Pub Date : 1997-06-29DOI: 10.1109/LICS.1997.614922
Hubert Comon-Lundh, Florent Jacquemard
We prove that ground reducibility is EXPTIME-complete in the general case. EXPTIME-hardness is proved by encoding the computations of an alternating Turing machine whose space is polynomially bounded. It is more difficult to show that ground reducibility belongs to DEXPTIME. We associate first an automaton with disequality constraints A/sub R,t/ to a rewrite system R and a term t. This automaton is deterministic and accepts a term u if and only if t is not ground reducible by R. The number of states of A/sub R,t/ is O(2/sup /spl par/R/spl par//spl times//spl par/t/spl par//) and the size of the constraints are polynomial in the size of R,t. Then we prove some new pumping lemmas, using a total ordering on the computations of the automaton. Thanks to these lemmas, we can give an upper bound to the number of distinct subtrees of a minimal successful computation of an automaton with disequality constraints. It follows that emptiness of such an automaton can be decided in time polynomial in the number of its states and exponential in the size of its constraints. Altogether, we get a simply exponential deterministic algorithm for ground reducibility.
{"title":"Ground reducibility is EXPTIME-complete","authors":"Hubert Comon-Lundh, Florent Jacquemard","doi":"10.1109/LICS.1997.614922","DOIUrl":"https://doi.org/10.1109/LICS.1997.614922","url":null,"abstract":"We prove that ground reducibility is EXPTIME-complete in the general case. EXPTIME-hardness is proved by encoding the computations of an alternating Turing machine whose space is polynomially bounded. It is more difficult to show that ground reducibility belongs to DEXPTIME. We associate first an automaton with disequality constraints A/sub R,t/ to a rewrite system R and a term t. This automaton is deterministic and accepts a term u if and only if t is not ground reducible by R. The number of states of A/sub R,t/ is O(2/sup /spl par/R/spl par//spl times//spl par/t/spl par//) and the size of the constraints are polynomial in the size of R,t. Then we prove some new pumping lemmas, using a total ordering on the computations of the automaton. Thanks to these lemmas, we can give an upper bound to the number of distinct subtrees of a minimal successful computation of an automaton with disequality constraints. It follows that emptiness of such an automaton can be decided in time polynomial in the number of its states and exponential in the size of its constraints. Altogether, we get a simply exponential deterministic algorithm for ground reducibility.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130521827","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}
Pub Date : 1997-06-29DOI: 10.1109/LICS.1997.614917
F. Baader
Reduction orderings that are compatible with an equational theory E and total on (the E-equivalence classes of) ground terms play an important role in automated deduction. This paper presents a general approach for combining such orderings: it shows how E/sub 1/-compatible reduction orderings total on /spl Sigma//sub 1/-ground terms and E/sub 2/-compatible reduction orderings total on /spl Sigma//sub 2/-ground terms can be used to construct an (E/sub 1//spl cup/E/sub 2/)-compatible reduction ordering total on (/spl Sigma//sub 1//spl cup//spl Sigma//sub 2/)-ground terms, provided that the signatures are disjoint and some other (rather weak) restrictions are satisfied. This work was motivated by the observation that it is often easier to construct such orderings for "small" signatures and theories separately, rather than directly for their union.
{"title":"Combination of compatible reduction orderings that are total on ground terms","authors":"F. Baader","doi":"10.1109/LICS.1997.614917","DOIUrl":"https://doi.org/10.1109/LICS.1997.614917","url":null,"abstract":"Reduction orderings that are compatible with an equational theory E and total on (the E-equivalence classes of) ground terms play an important role in automated deduction. This paper presents a general approach for combining such orderings: it shows how E/sub 1/-compatible reduction orderings total on /spl Sigma//sub 1/-ground terms and E/sub 2/-compatible reduction orderings total on /spl Sigma//sub 2/-ground terms can be used to construct an (E/sub 1//spl cup/E/sub 2/)-compatible reduction ordering total on (/spl Sigma//sub 1//spl cup//spl Sigma//sub 2/)-ground terms, provided that the signatures are disjoint and some other (rather weak) restrictions are satisfied. This work was motivated by the observation that it is often easier to construct such orderings for \"small\" signatures and theories separately, rather than directly for their union.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132541508","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}
Pub Date : 1997-06-29DOI: 10.1109/LICS.1997.614958
L. Pacholski, W. Szwast, Lidia Tendera
Let C/sub k//sup 2/ denote the class of first order sentences with two variables and with additional quantifiers "there exists exactly (at most, at least) m", for m/spl les/k, and let C/sup 2/ be the union of C/sub k//sup 2/ taken over all integers k. We prove that the problem of satisfiability of sentences of C/sub 1//sup 2/ is NEXPTIME-complete. This strengthens a recent result of E. Gradel, Ph. Kolaitis and M. Vardi (1997) who proved that the satisfiability problem for the first order two-variable logic L/sup 2/ is NEXPTIME-complete and a very recent result by E. Gradel, M. Otto and E. Rosen (1997) who proved the decidability of C/sup 2/. Our result easily implies that the satisfiability problem for C/sup 2/ is in non-deterministic, doubly exponential time. It is interesting that C/sub 1//sup 2/ is in NEXPTIME in spite of the fact, that there are sentences whose minimal (and only) models are of doubly exponential size.
{"title":"Complexity of two-variable logic with counting","authors":"L. Pacholski, W. Szwast, Lidia Tendera","doi":"10.1109/LICS.1997.614958","DOIUrl":"https://doi.org/10.1109/LICS.1997.614958","url":null,"abstract":"Let C/sub k//sup 2/ denote the class of first order sentences with two variables and with additional quantifiers \"there exists exactly (at most, at least) m\", for m/spl les/k, and let C/sup 2/ be the union of C/sub k//sup 2/ taken over all integers k. We prove that the problem of satisfiability of sentences of C/sub 1//sup 2/ is NEXPTIME-complete. This strengthens a recent result of E. Gradel, Ph. Kolaitis and M. Vardi (1997) who proved that the satisfiability problem for the first order two-variable logic L/sup 2/ is NEXPTIME-complete and a very recent result by E. Gradel, M. Otto and E. Rosen (1997) who proved the decidability of C/sup 2/. Our result easily implies that the satisfiability problem for C/sup 2/ is in non-deterministic, doubly exponential time. It is interesting that C/sub 1//sup 2/ is in NEXPTIME in spite of the fact, that there are sentences whose minimal (and only) models are of doubly exponential size.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131842650","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}
Pub Date : 1997-06-29DOI: 10.1109/LICS.1997.614964
M. Hofmann, T. Streicher
We show that a certain simple call-by-name continuation semantics of Parigot's /spl lambda//sub /spl mu//-calculus (1992) is complete. More precisely, for every /spl lambda//spl mu/-theory we construct a cartesian closed category such that the ensuing continuation-style interpretation of /spl lambda//sub /spl mu//, which maps terms to functions sending abstract continuations to responses, is full and faithful. Thus, any /spl lambda//sub /spl mu//-category in the sense of is isomorphic to a continuation model derived from a cartesian-closed category of continuations.
{"title":"Continuation models are universal for /spl lambda//sub /spl mu//-calculus","authors":"M. Hofmann, T. Streicher","doi":"10.1109/LICS.1997.614964","DOIUrl":"https://doi.org/10.1109/LICS.1997.614964","url":null,"abstract":"We show that a certain simple call-by-name continuation semantics of Parigot's /spl lambda//sub /spl mu//-calculus (1992) is complete. More precisely, for every /spl lambda//spl mu/-theory we construct a cartesian closed category such that the ensuing continuation-style interpretation of /spl lambda//sub /spl mu//, which maps terms to functions sending abstract continuations to responses, is full and faithful. Thus, any /spl lambda//sub /spl mu//-category in the sense of is isomorphic to a continuation model derived from a cartesian-closed category of continuations.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129025714","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}
Pub Date : 1997-06-29DOI: 10.1109/LICS.1997.614962
Witold Charatonik, A. Podelski
Set constraints are inclusions between expressions denoting sets of trees. The efficiency of their satisfiability test is a central issue in set-based program analysis, their main application domain. We introduce the class of set constraints with intersection (the only operators forming the expressions are constructors and intersection) and show that its satisfiability problem is DEXPTIME-complete. The complexity characterization continues to hold for negative set constraints with intersection (which have positive and negated inclusions). We reduce the satisfiability problem for these constraints to one over the interpretation domain of nonempty sets of trees. Set constraints with intersection over the domain of nonempty sets of trees enjoy the fundamental property of independence of negated conjuncts. This allows us to handle each negated inclusion separately by the entailment algorithm that we devise. We furthermore prove that set constraints with intersection are equivalent to the class of definite set constraints and thereby settle the complexity question of the historically first class for which the decidability question was solved.
{"title":"Set constraints with intersection","authors":"Witold Charatonik, A. Podelski","doi":"10.1109/LICS.1997.614962","DOIUrl":"https://doi.org/10.1109/LICS.1997.614962","url":null,"abstract":"Set constraints are inclusions between expressions denoting sets of trees. The efficiency of their satisfiability test is a central issue in set-based program analysis, their main application domain. We introduce the class of set constraints with intersection (the only operators forming the expressions are constructors and intersection) and show that its satisfiability problem is DEXPTIME-complete. The complexity characterization continues to hold for negative set constraints with intersection (which have positive and negated inclusions). We reduce the satisfiability problem for these constraints to one over the interpretation domain of nonempty sets of trees. Set constraints with intersection over the domain of nonempty sets of trees enjoy the fundamental property of independence of negated conjuncts. This allows us to handle each negated inclusion separately by the entailment algorithm that we devise. We furthermore prove that set constraints with intersection are equivalent to the class of definite set constraints and thereby settle the complexity question of the historically first class for which the decidability question was solved.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131033614","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}
Pub Date : 1997-06-29DOI: 10.1109/LICS.1997.614948
L. Libkin
Most proofs showing limitations of expressive power of first-order logic rely on Ehrenfeucht-Fraisse games. Playing the game often involves a nontrivial combinatorial argument, so it was proposed to find easier tools for proving expressivity bounds. Most of those known for first-order logic are based on its "locality", that is defined in different ways. In this paper we characterize the relationship between those notions of locality. We note that Gaifman's locality theorem gives rise to two notions: one deals with sentences and one with open formulae. We prove that the former implies Hauf's notion of locality, which in turn implies Gaifman's locality for open formulae. Each of these implies the bounded degree property, which is one of the easiest tools for proving expressivity bounds. These results apply beyond the first-order case. We use them to derive expressivity bounds for first-order logic with unary quantifiers and counting. Finally, we apply these results to relational database languages with aggregate functions, and prove that purely relational queries defined in such languages satisfy Gaifman's notion of locality. From this we derive a number of expressivity bounds for languages with aggregates.
{"title":"On the forms of locality over finite models","authors":"L. Libkin","doi":"10.1109/LICS.1997.614948","DOIUrl":"https://doi.org/10.1109/LICS.1997.614948","url":null,"abstract":"Most proofs showing limitations of expressive power of first-order logic rely on Ehrenfeucht-Fraisse games. Playing the game often involves a nontrivial combinatorial argument, so it was proposed to find easier tools for proving expressivity bounds. Most of those known for first-order logic are based on its \"locality\", that is defined in different ways. In this paper we characterize the relationship between those notions of locality. We note that Gaifman's locality theorem gives rise to two notions: one deals with sentences and one with open formulae. We prove that the former implies Hauf's notion of locality, which in turn implies Gaifman's locality for open formulae. Each of these implies the bounded degree property, which is one of the easiest tools for proving expressivity bounds. These results apply beyond the first-order case. We use them to derive expressivity bounds for first-order logic with unary quantifiers and counting. Finally, we apply these results to relational database languages with aggregate functions, and prove that purely relational queries defined in such languages satisfy Gaifman's notion of locality. From this we derive a number of expressivity bounds for languages with aggregates.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132276377","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}
Pub Date : 1997-06-29DOI: 10.1109/LICS.1997.614952
P. J. Potts, A. Edalat, M. Escardó
In this paper, we incorporate a representation of the non-negative extended real numbers based on the composition of linear fractional transformations with non-negative integer coefficients into the Programming Language for Computable Functions (PCF) with products. We present two models for the extended language and show that they are computationally adequate with respect to the operational semantics.
{"title":"Semantics of exact real arithmetic","authors":"P. J. Potts, A. Edalat, M. Escardó","doi":"10.1109/LICS.1997.614952","DOIUrl":"https://doi.org/10.1109/LICS.1997.614952","url":null,"abstract":"In this paper, we incorporate a representation of the non-negative extended real numbers based on the composition of linear fractional transformations with non-negative integer coefficients into the Programming Language for Computable Functions (PCF) with products. We present two models for the extended language and show that they are computationally adequate with respect to the operational semantics.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115138219","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}
Pub Date : 1997-06-29DOI: 10.1109/LICS.1997.614968
R. McDowell, D. Miller
Logical frameworks based on intuitionistic or linear logics with higher-type quantification have been successfully used to give high-level, modular, and formal specifications of many important judgments in the area of programming languages and inference systems. Given such specifications, it is natural to consider proving properties about the specified systems in the framework: for example, given the specification of evaluation for a functional programming language, prove that the language is deterministic or that the subject-reduction theorem holds. One challenge in developing a framework for such reasoning is that higher-order abstract syntax (HOAS), an elegant and declarative treatment of object-level abstraction and substitution, is difficult to treat in proofs involving induction. In this paper we present a meta-logic that can be used to reason about judgments coded using HOAS; this meta-logic is an extension of a simple intuitionistic logic that admits higher-order quantification over simply typed /spl lambda/-terms (key ingredients for HOAS) as well as induction and a notion of definition. The latter concept of a definition is a proof-theoretic device that allows certain theories to be treated as "closed" or as defining fixed points. The resulting meta-logic can specify various logical frameworks and a large range of judgments regarding programming languages and inference systems. We illustrate this point through examples, including the admissibility of cut for a simple logic and subject reduction, determinacy of evaluation, and the equivalence of SOS and natural semantics presentations of evaluation for a simple functional programming language.
{"title":"A logic for reasoning with higher-order abstract syntax","authors":"R. McDowell, D. Miller","doi":"10.1109/LICS.1997.614968","DOIUrl":"https://doi.org/10.1109/LICS.1997.614968","url":null,"abstract":"Logical frameworks based on intuitionistic or linear logics with higher-type quantification have been successfully used to give high-level, modular, and formal specifications of many important judgments in the area of programming languages and inference systems. Given such specifications, it is natural to consider proving properties about the specified systems in the framework: for example, given the specification of evaluation for a functional programming language, prove that the language is deterministic or that the subject-reduction theorem holds. One challenge in developing a framework for such reasoning is that higher-order abstract syntax (HOAS), an elegant and declarative treatment of object-level abstraction and substitution, is difficult to treat in proofs involving induction. In this paper we present a meta-logic that can be used to reason about judgments coded using HOAS; this meta-logic is an extension of a simple intuitionistic logic that admits higher-order quantification over simply typed /spl lambda/-terms (key ingredients for HOAS) as well as induction and a notion of definition. The latter concept of a definition is a proof-theoretic device that allows certain theories to be treated as \"closed\" or as defining fixed points. The resulting meta-logic can specify various logical frameworks and a large range of judgments regarding programming languages and inference systems. We illustrate this point through examples, including the admissibility of cut for a simple logic and subject reduction, determinacy of evaluation, and the equivalence of SOS and natural semantics presentations of evaluation for a simple functional programming language.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132261262","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}
Pub Date : 1997-06-29DOI: 10.1109/LICS.1997.614965
M. Dezani-Ciancaglini, J. Tiuryn, P. Urzyczyn
The main result of the paper is a proof of the following equivalence: two pure lambda terms are observationally equivalent in the lazy concurrent lambda calculus if they have the same Levy-Longo trees. It follows that contextual equivalence coincides with behavioural equivalence (bisimulation) as considered by Sangiorgi (1994). Another consequence is that the discriminating power of concurrent lambda contexts is the same as that of Boudol-Laneve's contexts with multiplicities (1996).
{"title":"Discrimination by parallel observers","authors":"M. Dezani-Ciancaglini, J. Tiuryn, P. Urzyczyn","doi":"10.1109/LICS.1997.614965","DOIUrl":"https://doi.org/10.1109/LICS.1997.614965","url":null,"abstract":"The main result of the paper is a proof of the following equivalence: two pure lambda terms are observationally equivalent in the lazy concurrent lambda calculus if they have the same Levy-Longo trees. It follows that contextual equivalence coincides with behavioural equivalence (bisimulation) as considered by Sangiorgi (1994). Another consequence is that the discriminating power of concurrent lambda contexts is the same as that of Boudol-Laneve's contexts with multiplicities (1996).","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114978673","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}
Pub Date : 1997-06-29DOI: 10.1109/LICS.1997.614957
E. Grädel, M. Otto, Eric Rosen
We prove that the satisfiability and the finite satisfiability problems for C/sup 2/ are decidable. C/sup 2/ is first-order logic with only two variables in the presence of arbitrary counting quantifiers 3/sup /spl ges/m/,m/spl ges/1. It considerably extends L/sup 2/ plain first-order with only two variables, which is known to be decidable by a result of Mortimer's. Unlike L/sup 2/, C/sup 2/ does not have the finite model property.
{"title":"Two-variable logic with counting is decidable","authors":"E. Grädel, M. Otto, Eric Rosen","doi":"10.1109/LICS.1997.614957","DOIUrl":"https://doi.org/10.1109/LICS.1997.614957","url":null,"abstract":"We prove that the satisfiability and the finite satisfiability problems for C/sup 2/ are decidable. C/sup 2/ is first-order logic with only two variables in the presence of arbitrary counting quantifiers 3/sup /spl ges/m/,m/spl ges/1. It considerably extends L/sup 2/ plain first-order with only two variables, which is known to be decidable by a result of Mortimer's. Unlike L/sup 2/, C/sup 2/ does not have the finite model property.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130257150","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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