wanyu/IteraTeR_v2 huggingface dataset:
Original: We consider the problem of determining whether a lacunary (also called a sparse or super-sparse) polynomial f is a perfect power, that is, f =h^r for some other polynomial h andr, and of finding h and rshould they exist.
Revised: We consider the problem of determining whether a lacunary (also called sparse or super-sparse) polynomial f is a perfect power, that is, f =h^r for some other polynomial h andr, and of finding h and rshould they exist.
Edit intent: fluency
Original:  We show how to determine if f is a perfect power in time polynomial in the number of non-zero terms of f , and in terms of log(deg (f) ), i.e., polynomial in the size of the lacunary representation .
Revised:  We show how to determine if f is a perfect power in time polynomial in the number of non-zero terms of f and in log(deg (f) ), i.e., polynomial in the size of the lacunary representation .
Edit intent: coherence
Original:  We show how to determine if f is a perfect power in time polynomial in the number of non-zero terms of f , and in terms of log(deg (f) ), i.e., polynomial in the size of the lacunary representation .
Revised:  We show how to determine if f is a perfect power in time polynomial in the number of non-zero terms of f , and in terms of log(deg f ), i.e., polynomial in the size of the lacunary representation .
Edit intent: clarity
Original:  The algorithm works over GF(q)[x] (for large characteristic) and over Z [x] , where the cost is also polynomial in log||f|| . We also give a Monte Carlo algorithm to find h if it exists, for which our proposed algorithm requires polynomial time in the output size, i. e., the sparsity and height of h. Conjectures of Erdosand Schinzel, and recent work of Zannier, suggest that h must be sparse.
Revised:  The algorithm works over GF(q)[x] (for large characteristic) and over Z [x] . We also give a Monte Carlo algorithm to find h if it exists, for which our proposed algorithm requires polynomial time in the output size, i. e., the sparsity and height of h. Conjectures of Erdosand Schinzel, and recent work of Zannier, suggest that h must be sparse.
Edit intent: clarity
Original:  We ] ]  ] demonstrate the efficiency of these algorithms with an implementation using the C++ library NTL.
Revised:  We ] x] ] demonstrate the efficiency of these algorithms with an implementation using the C++ library NTL.
Edit intent: fluency
Original:  We ] ]  ] demonstrate the efficiency of these algorithms with an implementation using the C++ library NTL.
Revised:  We ] ] x] demonstrate the efficiency of these algorithms with an implementation using the C++ library NTL.
Edit intent: fluency
Original:  We ] ]  ] demonstrate the efficiency of these algorithms with an implementation using the C++ library NTL.
Revised:  We ] ] ] demonstrate the efficiency of these algorithms with an implementation in the C++ library NTL.
Edit intent: fluency
Original:  The viability assumption imposed on the market model is significantly weaker than those appearing previously in the literature.
Revised:  The viability assumption imposed on the market model is weaker than those appearing previously in the literature.
Edit intent: clarity
Original:  The model is based on three principles: duality principle postulates that any element is a couple consisting of one identity and one entity, inclusion principle postulates that any element has a super-element within a hierarchy , and order principle assumes that any element has a number of greater elements within a partially ordered set.
Revised:  The model is based on three principles: duality principle postulates that any element is a couple consisting of one identity and one entity, inclusion principle postulates that any element has a super-element within a nested set , and order principle assumes that any element has a number of greater elements within a partially ordered set.
Edit intent: clarity
Original:  These three principles are combined within a new formal setting  , called nested partially ordered sets, which is a formal basis for CoM.
Revised:  A new formal setting , called nested partially ordered sets, which is a formal basis for CoM.
Edit intent: clarity
Original:  A novel concept-oriented query language ( CoQL ) is described which is based on a new data modeling construct, called concept, inclusion relation between concepts, and concept ordering using its field types representing greater concepts in a partially ordered set.
Revised:  A novel concept-oriented query language ( COQL ) is described which is based on a new data modeling construct, called concept, inclusion relation between concepts, and concept ordering using its field types representing greater concepts in a partially ordered set.
Edit intent: fluency
Original:  The model is based on three principles: duality principle postulates that any element is a couple consisting of one identity and one entity, inclusion principle postulates that any element has a super-element within a nested set , and order principle assumes that any element has a number of greater elements within a partially ordered set.
Revised:  The model is based on three principles: duality principle postulates that any element is a couple consisting of one identity and one entity, inclusion principle postulates that any element has a super-element , and order principle assumes that any element has a number of greater elements within a partially ordered set.
Edit intent: clarity
Original:  The model is based on three principles: duality principle postulates that any element is a couple consisting of one identity and one entity, inclusion principle postulates that any element has a super-element within a nested set , and order principle assumes that any element has a number of greater elements within a partially ordered set.
Revised:  The model is based on three principles: duality principle postulates that any element is a couple consisting of one identity and one entity, inclusion principle postulates that any element has a super-element within a nested set , and order principle assumes that any element has a number of greater elements while all elements exist in a partially ordered set.
Edit intent: clarity
Original: In this paper we present a new approach to data modeling, called the concept-oriented model (COM), and a novel concept-oriented query language (COQL).
Revised: We describe a new approach to data modeling, called the concept-oriented model (COM), and a novel concept-oriented query language (COQL).
Edit intent: clarity
Original:  The model is based on three principles: duality principle postulates that any element is a couple consisting of one identity and one entity, inclusion principle postulates that any element has a super-element, and order principle assumes that any element has a number of greater elements while all elements exist in a partially ordered set.
Revised:  The model is based on three principles: duality principle postulates that any element is a couple consisting of one identity and one entity, inclusion principle postulates that any element has a super-element, and order principle assumes that any element has a number of greater elements within a partially ordered set.
Edit intent: clarity
Original:  It is demonstrated how COM and COQL can be used to solve typical data modeling tasks such as logical navigation, multi-dimensional analysis and automatic constraint propagation .
Revised:  It is demonstrated how COM and COQL can be used to solve typical data modeling tasks : logical navigation, multi-dimensional analysis and automatic constraint propagation .
Edit intent: clarity
Original: Recently, it has been shown that CSMA-type random access algorithms can achieve the maximum  throughput in wireless ad hoc networks.
Revised: Recently, it has been shown that CSMA-type random access algorithms can achieve the maximum possible throughput in wireless ad hoc networks.
Edit intent: clarity
Original:  Central to these results is a distributed randomized algorithm which selects schedules according  a product-form distribution.
Revised:  Central to these results is a distributed randomized algorithm which selects schedules according to a product-form distribution.
Edit intent: fluency
Original:  In this paper, we present an algorithm which achieves the same product-form distribution in a discrete-time setting where collision of data packets is avoided through the exchange of control messages (however, the control messages are allowed to collide as in the 802.11 suite of protocols).
Revised:  In this paper, we present an algorithm which achieves the same product-form distribution in a discrete-time setting where collisions of data packets is avoided through the exchange of control messages (however, the control messages are allowed to collide as in the 802.11 suite of protocols).
Edit intent: fluency
Original:  In this paper, we present an algorithm which achieves the same product-form distribution in a discrete-time setting where collision of data packets is avoided through the exchange of control messages (however, the control messages are allowed to collide as in the 802.11 suite of protocols).
Revised:  In this paper, we present an algorithm which achieves the same product-form distribution in a discrete-time setting where collision of data packets are avoided through the exchange of control messages (however, the control messages are allowed to collide as in the 802.11 suite of protocols).
Edit intent: fluency
Original:  In this paper, we present an algorithm which achieves the same product-form distribution in a discrete-time setting where collisions of data packets are avoided through the exchange of control messages (however, the control messages are allowed to collide as in the 802.11 suite of protocols).
Revised:  In this paper, we propose a discrete-time setting where collisions of data packets are avoided through the exchange of control messages (however, the control messages are allowed to collide as in the 802.11 suite of protocols).
Edit intent: clarity
Original: Recently, it has been shown that CSMA-type random access algorithms can achieve the maximum possible throughput in wireless ad hoc networks.
Revised: Recently, it has been shown that CSMA-type random access algorithms can achieve the maximum possible throughput in ad hoc wireless networks.
Edit intent: fluency
Original:  In this paper, we propose a discrete-time version of the CSMA-type random access algorithmthat allows us to incorporate simple heuristics which lead to very good delay performance while retaining the throughput-optimality property .
Revised:  In this paper, we propose a discrete-time version of the CSMA algorithm .
Edit intent: coherence
Original:  To quantify the dependency and influence between banks and firms, we propose to define a set of scores of banks and firms, which can be calculated by solving an eigenvalue problem determined by the weight of the credit network.
Revised:  To quantify the dependency and influence between banks and firms, we propose a set of scores of banks and firms, which can be calculated by solving an eigenvalue problem determined by the weight of the credit network.
Edit intent: clarity
Original: We present a new approach to understanding credit relationships between commercial banks and quoted firms  and with this approach  examine the temporal change in the structure of the Japanese credit network from 1980 to 2005.
Revised: We present a new approach to understanding credit relationships between commercial banks and quoted firms , and with this approach examine the temporal change in the structure of the Japanese credit network from 1980 to 2005.
Edit intent: fluency
Original: We present a new approach to understanding credit relationships between commercial banks and quoted firms  and with this approach  examine the temporal change in the structure of the Japanese credit network from 1980 to 2005.
Revised: We present a new approach to understanding credit relationships between commercial banks and quoted firms and with this approach , examine the temporal change in the structure of the Japanese credit network from 1980 to 2005.
Edit intent: fluency
Original:  The model is used to investigate the role of cooperativity on the intrinsic fluctuations of gene expression, by means of master equation formalism and computer simulation .
Revised:  The model is used to investigate the role of cooperativity on the intrinsic fluctuations of gene expression, by means of master equation formalism .
Edit intent: clarity
Original:  Unlike their probabilistic counterparts, allowing the tape head to stay put for some steps during its traversal of the input enlarges the class of languages recognized by GQFA 's with unbounded error. 
Revised:  Unlike their probabilistic counterparts, allowing the tape head to stay put for some steps during its traversal of the input does enlarge the class of languages recognized by GQFA 's with unbounded error. 
Edit intent: clarity
Original:  Unlike their probabilistic counterparts, allowing the tape head to stay put for some steps during its traversal of the input enlarges the class of languages recognized by GQFA 's with unbounded error. 
Revised:  Unlike their probabilistic counterparts, allowing the tape head to stay put for some steps during its traversal of the input enlarges the class of languages recognized by such QFA 's with unbounded error. 
Edit intent: clarity
Original: In this paper, we propose a scheme, called the algebraic watchdog for wireless network coding, in which nodes can detect malicious behaviors probabilistically, police their downstream neighbors locally using overheard messages, and, thus, provide a secure global  self-checking network  . Unlike traditional Byzantine detection protocols which are receiver-based, this protocol gives the senders an active role in checking the node downstream.
Revised: In this paper, we propose a scheme, called the "algebraic watchdog" for wireless network coding, in which nodes can detect malicious behaviors probabilistically, police their downstream neighbors locally using overheard messages, and, thus, provide a secure global self-checking network . Unlike traditional Byzantine detection protocols which are receiver-based, this protocol gives the senders an active role in checking the node downstream.
Edit intent: fluency
Original: In this paper, we propose a scheme, called the algebraic watchdog for wireless network coding, in which nodes can detect malicious behaviors probabilistically, police their downstream neighbors locally using overheard messages, and, thus, provide a secure global  self-checking network  . Unlike traditional Byzantine detection protocols which are receiver-based, this protocol gives the senders an active role in checking the node downstream.
Revised: In this paper, we propose a scheme, called the algebraic watchdog for wireless network coding, in which nodes can detect malicious behaviors probabilistically, police their downstream neighbors locally using overheard messages, and, thus, provide a secure global " self-checking network . Unlike traditional Byzantine detection protocols which are receiver-based, this protocol gives the senders an active role in checking the node downstream.
Edit intent: fluency
Original: In this paper, we propose a scheme, called the algebraic watchdog for wireless network coding, in which nodes can detect malicious behaviors probabilistically, police their downstream neighbors locally using overheard messages, and, thus, provide a secure global  self-checking network  . Unlike traditional Byzantine detection protocols which are receiver-based, this protocol gives the senders an active role in checking the node downstream.
Revised: In this paper, we propose a scheme, called the algebraic watchdog for wireless network coding, in which nodes can detect malicious behaviors probabilistically, police their downstream neighbors locally using overheard messages, and, thus, provide a secure global self-checking network " . Unlike traditional Byzantine detection protocols which are receiver-based, this protocol gives the senders an active role in checking the node downstream.
Edit intent: fluency
Original:  This work is inspired by Marti et al 's watchdog-pathrater, which attempts to detect and mitigate the effects of routing misbehavior.
Revised:  This work is inspired by Marti et . al. 's watchdog-pathrater, which attempts to detect and mitigate the effects of routing misbehavior.
Edit intent: fluency
Original:  In other words, marginalization or maximization of a joint PMF is equivalent to a  decoding task as long as a finite field can be constructed over the alphabet of the PMF.
Revised:  In other words, marginalization of a joint PMF is equivalent to a decoding task as long as a finite field can be constructed over the alphabet of the PMF.
Edit intent: clarity
Original:  Finally we present exact values of  g(n) up to n=17 and disprove a conjecture of Cohen and Blum by showing that  -I _15 is not the worst stack for n=15.
Revised:  Finally we present exact values of g(n) up to n=17 and disprove a conjecture of Cohen and Blum by showing that -I _15 is not the worst one for n=15.
Edit intent: clarity
Original: Let n be an even positive integer and F be the field GF(2) \GF(2) . A word in F  is called balanced if its Hamming weight is n/2.
Revised: Let n be an even positive integer and F be the field \GF(2) . A word in F is called balanced if its Hamming weight is n/2.
Edit intent: coherence
Original:  It is shown that most linear subspaces of F^n of dimension slightly larger than ( 3/2 ) \log_2(n) are balancing sets  .
Revised:  It is shown that most linear subspaces of F^n of dimension slightly larger than 3/2 ) \log_2(n) are balancing sets .
Edit intent: coherence
Original:  It is shown that most linear subspaces of F^n of dimension slightly larger than ( 3/2 ) \log_2(n) are balancing sets  .
Revised:  It is shown that most linear subspaces of F^n of dimension slightly larger than ( 3/2 \log_2(n) are balancing sets .
Edit intent: fluency
Original:  Assuming a constant rate of mutation, these genetic distances are random and proportional only on average to genealogical distances .
Revised:  Assuming a constant rate of mutation, these genetic distances are random and proportional only on average to genealogical ones .
Edit intent: clarity
Original:  In this paper, we argue that a sizable fraction of networks lies between these extremes , and are characterized by the existence of partial paths, i.e. multi-hop path segments that allow forwarding data closer to the destination even when no end-to-end path is available.
Revised:  In this paper, we argue that a sizable fraction of networks lies between these extremes and is characterized by the existence of partial paths, i.e. multi-hop path segments that allow forwarding data closer to the destination even when no end-to-end path is available.
Edit intent: fluency
Original:  We optimally improve on their result by raising this NP-hardness lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and by providing a matching upper bound: MC_{u , we show that other problems related to minimal upward covering sets, such as deciding whether a given set is a minimal upward covering set, are coNP-hard.
Revised:  We raise their NP-hardness lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and by providing a matching upper bound: MC_{u , we show that other problems related to minimal upward covering sets, such as deciding whether a given set is a minimal upward covering set, are coNP-hard.
Edit intent: clarity
Original:  We optimally improve on their result by raising this NP-hardness lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and by providing a matching upper bound: MC_{u , we show that other problems related to minimal upward covering sets, such as deciding whether a given set is a minimal upward covering set, are coNP-hard.
Revised:  We optimally improve on their result by raising this NP-hardness lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and by providing a matching upper bound: MC_{u , we show that other problems regarding minimal upward covering sets, such as deciding whether a given set is a minimal upward covering set, are coNP-hard.
Edit intent: clarity
Original:  We optimally improve on their result by raising this NP-hardness lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and by providing a matching upper bound: MC_{u , we show that other problems related to minimal upward covering sets, such as deciding whether a given set is a minimal upward covering set, are coNP-hard.
Revised:  We optimally improve on their result by raising this NP-hardness lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and by providing a matching upper bound: MC_{u , we show that other problems related to minimal upward covering sets, such as deciding whether the set of all alternatives is a minimal upward covering set, are coNP-hard.
Edit intent: clarity
Original:  Thus , minimal upward covering sets cannot even be recognized in polynomial time , unless P = coNP .
Revised:  As a consequence , minimal upward covering sets cannot even be recognized in polynomial time , unless P = coNP .
Edit intent: coherence
Original:  Thus , minimal upward covering sets cannot even be recognized in polynomial time , unless P = coNP .
Revised:  Thus , minimal upward covering sets cannot be found in polynomial time , unless P = coNP .
Edit intent: clarity
Original:  Thus , minimal upward covering sets cannot even be recognized in polynomial time , unless P = coNP .
Revised:  Thus , minimal upward covering sets cannot even be recognized in polynomial time unless P = coNP .
Edit intent: fluency
Original:  Thus , minimal upward covering sets cannot even be recognized in polynomial time , unless P = coNP .
Revised:  Thus , minimal upward covering sets cannot even be recognized in polynomial time , unless P = NP .
Edit intent: clarity
Original: A common thread in the social sciences is to identify the "most desirable" elements of a set of alternatives according to some binary dominance relation . Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory.
Revised: Given a binary dominance relation on a set of alternatives, a common thread in the social sciences is to identify the "most desirable" elements of a set of alternatives according to some binary dominance relation . Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory.
Edit intent: clarity
Original: A common thread in the social sciences is to identify the "most desirable" elements of a set of alternatives according to some binary dominance relation . Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory.
Revised: A common thread in the social sciences is to identify subsets of alternatives that satisfy certain notions of stability . Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory.
Edit intent: clarity
Original:  Brandt and Fischer [BF08] proved that MC_{u whether an alternative is contained in some inclusion-minimal upward covering set--a subset of alternatives that satisfies certain notions of internal and external stability--is NP-hard.
Revised:  Brandt and Fischer [BF08] proved that it is NP-hard to decide whether an alternative is contained in some inclusion-minimal upward covering set--a subset of alternatives that satisfies certain notions of internal and external stability--is NP-hard.
Edit intent: clarity
Original: A representative investor who sells the market asset if it has two consecutive upticks or two consecutive downticks, and buys otherwise, generates realistic and complex security price paths if his order is delayed a few ticks .
Revised: A representative investor who sells the market asset had two consecutive upticks or two consecutive downticks, and buys otherwise, generates realistic and complex security price paths if his order is delayed a few ticks .
Edit intent: clarity