applied to top-down parsers are not directly applicable to PEGs.
Edit intent: fluency
Original:  This problem is usually solved in PEG implementations by using an heuristic that helps to simulate the error reporting technique from top-down parsers.
Revised:  This problem is usually solved by using an heuristic that helps to simulate the error reporting technique from top-down parsers.
Edit intent: clarity
Original:  We show how implementations that have semantic actions can have grammars that use this heuristic even if the implementation does not implement it direcly .
Revised:  We show how implementations that have semantic actions can use this heuristic even if the implementation does not implement it direcly .
Edit intent: clarity
Original:  We show how implementations that have semantic actions can have grammars that use this heuristic even if the implementation does not implement it direcly .
Revised:  We show how implementations that have semantic actions can have grammars that use this heuristic even if the implementation does not implement it directly .
Edit intent: fluency
Original:  We also propose a complementary error reporting strategy that can lead to better error messages: labeled failures.
Revised:  We also propose a complementary error reporting strategy that may lead to better error messages: labeled failures.
Edit intent: clarity
Original: Parsing Expression Grammars (PEGs) are a formalism to describe a top-down parser for a language .
Revised: Parsing Expression Grammars (PEGs) describe top-down parser for a language .
Edit intent: clarity
Original: Parsing Expression Grammars (PEGs) are a formalism to describe a top-down parser for a language .
Revised: Parsing Expression Grammars (PEGs) are a formalism to describe a top-down parsers .
Edit intent: clarity
Original:  Unfortunately, error handling techniques that are often applied to top-down parsers are not directly applicable to PEGs.
Revised:  Unfortunately, the error-reporting techniques used in conventional top-down parsers are not directly applicable to PEGs.
Edit intent: clarity
Original:  This approach is inspired by standard exception handling of programming languages, and lets a PEG define different kinds of failure, with each ordered choice operator specifying which kinds it catches.
Revised:  This approach is inspired by exception handling of programming languages, and lets a PEG define different kinds of failure, with each ordered choice operator specifying which kinds it catches.
Edit intent: clarity
Original:  Labeled failures not only give a way to annotate grammars for better error reporting, but also are expressive enough to express some of the error reporting strategies used by deterministic parser combinators, and give a way of encoding predictive top-down parsing in a PEG.
Revised:  Labeled failures give a way to annotate grammars for better error reporting, but also are expressive enough to express some of the error reporting strategies used by deterministic parser combinators, and give a way of encoding predictive top-down parsing in a PEG.
Edit intent: coherence
Original:  Labeled failures not only give a way to annotate grammars for better error reporting, but also are expressive enough to express some of the error reporting strategies used by deterministic parser combinators, and give a way of encoding predictive top-down parsing in a PEG.
Revised:  Labeled failures not only give a way to annotate grammars for better error reporting, to express some of the error reporting strategies used by deterministic parser combinators, and give a way of encoding predictive top-down parsing in a PEG.
Edit intent: coherence
Original:  Labeled failures not only give a way to annotate grammars for better error reporting, but also are expressive enough to express some of the error reporting strategies used by deterministic parser combinators, and give a way of encoding predictive top-down parsing in a PEG.
Revised:  Labeled failures not only give a way to annotate grammars for better error reporting, but also are expressive enough to express some of the error reporting strategies used by deterministic parser combinators, and to encode predictive top-down parsing in a PEG.
Edit intent: fluency
Original:  On the other hand, we show that the tight quadratic gap between Las Vegas realtime probabilistic automata and realtime deterministic automata given for language recognition can be replaced with a tight exponential gap on promise problems.
Revised:  Second, despite of the existing quadratic gap between Las Vegas realtime probabilistic automata and realtime deterministic automata given for language recognition can be replaced with a tight exponential gap on promise problems.
Edit intent: coherence
Original:  On the other hand, we show that the tight quadratic gap between Las Vegas realtime probabilistic automata and realtime deterministic automata given for language recognition can be replaced with a tight exponential gap on promise problems.
Revised:  On the other hand, we show that the tight quadratic gap between Las Vegas realtime probabilistic automata and one-way deterministic automata for language recognition can be replaced with a tight exponential gap on promise problems.
Edit intent: clarity
Original:  Similar to quantum case, we present a probabilistically very cheap family of unary promise problems , i.e. solvable by a 2-state automaton with bounded-error.
Revised:  We present a family of unary promise problems , i.e. solvable by a 2-state automaton with bounded-error.
Edit intent: coherence
Original:  Then, we show that this family is not cheap for any of the aforementioned classical models . Moreover, we show that  bounded-error probabilistic automata are more powerful than any other classical model on promise problems .
Revised:  Then, we show that this family is not cheap for any of the aforementioned classical models . Moreover, we show that bounded-error probabilistic automata are more powerful than any other classical model .
Edit intent: clarity
Original:  This was first proved by Blais et al. (2008) via a more involved and general argument.
Revised:  This was first proved by Blais et al. (2008) via a more involved argument.
Edit intent: clarity
Original: In this paper, we show an O(1.415^n)-time exact algorithm for the feasibility problem of 0-1 integer programs whose constraints are only linear equalities .
Revised: In this paper, we show O(1.415^n)-time exact algorithm for the feasibility problem of 0-1 integer programs whose constraints are only linear equalities .
Edit intent: clarity
Original:  The algorithm is quadratically faster than exhaustive search and also almost quadratically faster than the algorithm for an inequality version of the feasibility problem by Impagliazzo, Lovett, Paturi and Schneider (arXiv:1401.5512), which motivated our work.
Revised:  The algorithm is quadratically faster than exhaustive search and almost quadratically faster than the algorithm for an inequality version of the feasibility problem by Impagliazzo, Lovett, Paturi and Schneider (arXiv:1401.5512), which motivated our work.
Edit intent: clarity
Original:  The algorithm is quadratically faster than exhaustive search and also almost quadratically faster than the algorithm for an inequality version of the feasibility problem by Impagliazzo, Lovett, Paturi and Schneider (arXiv:1401.5512), which motivated our work.
Revised:  The algorithm is quadratically faster than exhaustive search and also almost quadratically faster than an algorithm for an inequality version of the feasibility problem by Impagliazzo, Lovett, Paturi and Schneider (arXiv:1401.5512), which motivated our work.
Edit intent: fluency
Original:  The algorithm is quadratically faster than exhaustive search and also almost quadratically faster than the algorithm for an inequality version of the feasibility problem by Impagliazzo, Lovett, Paturi and Schneider (arXiv:1401.5512), which motivated our work.
Revised:  The algorithm is quadratically faster than exhaustive search and also almost quadratically faster than the algorithm for an inequality version of the problem by Impagliazzo, Lovett, Paturi and Schneider (arXiv:1401.5512), which motivated our work.
Edit intent: clarity
Original:  We also extend our algorithm to the optimization problem of 0-1 integer programs with linear equality constraints .
Revised:  Specifically, we extend our algorithms to linear optimization problems .
Edit intent: coherence
Original:  We further demonstrate that when we consider the sampling distribution as an asymptotic expansion in inverse powers of the recombination parameter, the sampling distributions of the two models agree with the standard ones up to the first two orders.
Revised:  We further demonstrate that when we consider the sampling distribution as an asymptotic expansion in inverse powers of the recombination parameter, the sampling distributions of the new models agree with the standard ones up to the first two orders.
Edit intent: clarity
Original:  We show that the probability of spontaneous service adoption is constant, the probability of adoption via social influence is linearly proportional to the fraction of adopting neighbours, and the probability of service termination is time-invariant and independent of the behaviour of peers.
Revised:  We show that the rate of spontaneous service adoption is constant, the probability of adoption via social influence is linearly proportional to the fraction of adopting neighbours, and the probability of service termination is time-invariant and independent of the behaviour of peers.
Edit intent: clarity
Original:  We show that the probability of spontaneous service adoption is constant, the probability of adoption via social influence is linearly proportional to the fraction of adopting neighbours, and the probability of service termination is time-invariant and independent of the behaviour of peers.
Revised:  We show that the probability of spontaneous service adoption is constant, the probability of adoption via social influence is linearly proportional to the fraction of adopting neighbours, and the rate of service termination is time-invariant and independent of the behaviour of peers.
Edit intent: clarity
Original: A path in an edge-colored graph G is rainbow if no two edges of it are colored the same.
Revised: A path in an edge-colored graph G is rainbow if no two edges of it are colored the same.
Edit intent: fluency
Original:  The graph G is rainbow colored if there is a rainbow path between every pair of vertices.
Revised:  The graph G is rainbow colored if there is a rainbow path between every pair of vertices.
Edit intent: fluency
Original:  If there is a rainbow shortest path between every pair of vertices, the graph G is strong rainbow colored \textit{ .
Revised:  If there is a rainbow shortest path between every pair of vertices, the graph G is \textit{ .
Edit intent: clarity
Original:  The minimum number of colors needed to make G rainbow colored is known as the rainbow connection number , and is denoted by \text{rc \rc (G).
Revised:  The minimum number of colors needed to make G rainbow colored is known as the rainbow connection number , and is denoted by \text{rc \rc (G).
Edit intent: fluency
Original:  The minimum number of colors needed to make G rainbow colored is known as the rainbow connection number , and is denoted by \text{rc \rc (G).
Revised:  The minimum number of colors needed to make G rainbow colored is known as the rainbow connection number , and is denoted by \rc (G).
Edit intent: coherence
Original:  The minimum number of colors needed to make G strong rainbow colored is known as the strong rainbow connection number , and is denoted by \text{src \src (G).
Revised:  The minimum number of colors needed to make G strong rainbow colored is known as the strong rainbow connection number , and is denoted by \text{src \src (G).
Edit intent: fluency
Original:  The minimum number of colors needed to make G strong rainbow colored is known as the strong rainbow connection number , and is denoted by \text{src \src (G).
Revised:  The minimum number of colors needed to make G strong rainbow colored is known as the strong rainbow connection number , and is denoted by \src (G).
Edit intent: fluency
Original:  A graph is chordal if it contains no induced cycle of length 4 or more.
Revised:  A graph is chordal if it contains no induced cycle of length 4 or more.
Edit intent: fluency
Original:  We consider the rainbow and strong rainbow connection numbers of block graphs , which form a subclass of chordal graphs.
Revised:  We consider the rainbow and strong rainbow connection numbers of block graphs , which form a subclass of chordal graphs.
Edit intent: fluency
Original:  We give an exact linear time algorithm for strong rainbow coloring block graphs exploiting a clique tree representation each chordal graph has.
Revised:  We give an exact linear time algorithm for strong rainbow coloring block graphs exploiting a clique tree representation each chordal graph has.
Edit intent: fluency
Original:  For every k \geq 2, deciding whether%DIFDELCMD < \rc%%% (G) \leq k is known to be%DIFDELCMD < \NP%%% -complete for chordal graphs .
Revised:  For every k \geq 2, deciding whether%DIFDELCMD < \rc%%% %DIFDELCMD < \NP%%% -complete for chordal graphs .
Edit intent: clarity
Original:  If there is a rainbow shortest path between every pair of vertices, the graph G is \textit{strong rainbow colored \emph{ .
Revised:  If there is a rainbow shortest path between every pair of vertices, the graph G is \textit{ \emph{ .
Edit intent: clarity
Original:  If there is a rainbow shortest path between every pair of vertices, the graph G is \textit{strong rainbow colored \emph{ .
Revised:  If there is a rainbow shortest path between every pair of vertices, the graph G is \textit{strong rainbow colored \emph{strong rainbow colored .
Edit intent: fluency
Original:  The minimum number of colors needed to make G rainbow colored is known as the rainbow connection number , and is denoted by \rc(G).
Revised:  The minimum number of colors needed to make G rainbow colored is known as the rainbow connection number , and is denoted by \rc(G).
Edit intent: fluency
Original:  The minimum number of colors needed to make G strong rainbow colored is known as the strong rainbow connection number , and is denoted by \src(G).
Revised:  Similarly, the minimum number of colors needed to make G strong rainbow colored is known as the strong rainbow connection number , and is denoted by \src(G).
Edit intent: coherence
Original:  The minimum number of colors needed to make G strong rainbow colored is known as the strong rainbow connection number , and is denoted by \src(G).
Revised:  The minimum number of colors needed to make G strong rainbow colored is known as the strong rainbow connection number , and is denoted by \src(G).
Edit intent: fluency
Original:  A graph ischordal if it contains no induced cycle of length 4 or more.
Revised:  chordal if it contains no induced cycle of length 4 or more.
Edit intent: clarity
Original:  A graph ischordal if it contains no induced cycle of length 4 or more.
Revised:  A graph is if it contains no induced cycle of length 4 or more.
Edit intent: clarity
Original:  We show that for every k \geq 3, deciding whether a chordal graph can be strong rainbow colored using k colors is \src \NP-complete  for any \epsilon > 0 unless \P = }\NP . We then consider the rainbow and strong rainbow connection numbers of block graphs , which form a subclass of chordal graphs.
Revised:  We show that for every k \geq 3, deciding whether \src \NP-complete for any \epsilon > 0 unless \P = }\NP . We then consider the rainbow and strong rainbow connection numbers of block graphs , which form a subclass of chordal graphs.
Edit intent: clarity
Original:  We show that for every k \geq 3, deciding whether a chordal graph can be strong rainbow colored using k colors is \src \NP-complete  for any \epsilon > 0 unless \P = }\NP . We then consider the rainbow and strong rainbow connection numbers of block graphs , which form a subclass of chordal graphs.
Revised:  We show that for every k \geq 3, deciding whether a chordal graph can be strong rainbow colored using k colors is \src \NP-complete for any \epsilon > 0 unless \P = }\NP . We then consider the rainbow and strong rainbow connection numbers of , which form a subclass of chordal graphs.
Edit intent: clarity
Original:  We show that for every k \geq 3, deciding whether a chordal graph can be strong rainbow colored using k colors is \src \NP-complete  for any \epsilon > 0 unless \P = }\NP . We then consider the rainbow and strong rainbow connection numbers of block graphs , which form a subclass of chordal graphs.
Revised:  We show that for every k \geq 3, deciding whether a chordal graph can be strong rainbow colored using k colors is \src \NP-complete for any \epsilon > 0 unless \P = }\NP . We then consider the rainbow and strong rainbow connection numbers of block graphs block graphs, which also form a subclass of chordal graphs.
Edit intent: clarity
Original:  We characterize the bridgeless block graphs having rainbow connection number 2, 3, or 4, and show that for every k \leq 4, it is in \P to decide whether%DIFDELCMD < \rc%%% (G) = k, where G is a bridgeless block graph.
Revised:  We %DIFDELCMD < \rc%%% (G) = k, where G is a bridgeless block graph.
Edit intent: coherence
Original:  If there is a rainbow shortest path between every pair of vertices, the graph G is \emph{strong rainbow colored .
Revised:  If there is a rainbow shortest path between every pair of vertices, the graph G is \emph{strongly rainbow-connected .
Edit intent: clarity
Original:  The minimum number of colors needed to make G rainbow colored is known as the rainbow connection number , and is denoted by %DIFDELCMD < \rc%%%  (G).
Revised:  The minimum number of colors needed to make G rainbow-connected is known as the rainbow connection number , and is denoted by %DIFDELCMD < \rc%%% (G).
Edit intent: clarity
Original:  The minimum number of colors needed to make G rainbow colored is known as the rainbow connection number , and is denoted by %DIFDELCMD < \rc%%%  (G).
Revised:  The minimum number of colors needed to make G rainbow colored is known as the rainbow connection number of G , and is denoted by %DIFDELCMD < \rc%%% (G).
Edit intent: clarity
Original:  Similarly, the minimum number of colors needed to make G strong rainbow colored is known as the strong rainbow connection number , and is denoted by %DIFDELCMD < \src%%%  (G).
Revised:  Similarly, the minimum number of colors needed to make G strongly rainbow-connected is known as the strong rainbow connection number , and is denoted by %DIFDELCMD < \src%%% (G).
Edit intent: clarity
Original:  Similarly, the minimum number of colors needed to make G strong rainbow colored is known as the strong rainbow connection number , and is denoted by %DIFDELCMD < \src%%%  (G).
Revised:  Similarly, the minimum number of colors needed to make G strong rainbow colored is known as the strong rainbow connection number of G , and is denoted by %DIFDELCMD < \src%%% (G).
Edit intent: clarity
Original:  Furthermore, there exists no polynomial time algorithm for approximating the strong rainbow connection number of an n-vertex split graph with a factor of n^{1/2-\epsilon} for any \epsilon > 0 unless \P = %DIFDELCMD < \NP%%%  . We then consider the rainbow and strong rainbow connection numbers of block graphs, which also form a subclass of chordal graphs.
Revised:  Furthermore, there exists no polynomial-time algorithm for approximating the strong rainbow connection number of an n-vertex split graph with a factor of n^{1/2-\epsilon} for any \epsilon > 0 unless \P = %DIFDELCMD < \NP%%% . We then consider the rainbow and strong rainbow connection numbers of block graphs, which also form a subclass of chordal graphs.
Edit intent: fluency
Original:  Furthermore, there exists no polynomial time algorithm for approximating the strong rainbow connection number of an n-vertex split graph with a factor of n^{1/2-\epsilon} for any \epsilon > 0 unless \P = %DIFDELCMD < \NP%%%  . We then consider the rainbow and strong rainbow connection numbers of block graphs, which also form a subclass of chordal graphs.
Revised:  Furthermore, there exists no polynomial time algorithm for approximating the strong rainbow connection number of an n-vertex split graph with a factor of n^{1/2-\epsilon} for any \epsilon > 0 unless P = %DIFDELCMD < \NP%%% . We then consider the rainbow and strong rainbow connection numbers of block graphs, which also form a subclass of chordal graphs.
Edit intent: fluency
Original:  Furthermore, there exists no polynomial time algorithm for approximating the strong rainbow connection number of an n-vertex split graph with a factor of n^{1/2-\epsilon} for any \epsilon > 0 unless \P = %DIFDELCMD < \NP%%%  . We then consider the rainbow and strong rainbow connection numbers of block graphs, which also form a subclass of chordal graphs.
Revised:  Furthermore, there exists no polynomial time algorithm for approximating the strong rainbow connection number of an n-vertex split graph with a factor of n^{1/2-\epsilon} for any \epsilon > 0 unless \P = %DIFDELCMD < \NP%%% NP . We then consider the rainbow and strong rainbow connection numbers of block graphs, which also form a subclass of chordal graphs.
Edit intent: clarity
Original:  Furthermore, there exists no polynomial time algorithm for approximating the strong rainbow connection number of an n-vertex split graph with a factor of n^{1/2-\epsilon} for any \epsilon > 0 unless \P = %DIFDELCMD < \NP%%%  . We then consider the rainbow and strong rainbow connection numbers of block graphs, which also form a subclass of chordal graphs.
Revised:  Furthermore, there exists no polynomial time algorithm for approximating the strong rainbow connection number of an n-vertex split graph with a factor of n^{1/2-\epsilon} for any \epsilon > 0 unless \P = %DIFDELCMD < \NP%%% . We then turn our attention to block graphs, which also form a subclass of chordal graphs.
Edit intent: clarity
Original:  In consequence, the difficulty of Jaeger's directed cycle double cover conjecture lies in discovering and overcoming implicit obstacles, which have an unknown and, so far, in any attempt of defining them, complex structure .
Revised:  One of the difficulties in proving the Jaeger's directed cycle double cover conjecture lies in discovering and overcoming implicit obstacles, which have an unknown and, so far, in any attempt of defining them, complex structure .
Edit intent: clarity
Original:  In consequence, the difficulty of Jaeger's directed cycle double cover conjecture lies in discovering and overcoming implicit obstacles, which have an unknown and, so far, in any attempt of defining them, complex structure .
Revised:  In consequence, the difficulty of Jaeger's conjecture lies in discovering and overcoming implicit obstacles, which have an unknown and, so far, in any attempt of defining them, complex structure .
Edit intent: coherence
Original:  We formulate a conjecture on graph connections, whose validity follows by the successful avoidance of an explicit cut-type obstacle that we call "cut-obstacle" .
Revised:  We formulate a conjecture on graph connections, whose validity follows by the successful avoidance of one cut-type obstacle that we call "cut-obstacle" .
Edit intent: clarity
Original:  We formulate a conjecture on graph connections, whose validity follows by the successful avoidance of an explicit cut-type obstacle that we call "cut-obstacle" .
Revised:  We formulate a conjecture on graph connections, whose validity follows by the successful avoidance of an explicit cut-type obstruction that we call "cut-obstacle" .
Edit intent: fluency