wanyu/IteraTeR_v2 huggingface dataset:
Original:  Next we consider the synchronization of reachable partial automata that has application for splicing systems in the theory of computational biology.
Revised:  After that we consider the synchronization of reachable partial automata that has application for splicing systems in the theory of computational biology.
Edit intent: coherence
Original:  Next we consider the synchronization of reachable partial automata that has application for splicing systems in the theory of computational biology.
Revised:  Next we consider the synchronization of reachable partial automata that has application for splicing systems in computational biology.
Edit intent: clarity
Original:  First we generalize results from  RandSynch,On2Problems for the case of strongly connected partial automata.
Revised:  First we generalize results from ~ RandSynch,On2Problems for the case of strongly connected partial automata.
Edit intent: fluency
Original:  First we generalize results from ~ RandSynch,On2Problems for the case of strongly connected partial automata.
Revised:  First we generalize results from RandSynch,On2Problems for the case of strongly connected partial automata.
Edit intent: fluency
Original: We consider the problem of characterizing isomorphisms of types, or equivalently constructive cardinality of sets, in  simultaneous presence of disjoint unions, Cartesian products, and exponentials.
Revised: We consider the problem of characterizing isomorphisms of types, or , equivalently, constructive cardinality of sets, in simultaneous presence of disjoint unions, Cartesian products, and exponentials.
Edit intent: fluency
Original: We consider the problem of characterizing isomorphisms of types, or equivalently constructive cardinality of sets, in  simultaneous presence of disjoint unions, Cartesian products, and exponentials.
Revised: We consider the problem of characterizing isomorphisms of types, or equivalently constructive cardinality of sets, in the simultaneous presence of disjoint unions, Cartesian products, and exponentials.
Edit intent: fluency
Original:  Mostly relying on classic results concerning polynomials with exponentiation that have not been used in our context, we derive: that the usual finite axiomatization known as High School Identities (HSI) is complete for a significant subclass of types;
Revised:  Mostly relying on results about polynomials with exponentiation that have not been used in our context, we derive: that the usual finite axiomatization known as High School Identities (HSI) is complete for a significant subclass of types;
Edit intent: clarity
Original:  Mostly relying on classic results concerning polynomials with exponentiation that have not been used in our context, we derive: that the usual finite axiomatization known as High School Identities (HSI) is complete for a significant subclass of types;
Revised:  Mostly relying on classic results concerning polynomials with exponentiation that have not been used in our context, we derive: that the usual finite axiomatization known as High-School Identities (HSI) is complete for a significant subclass of types;
Edit intent: fluency
Original:  and that, for the whole of the set of types, the question  whether two types are isomorphic is decidable , that is, at least when base types are to be interpreted by finite sets.
Revised:  and that, for the whole of the set of types, the question as to whether two types are isomorphic is decidable , that is, at least when base types are to be interpreted by finite sets.
Edit intent: clarity
Original:  and that, for the whole of the set of types, the question  whether two types are isomorphic is decidable , that is, at least when base types are to be interpreted by finite sets.
Revised:  and that, for the whole of the set of types, the question whether two types are isomorphic is decidable when base types are to be interpreted by finite sets.
Edit intent: coherence
Original:  and that, for the whole of the set of types, the question  whether two types are isomorphic is decidable , that is, at least when base types are to be interpreted by finite sets.
Revised:  and that, for the whole of the set of types, the question whether two types are isomorphic is decidable , that is, at least when base types are to be interpreted as finite sets.
Edit intent: fluency
Original:  The recently developed Cooperative Patent Classifications (CPC) of the U.S. Patent and Trade Office (USPTO) and the European Patent Office (EPO) provide new options for a precise delineation of samples in both USPTO data and the worldwide patent database PatStat of EPO.
Revised:  The recently developed Cooperative Patent Classifications (CPC) of the U.S. Patent and Trade Office (USPTO) and the European Patent Office (EPO) provide new options for a precise delineation of samples in both USPTO data and the Worldwide Patent Statistics Database (PatStat) of EPO.
Edit intent: clarity
Original:  We show that in comparison to a global multilinear model, our model better preserves fine detail and is computationally faster, while in comparison to a localized PCA model, our model better handles variation in expression, is faster, and allows us to fix identity parameters  .
Revised:  We show that in comparison to a global multilinear model, our model better preserves fine detail and is computationally faster, while in comparison to a localized PCA model, our model better handles variation in expression, is faster, and allows us to fix identity parameters for a given subject .
Edit intent: clarity
Original: Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors studied in 2004  the computational power of quantum interactive proof systems whose verifiers are particularly limited to quantum finite automata.
Revised: Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors initiated in 2004 the computational power of quantum interactive proof systems whose verifiers are particularly limited to quantum finite automata.
Edit intent: clarity
Original: Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors studied in 2004  the computational power of quantum interactive proof systems whose verifiers are particularly limited to quantum finite automata.
Revised: Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors studied in 2004 a study on the computational power of quantum interactive proof systems whose verifiers are particularly limited to quantum finite automata.
Edit intent: clarity
Original:  As a follow-up to this early study, ] we further investigate the quantum nature of interactions between provers and verifiers by studying how various restrictions on quantum interactive proof systems affect the language recognition power of  systems.
Revised:  As a follow-up to this early study, ], we further investigate the quantum nature of interactions between provers and verifiers by studying how various restrictions on quantum interactive proof systems affect the language recognition power of systems.
Edit intent: fluency
Original:  As a follow-up to this early study, ] we further investigate the quantum nature of interactions between provers and verifiers by studying how various restrictions on quantum interactive proof systems affect the language recognition power of  systems.
Revised:  As a follow-up to this early study, ] we further investigate the quantum nature of interactions between provers and verifiers by studying how various restrictions on quantum interactive proof systems affect the language recognition power of the proof systems.
Edit intent: clarity
Original:  In particular, we examine three intriguing restrictions for which (i) provers always behave in a classical fashion, (ii) verifiers always reveal  the information on next moves to provers , and (iii) the number of interactions between provers and verifiers is bounded.
Revised:  In particular, we examine three intriguing restrictions that (i) provers always behave in a classical fashion, (ii) verifiers always reveal the information on next moves to provers , and (iii) the number of interactions between provers and verifiers is bounded.
Edit intent: clarity
Original:  In particular, we examine three intriguing restrictions for which (i) provers always behave in a classical fashion, (ii) verifiers always reveal  the information on next moves to provers , and (iii) the number of interactions between provers and verifiers is bounded.
Revised:  In particular, we examine three intriguing restrictions for which (i) provers always behave in a classical fashion, (ii) verifiers always reveal to provers the information on next moves to provers , and (iii) the number of interactions between provers and verifiers is bounded.
Edit intent: fluency
Original:  In particular, we examine three intriguing restrictions for which (i) provers always behave in a classical fashion, (ii) verifiers always reveal  the information on next moves to provers , and (iii) the number of interactions between provers and verifiers is bounded.
Revised:  In particular, we examine three intriguing restrictions for which (i) provers always behave in a classical fashion, (ii) verifiers always reveal the information on next moves , and (iii) the number of interactions between provers and verifiers is bounded.
Edit intent: clarity
Original:  The running time of this algorithm is O(n \cdot h \cdot \mbox{diam (P)) where n is the number of vertices, h is the number of obstacles and \mbox{diam (P) is the diameter of P.
Revised:  The running time of this algorithm is O(n \cdot h \cdot diam (P)) where n is the number of vertices, h is the number of obstacles and \mbox{diam (P) is the diameter of P.
Edit intent: fluency
Original:  The running time of this algorithm is O(n \cdot h \cdot \mbox{diam (P)) where n is the number of vertices, h is the number of obstacles and \mbox{diam (P) is the diameter of P.
Revised:  The running time of this algorithm is O(n \cdot h \cdot \mbox{diam (P)) where n is the number of vertices, h is the number of obstacles and diam (P) is the diameter of P.
Edit intent: fluency
Original: In this paper, we investigate the use of N cognitive relays to assist primary and secondary transmissions in a time-slotted cognitive setting with one primary user (PU) and one secondary user (SU) . We propose an overlapped spectrum sensing strategy  for channel sensing, where the SU senses the channel for \tau seconds from the beginning of the time slot and the cognitive relays sense the channel for 2 \tau seconds from the beginning of the time slot .
Revised: The use of N cognitive relays to assist primary and secondary transmissions in a time-slotted cognitive setting with one primary user (PU) and one secondary user (SU) . We propose an overlapped spectrum sensing strategy for channel sensing, where the SU senses the channel for \tau seconds from the beginning of the time slot and the cognitive relays sense the channel for 2 \tau seconds from the beginning of the time slot .
Edit intent: clarity
Original: In this paper, we investigate the use of N cognitive relays to assist primary and secondary transmissions in a time-slotted cognitive setting with one primary user (PU) and one secondary user (SU) . We propose an overlapped spectrum sensing strategy  for channel sensing, where the SU senses the channel for \tau seconds from the beginning of the time slot and the cognitive relays sense the channel for 2 \tau seconds from the beginning of the time slot .
Revised: In this paper, we investigate the use of N cognitive relays to assist primary and secondary transmissions in a time-slotted cognitive setting with one primary user (PU) and one secondary user (SU) is investigated. An overlapped spectrum sensing strategy for channel sensing, where the SU senses the channel for \tau seconds from the beginning of the time slot and the cognitive relays sense the channel for 2 \tau seconds from the beginning of the time slot .
Edit intent: clarity
Original: In this paper, we investigate the use of N cognitive relays to assist primary and secondary transmissions in a time-slotted cognitive setting with one primary user (PU) and one secondary user (SU) . We propose an overlapped spectrum sensing strategy  for channel sensing, where the SU senses the channel for \tau seconds from the beginning of the time slot and the cognitive relays sense the channel for 2 \tau seconds from the beginning of the time slot .
Revised: In this paper, we investigate the use of N cognitive relays to assist primary and secondary transmissions in a time-slotted cognitive setting with one primary user (PU) and one secondary user (SU) . We propose an overlapped spectrum sensing strategy is proposed for channel sensing, where the SU senses the channel for \tau seconds from the beginning of the time slot and the cognitive relays sense the channel for 2 \tau seconds from the beginning of the time slot .
Edit intent: clarity
Original:  The relays help  the PU and the SU to deliver their undelivered packets and transmit when both the PU and the SU are idle.
Revised:  The relays help both the PU and the SU to deliver their undelivered packets and transmit when both the PU and the SU are idle.
Edit intent: fluency
Original:  The relays help  the PU and the SU to deliver their undelivered packets and transmit when both the PU and the SU are idle.
Revised:  The relays help the PU and SU to deliver their undelivered packets and transmit when both the PU and the SU are idle.
Edit intent: fluency
Original:  The relays help  the PU and the SU to deliver their undelivered packets and transmit when both the PU and the SU are idle.
Revised:  The relays help the PU and the SU to deliver their undelivered packets and transmit when both are idle.
Edit intent: fluency
Original:  We study two optimization-based formulations with quality of service (QoS) constraints involving queueing delay .
Revised:  Two optimization-based formulations with quality of service (QoS) constraints involving queueing delay .
Edit intent: clarity
Original:  We study two optimization-based formulations with quality of service (QoS) constraints involving queueing delay .
Revised:  We study two optimization-based formulations with quality of service constraints involving queueing delay .
Edit intent: clarity
Original:  We also investigate three packet decoding strategies at the relays and compare their performance .
Revised:  Three packet decoding strategies at the relays and compare their performance .
Edit intent: clarity
Original:  We also investigate three packet decoding strategies at the relays and compare their performance .
Revised:  We also investigate three packet decoding strategies at the relays are also investigated and their performance is compared .
Edit intent: clarity
Original:  We present here a research program seeking to build the foundations of biology  in terms of elements, logic and principles, using both the language and the general methods employed in other disciplines.
Revised:  We present here a research program seeking to build the foundations of biology . The foundations of biology are built in terms of elements, logic and principles, using both the language and the general methods employed in other disciplines.
Edit intent: clarity
Original:  Here we evaluate consequences of aviaian morphology for aerial performance (1,2) by quantifying static stability and control effectiveness of physical models (3) for numerous taxa sampled from within the lineage leading to birds ( Avialae , 4).
Revised:  Here we evaluate consequences of aviaian morphology for aerial performance (1,2) by quantifying static stability and control effectiveness of physical models (3) for numerous taxa sampled from within the lineage leading to birds ( Paraves , 4).
Edit intent: clarity
Original:  The timing of shifts suggests features normally considered in light of development of a power stroke also play important roles in control.
Revised:  The timing of shifts also suggests some features normally considered in light of development of a power stroke also play important roles in control.
Edit intent: clarity
Original:  The timing of shifts suggests features normally considered in light of development of a power stroke also play important roles in control.
Revised:  The timing of shifts suggests features normally considered in light of development of a power stroke may play important roles in control.
Edit intent: clarity
Original: In this paper we show that %DIFDELCMD < \omegaB%%% - and%DIFDELCMD < \omegaS%%% -regular {  languages satisfy the following separation-type theorem If L_1,L_2 are disjoint languages of \omega -words both recognised by %DIFDELCMD < \omegaB%%% -  (resp. %DIFDELCMD < \omegaS%%%   )-automata then there exists an \omega -regular language L_{\mathrm{sep} such that }%DIFDELCMD < \[L_1\subseteq %DIFDELCMD < L_{\mathrm{sep}}\quad\mathrm{and}\quad L_2\subseteq L_{\mathrm{sep}}^c.
Revised: In this paper we show that %DIFDELCMD < \omegaB%%% %DIFDELCMD < \omegaS%%% -regular { languages satisfy the following separation-type theorem If L_1,L_2 are disjoint languages of \omega -words both recognised by %DIFDELCMD < \omegaB%%% - (resp. %DIFDELCMD < \omegaS%%% )-automata then there exists an \omega -regular language L_{\mathrm{sep} such that }%DIFDELCMD < \[L_1\subseteq %DIFDELCMD < L_{\mathrm{sep}}\quad\mathrm{and}\quad L_2\subseteq L_{\mathrm{sep}}^c.
Edit intent: coherence
Original: In this paper we show that %DIFDELCMD < \omegaB%%% - and%DIFDELCMD < \omegaS%%% -regular {  languages satisfy the following separation-type theorem If L_1,L_2 are disjoint languages of \omega -words both recognised by %DIFDELCMD < \omegaB%%% -  (resp. %DIFDELCMD < \omegaS%%%   )-automata then there exists an \omega -regular language L_{\mathrm{sep} such that }%DIFDELCMD < \[L_1\subseteq %DIFDELCMD < L_{\mathrm{sep}}\quad\mathrm{and}\quad L_2\subseteq L_{\mathrm{sep}}^c.
Revised: In this paper we show that %DIFDELCMD < \omegaB%%% - and%DIFDELCMD < \omegaS%%% -regular { languages satisfy the following separation-type theorem If L1,L2 are disjoint languages of \omega -words both recognised by %DIFDELCMD < \omegaB%%% - (resp. %DIFDELCMD < \omegaS%%% )-automata then there exists an \omega -regular language L_{\mathrm{sep} such that }%DIFDELCMD < \[L_1\subseteq %DIFDELCMD < L_{\mathrm{sep}}\quad\mathrm{and}\quad L_2\subseteq L_{\mathrm{sep}}^c.
Edit intent: fluency
Original: In this paper we show that %DIFDELCMD < \omegaB%%% - and%DIFDELCMD < \omegaS%%% -regular {  languages satisfy the following separation-type theorem If L_1,L_2 are disjoint languages of \omega -words both recognised by %DIFDELCMD < \omegaB%%% -  (resp. %DIFDELCMD < \omegaS%%%   )-automata then there exists an \omega -regular language L_{\mathrm{sep} such that }%DIFDELCMD < \[L_1\subseteq %DIFDELCMD < L_{\mathrm{sep}}\quad\mathrm{and}\quad L_2\subseteq L_{\mathrm{sep}}^c.
Revised: In this paper we show that %DIFDELCMD < \omegaB%%% - and%DIFDELCMD < \omegaS%%% -regular { languages satisfy the following separation-type theorem If L_1,L_2 are disjoint languages of \omega -words both recognised by %DIFDELCMD < \omegaB%%% - (resp. %DIFDELCMD < \omegaS%%% )-automata then there exists an \omega -regular language L_{\mathrm{sep} such that }%DIFDELCMD < \[L_1\subseteq %DIFDELCMD < L_{\mathrm{sep}}\quad\mathrm{and}\quad L_2\subseteq L_{\mathrm{sep}}^c.
Edit intent: fluency
Original: In this paper we show that %DIFDELCMD < \omegaB%%% - and%DIFDELCMD < \omegaS%%% -regular {  languages satisfy the following separation-type theorem If L_1,L_2 are disjoint languages of \omega -words both recognised by %DIFDELCMD < \omegaB%%% -  (resp. %DIFDELCMD < \omegaS%%%   )-automata then there exists an \omega -regular language L_{\mathrm{sep} such that }%DIFDELCMD < \[L_1\subseteq %DIFDELCMD < L_{\mathrm{sep}}\quad\mathrm{and}\quad L_2\subseteq L_{\mathrm{sep}}^c.
Revised: In this paper we show that %DIFDELCMD < \omegaB%%% - and%DIFDELCMD < \omegaS%%% -regular { languages satisfy the following separation-type theorem If L_1,L_2 are disjoint languages of \omega -words both recognised by %DIFDELCMD < \omegaB%%% - B- (resp. %DIFDELCMD < \omegaS%%% )-automata then there exists an \omega -regular language L_{\mathrm{sep} such that }%DIFDELCMD < \[L_1\subseteq %DIFDELCMD < L_{\mathrm{sep}}\quad\mathrm{and}\quad L_2\subseteq L_{\mathrm{sep}}^c.
Edit intent: fluency
Original: In this paper we show that %DIFDELCMD < \omegaB%%% - and%DIFDELCMD < \omegaS%%% -regular {  languages satisfy the following separation-type theorem If L_1,L_2 are disjoint languages of \omega -words both recognised by %DIFDELCMD < \omegaB%%% -  (resp. %DIFDELCMD < \omegaS%%%   )-automata then there exists an \omega -regular language L_{\mathrm{sep} such that }%DIFDELCMD < \[L_1\subseteq %DIFDELCMD < L_{\mathrm{sep}}\quad\mathrm{and}\quad L_2\subseteq L_{\mathrm{sep}}^c.
Revised: In this paper we show that %DIFDELCMD < \omegaB%%% - and%DIFDELCMD < \omegaS%%% -regular { languages satisfy the following separation-type theorem If L_1,L_2 are disjoint languages of \omega -words both recognised by %DIFDELCMD < \omegaB%%% - (resp. %DIFDELCMD < \omegaS%%% )-automata then there exists an \omega -regular language } such that }%DIFDELCMD < \[L_1\subseteq %DIFDELCMD < L_{\mathrm{sep}}\quad\mathrm{and}\quad L_2\subseteq L_{\mathrm{sep}}^c.
Edit intent: fluency
Original: \] %DIFDELCMD < %%%  In particular, if a language and its complement are recognised by %DIFDELCMD < \omegaB%%% -  (resp. %DIFDELCMD < \omegaS%%%   )-automata then the language is \omega -regular.
Revised: \] %DIFDELCMD < %%% In particular, if a language and its complement are recognised by %DIFDELCMD < \omegaB%%% - (resp. %DIFDELCMD < \omegaS%%% )-automata then the language is \omega -regular.
Edit intent: fluency
Original:  Usually (e.g. in descriptive set theory or recursion theory) exactly one class from a pair \mathcal C, \mathcal C^c has the separation property.
Revised:  Usually (e.g. in descriptive set theory or recursion theory) exactly one class from a pair C, Cc has the separation property.
Edit intent: clarity
Original:  The proof technique reduces the separation property for \omega -word languages to profinite languages using Ramsey's theorem and topological methods.
Revised:  The proof technique reduces the separation property for \omega -word languages to profinite languages using Ramsey's theorem and topological methods.
Edit intent: fluency
Original: We develop a new framework for investigating linear equivalence of divisors on graphs using a generalization of Gioan's cocycle reversal system for partial orientations.
Revised: We develop a new framework for investigating linear equivalence of divisors on graphs using a generalization of Gioan's cycle-cocycle reversal system for partial orientations.
Edit intent: fluency
Original:  We then show that the Baker-Norine rank of a partially orientable divisor is one less than the minimum number of directed paths which need to be reversed in the generalized cocycle reversal system to produce an acyclic partial orientation.
Revised:  We then show that the Baker-Norine rank of a partially orientable divisor is one less than the minimum number of directed paths which need to be reversed in the generalized cycle-cocycle reversal system to produce an acyclic partial orientation.
Edit intent: fluency
Original:  We demonstrate that  max-flow min-cut  is equivalent to the Euler characteristic description of orientable divisors, and extend this characterization to the setting of partial orientations.
Revised:  We demonstrate that the max-flow min-cut is equivalent to the Euler characteristic description of orientable divisors, and extend this characterization to the setting of partial orientations.
Edit intent: fluency