We investigate the notions of may- and must-approximation in Erratic Idealized Algol (a nondeterministic extension of Idealized Algol), and give explicit characterizations of both using its game model. Notably, must-approximation is captured by a novel preorder on nondeterministic strategies, whose definition is formulated in terms of winning regions in a reachability game. The game is played on traces of one of the strategies and its objective is reaching a complete position without encountering any divergences. The concrete accounts of may- and must-approximation make it possible to derive tight complexity bounds for the corresponding decision problems in the finitary (finite datatypes) variant EIAf of Erratic Idealized Algol. In fact we give a complete classification of the complexity of may- and must-approximation for fragments of EIAf of bounded type order (for terms in beta-normal form). The complexity of the decidable cases ranges from PSPACE to 2-EXPTIME for may-approximation and from EXPSPACE to 3-EXPTIME for must-approximation. Our decidability results rely on a representation theorem for nondeterministic strategies which, for a given term, yields a single (finite or visibly pushdown) automaton capturing both traces and divergences of the corresponding strategy with two distinct sets of final states. The decision procedures producing optimal bounds incorporate numerous automata-theoretic techniques: complementation, determinization, computation of winning regions in reachability games over finite and pushdown graphs as well as product constructions. We see our work as a starting point of research that relates game semantics with other game-based theories.
{"title":"Reachability Games and Game Semantics: Comparing Nondeterministic Programs","authors":"A. Murawski","doi":"10.1109/LICS.2008.24","DOIUrl":"https://doi.org/10.1109/LICS.2008.24","url":null,"abstract":"We investigate the notions of may- and must-approximation in Erratic Idealized Algol (a nondeterministic extension of Idealized Algol), and give explicit characterizations of both using its game model. Notably, must-approximation is captured by a novel preorder on nondeterministic strategies, whose definition is formulated in terms of winning regions in a reachability game. The game is played on traces of one of the strategies and its objective is reaching a complete position without encountering any divergences. The concrete accounts of may- and must-approximation make it possible to derive tight complexity bounds for the corresponding decision problems in the finitary (finite datatypes) variant EIAf of Erratic Idealized Algol. In fact we give a complete classification of the complexity of may- and must-approximation for fragments of EIAf of bounded type order (for terms in beta-normal form). The complexity of the decidable cases ranges from PSPACE to 2-EXPTIME for may-approximation and from EXPSPACE to 3-EXPTIME for must-approximation. Our decidability results rely on a representation theorem for nondeterministic strategies which, for a given term, yields a single (finite or visibly pushdown) automaton capturing both traces and divergences of the corresponding strategy with two distinct sets of final states. The decision procedures producing optimal bounds incorporate numerous automata-theoretic techniques: complementation, determinization, computation of winning regions in reachability games over finite and pushdown graphs as well as product constructions. We see our work as a starting point of research that relates game semantics with other game-based theories.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"216 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134089768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The continuous run-time monitoring of the behavior of a system is a technique that is used both as a complementary approach to formal verification and testing to ensure reliability, as well as a means to discover emergent properties in a distributed system, like intrusion and event correlation. The monitors in all these scenarios can be abstractly viewed as automata that process a (unbounded) stream of events to and from the component being observed, and raise an ``alarm'' when an error or intrusion is discovered. These monitors indicate the absence of error or intrusion in a behavior implicitly by the absence of an alarm.In this paper we study the power of randomization in run-time monitoring. Specifically, we examine finite memory monitoring algorithms that toss coins to make decisions on the behavior they are observing. We give a number of results that characterize, topologically as well as with respect to their computational power, the sets of sequences the monitors permit. We also present results on the complexity of deciding non-emptiness of the set of sequences permitted by a monitor.
{"title":"On the Expressiveness and Complexity of Randomization in Finite State Monitors","authors":"Rohit Chadha, A. Sistla, Mahesh Viswanathan","doi":"10.1145/1552285.1552287","DOIUrl":"https://doi.org/10.1145/1552285.1552287","url":null,"abstract":"The continuous run-time monitoring of the behavior of a system is a technique that is used both as a complementary approach to formal verification and testing to ensure reliability, as well as a means to discover emergent properties in a distributed system, like intrusion and event correlation. The monitors in all these scenarios can be abstractly viewed as automata that process a (unbounded) stream of events to and from the component being observed, and raise an ``alarm'' when an error or intrusion is discovered. These monitors indicate the absence of error or intrusion in a behavior implicitly by the absence of an alarm.In this paper we study the power of randomization in run-time monitoring. Specifically, we examine finite memory monitoring algorithms that toss coins to make decisions on the behavior they are observing. We give a number of results that characterize, topologically as well as with respect to their computational power, the sets of sequences the monitors permit. We also present results on the complexity of deciding non-emptiness of the set of sequences permitted by a monitor.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"257 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132597178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper answers the open problem of finding a type system that characterizes hereditary permutators. First this paper shows that there does not exist such a type system by showing that the set of hereditary permutators is not recursively enumerable. The set of positive primitive recursive functions is used to prove it. Secondly this paper gives a best-possible solution by providing a countably infinite set of types such that a term has every type in the set if and only if the term is a hereditary permutator. By the same technique for the first claim, this paper also shows that a set of normalizing terms in infinite lambda-calculus is not recursively enumerable if it contains some term having a computable infinite path,and shows the set of streams is not recursively enumerable.
{"title":"Types for Hereditary Permutators","authors":"M. Tatsuta","doi":"10.1109/LICS.2008.18","DOIUrl":"https://doi.org/10.1109/LICS.2008.18","url":null,"abstract":"This paper answers the open problem of finding a type system that characterizes hereditary permutators. First this paper shows that there does not exist such a type system by showing that the set of hereditary permutators is not recursively enumerable. The set of positive primitive recursive functions is used to prove it. Secondly this paper gives a best-possible solution by providing a countably infinite set of types such that a term has every type in the set if and only if the term is a hereditary permutator. By the same technique for the first claim, this paper also shows that a set of normalizing terms in infinite lambda-calculus is not recursively enumerable if it contains some term having a computable infinite path,and shows the set of streams is not recursively enumerable.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125236911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tait's method (a.k.a. proof by logical relations) is a powerful proof technique frequently used for showing foundational properties of languages based on typed lambda-calculi. Historically, these proofs have been extremely difficult to formalize in proof assistants with weak meta-logics, such as Twelf, and yet they are often straightforward in proof assistants with stronger meta-logics. In this paper, we propose structural logical relations as a technique for conducting these proofs in systems with limited meta-logical strength by explicitly representing and reasoning about an auxiliary logic. In support of our claims, we give a Twelf-checked proof of the completeness of an algorithm for checking equality of simply typed lambda-terms.
{"title":"Structural Logical Relations","authors":"C. Schürmann, Jeffrey Sarnat","doi":"10.1109/LICS.2008.44","DOIUrl":"https://doi.org/10.1109/LICS.2008.44","url":null,"abstract":"Tait's method (a.k.a. proof by logical relations) is a powerful proof technique frequently used for showing foundational properties of languages based on typed lambda-calculi. Historically, these proofs have been extremely difficult to formalize in proof assistants with weak meta-logics, such as Twelf, and yet they are often straightforward in proof assistants with stronger meta-logics. In this paper, we propose structural logical relations as a technique for conducting these proofs in systems with limited meta-logical strength by explicitly representing and reasoning about an auxiliary logic. In support of our claims, we give a Twelf-checked proof of the completeness of an algorithm for checking equality of simply typed lambda-terms.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116137625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
T. Brázdil, Vojtěch Forejt, Jan Křetínský, A. Kucera
We study the satisfiability problem for qualitative PCTL (probabilistic computation tree logic), which is obtained from "ordinary" CTL by replacing the EX, AX, EU, and AU operators with their qualitative counterparts X > 0, X = 1, U > 0, and U = 1, respectively. As opposed to CTL, qualitative PCTL does not have a small model property, and there are even qualitative PCTL formulae which have only infinite- state models. Nevertheless, we show that the satisfiability problem for qualitative PCTL is EXPTIME-complete and we give an exponential-time algorithm which for a given formula phi computes a finite description of a model (if it exists), or answers "not satisfiable" (otherwise). We also consider the finite satisfiability problem and provide analogous results. That is, we show that the finite satisfiability problem for qualitative PCTL is EXPTIME-complete, and every finite satisfiable formula has a model of an exponential size which can effectively be constructed in exponential time. Finally, we give some results about the quantitative PCTL, where the numerical bounds in probability constraints can be arbitrary rationals between 0 and 1. We prove that the problem whether a given quantitative PCTL formula phi has a model of the branching degree at most k, where k > 2 is an arbitrary but fixed constant, is highly undecidable. We also show that every satisfiable formula phi has a model with branching degree at most phi + 2. However, this does not yet imply the undecidability of the satisfiability problem for quantitative PCTL, and we in fact conjecture the opposite.
{"title":"The Satisfiability Problem for Probabilistic CTL","authors":"T. Brázdil, Vojtěch Forejt, Jan Křetínský, A. Kucera","doi":"10.1109/LICS.2008.21","DOIUrl":"https://doi.org/10.1109/LICS.2008.21","url":null,"abstract":"We study the satisfiability problem for qualitative PCTL (probabilistic computation tree logic), which is obtained from \"ordinary\" CTL by replacing the EX, AX, EU, and AU operators with their qualitative counterparts X > 0, X = 1, U > 0, and U = 1, respectively. As opposed to CTL, qualitative PCTL does not have a small model property, and there are even qualitative PCTL formulae which have only infinite- state models. Nevertheless, we show that the satisfiability problem for qualitative PCTL is EXPTIME-complete and we give an exponential-time algorithm which for a given formula phi computes a finite description of a model (if it exists), or answers \"not satisfiable\" (otherwise). We also consider the finite satisfiability problem and provide analogous results. That is, we show that the finite satisfiability problem for qualitative PCTL is EXPTIME-complete, and every finite satisfiable formula has a model of an exponential size which can effectively be constructed in exponential time. Finally, we give some results about the quantitative PCTL, where the numerical bounds in probability constraints can be arbitrary rationals between 0 and 1. We prove that the problem whether a given quantitative PCTL formula phi has a model of the branching degree at most k, where k > 2 is an arbitrary but fixed constant, is highly undecidable. We also show that every satisfiable formula phi has a model with branching degree at most phi + 2. However, this does not yet imply the undecidability of the satisfiability problem for quantitative PCTL, and we in fact conjecture the opposite.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129193831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The authors revisit the correctness criterion for the multiplicative additive fragment of linear logic. We prove that deciding the correctness of corresponding proof structures is NL-complete.
本文重新讨论了线性逻辑的乘法加性片段的正确性判据。证明了判定相应证明结构的正确性是nl完全的。
{"title":"Correctness of Multiplicative Additive Proof Structures is NL-Complete","authors":"Paulin Jacobé de Naurois, Virgile Mogbil","doi":"10.1109/LICS.2008.20","DOIUrl":"https://doi.org/10.1109/LICS.2008.20","url":null,"abstract":"The authors revisit the correctness criterion for the multiplicative additive fragment of linear logic. We prove that deciding the correctness of corresponding proof structures is NL-complete.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"2007 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125624835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's judgments. Although detailed informal proofs of these properties have been published, they have not been formally verified in a theorem prover. We have formalized these properties within Isabelle/HOL using the nominal datatype package, closely following a recent article by Harper and Pfenning. In the process, we identified and resolved a gap in one of the proofs and a small number of minor lacunae in others. Besides its intrinsic interest, our formalization provides a foundation for studying the adequacy of LF encodings, the correctness of Twelf-style metatheoretic reasoning, and the metatheory of extensions to LF.
{"title":"Mechanizing the Metatheory of LF","authors":"Christian Urban, J. Cheney, Stefan Berghofer","doi":"10.1145/1877714.1877721","DOIUrl":"https://doi.org/10.1145/1877714.1877721","url":null,"abstract":"LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's judgments. Although detailed informal proofs of these properties have been published, they have not been formally verified in a theorem prover. We have formalized these properties within Isabelle/HOL using the nominal datatype package, closely following a recent article by Harper and Pfenning. In the process, we identified and resolved a gap in one of the proofs and a small number of minor lacunae in others. Besides its intrinsic interest, our formalization provides a foundation for studying the adequacy of LF encodings, the correctness of Twelf-style metatheoretic reasoning, and the metatheory of extensions to LF.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126748601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The geometry of interaction purpose is to give a semantic of proofs or programs accounting for their dynamics. The initial presentation, translated as an algebraic weighting of paths in proofnets, led to a better characterization of the lambda-lambda-calculus optimal reduction. Recently Ehrhard and Regnier have introduced an extension of the multiplicative exponential fragment of linear logic (MELL) that is able to express non-deterministic behaviour of programs and a proofnet-like calculus: differential interaction nets. This paper constructs a proper geometry of interaction (GoI) for this extension. We consider it both as an algebraic theory and as a concrete reversible computation. We draw links between this GoI and the one of MELL. As a by-product we give for the first time an equational theory suitable for the GoI of the multiplicative additive fragment of linear logic.
{"title":"The Geometry of Interaction of Differential Interaction Nets","authors":"M. D. Falco","doi":"10.1109/LICS.2008.23","DOIUrl":"https://doi.org/10.1109/LICS.2008.23","url":null,"abstract":"The geometry of interaction purpose is to give a semantic of proofs or programs accounting for their dynamics. The initial presentation, translated as an algebraic weighting of paths in proofnets, led to a better characterization of the lambda-lambda-calculus optimal reduction. Recently Ehrhard and Regnier have introduced an extension of the multiplicative exponential fragment of linear logic (MELL) that is able to express non-deterministic behaviour of programs and a proofnet-like calculus: differential interaction nets. This paper constructs a proper geometry of interaction (GoI) for this extension. We consider it both as an algebraic theory and as a concrete reversible computation. We draw links between this GoI and the one of MELL. As a by-product we give for the first time an equational theory suitable for the GoI of the multiplicative additive fragment of linear logic.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133400248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the (in)equational theory of impossible futures semantics over the process algebra BCCSP. We prove that no finite, sound axiomatization for BCCSP modulo impossible futures equivalence is ground-complete. By contrast, we present a finite, sound, ground-complete axiomatization for BCCSP modulo impossible futures preorder. If the alphabet of actions is infinite, then this axiomatization is shown to be omega-complete. If the alphabet is finite, we prove that the in equational theory of BCCSP modulo impossible futures preorder lacks such a finite basis. We also derive non-finite axiomatizability results for nested impossible futures semantics.
{"title":"On the Axiomatizability of Impossible Futures: Preorder versus Equivalence","authors":"Taolue Chen, W. Fokkink","doi":"10.1109/LICS.2008.13","DOIUrl":"https://doi.org/10.1109/LICS.2008.13","url":null,"abstract":"We investigate the (in)equational theory of impossible futures semantics over the process algebra BCCSP. We prove that no finite, sound axiomatization for BCCSP modulo impossible futures equivalence is ground-complete. By contrast, we present a finite, sound, ground-complete axiomatization for BCCSP modulo impossible futures preorder. If the alphabet of actions is infinite, then this axiomatization is shown to be omega-complete. If the alphabet is finite, we prove that the in equational theory of BCCSP modulo impossible futures preorder lacks such a finite basis. We also derive non-finite axiomatizability results for nested impossible futures semantics.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"60 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131308192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that allow direct, logic-based reasoning about such descriptions: the treatment of atomic judgments as fixed points (recursive definitions) and an encoding of binding constructs via generic judgments. However, the logics encompassing these two features have thus far treated them orthogonally: that is, they do not provide the ability to define object-logic properties that themselves depend on an intrinsic treatment of binding. We propose a new and simple integration of these features within an intuitionistic logic enhanced with induction over natural numbers and we show that the resulting logic is consistent. The pivotal benefit of the integration is that it allows recursive definitions to not just encode simple, traditional forms of atomic judgments but also to capture generic properties pertaining to such judgments. The usefulness of this logic is illustrated by showing how it can provide elegant treatments of object-logic contexts that appear in proofs involving typing calculi and of arbitrarily cascading substitutions that play a role in reducibility arguments.
{"title":"Combining Generic Judgments with Recursive Definitions","authors":"Andrew Gacek, D. Miller, G. Nadathur","doi":"10.1109/LICS.2008.33","DOIUrl":"https://doi.org/10.1109/LICS.2008.33","url":null,"abstract":"Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that allow direct, logic-based reasoning about such descriptions: the treatment of atomic judgments as fixed points (recursive definitions) and an encoding of binding constructs via generic judgments. However, the logics encompassing these two features have thus far treated them orthogonally: that is, they do not provide the ability to define object-logic properties that themselves depend on an intrinsic treatment of binding. We propose a new and simple integration of these features within an intuitionistic logic enhanced with induction over natural numbers and we show that the resulting logic is consistent. The pivotal benefit of the integration is that it allows recursive definitions to not just encode simple, traditional forms of atomic judgments but also to capture generic properties pertaining to such judgments. The usefulness of this logic is illustrated by showing how it can provide elegant treatments of object-logic contexts that appear in proofs involving typing calculi and of arbitrarily cascading substitutions that play a role in reducibility arguments.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131312182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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