Pub Date : 2001-06-16DOI: 10.1109/LICS.2001.932508
A. Jeffrey, DePaul
F/sub /spl les// is a typed /spl lambda/-calculus with subtyping and bounded polymorphism. Type checking for F/sub /spl les// is known to be undecidable, because the subtyping relation on types is undecidable. F/sub /spl mu//spl les// is an extension of F/sub /spl les// with recursive types. In this paper, we show how symbolic labelled transition system techniques from concurrency theory can be used to reason about subtyping for F/sub /spl mu//spl les//. We provide a symbolic labelled transition system for F/sub /spl mu//spl les// types, together with an appropriate notion of simulation, which coincides with the existing co-inductive definition of subtyping. We then provide a 'simulation up to' technique for proving subtyping, for which there is a simple model-checking algorithm. The algorithm is more powerful than the usual one for F/sub /spl les//, e.g. it terminates on G. Ghelli's (1995) canonical example of non-termination.
{"title":"A symbolic labelled transition system for coinductive subtyping of F/sub /spl mu//spl les// types","authors":"A. Jeffrey, DePaul","doi":"10.1109/LICS.2001.932508","DOIUrl":"https://doi.org/10.1109/LICS.2001.932508","url":null,"abstract":"F/sub /spl les// is a typed /spl lambda/-calculus with subtyping and bounded polymorphism. Type checking for F/sub /spl les// is known to be undecidable, because the subtyping relation on types is undecidable. F/sub /spl mu//spl les// is an extension of F/sub /spl les// with recursive types. In this paper, we show how symbolic labelled transition system techniques from concurrency theory can be used to reason about subtyping for F/sub /spl mu//spl les//. We provide a symbolic labelled transition system for F/sub /spl mu//spl les// types, together with an appropriate notion of simulation, which coincides with the existing co-inductive definition of subtyping. We then provide a 'simulation up to' technique for proving subtyping, for which there is a simple model-checking algorithm. The algorithm is more powerful than the usual one for F/sub /spl les//, e.g. it terminates on G. Ghelli's (1995) canonical example of non-termination.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121458315","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 : 2001-06-16DOI: 10.1109/LICS.2001.932493
T. Huuskonen, Tapani Hyttinen
We will answer questions due to Blass and Gurevich (2000) on definability of order in the first-order logic with Hilbert's epsilon operation. We show that a linear ordering is almost surely definable in models with random choice.
{"title":"On definability of order in logic with choice","authors":"T. Huuskonen, Tapani Hyttinen","doi":"10.1109/LICS.2001.932493","DOIUrl":"https://doi.org/10.1109/LICS.2001.932493","url":null,"abstract":"We will answer questions due to Blass and Gurevich (2000) on definability of order in the first-order logic with Hilbert's epsilon operation. We show that a linear ordering is almost surely definable in models with random choice.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129205040","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 : 2001-06-16DOI: 10.1109/LICS.2001.932512
P. Manolios, Richard J. Trefler
Extends B. Alpern & F.B. Schneider's linear time characterization of safety and liveness properties to branching time, where properties are sets of trees. We define two closure operators that give rise to the following four extremal types of properties: universally safe, existentially safe, universally live and existentially live. The distinction between universal and existential properties captures the difference between the CTL (computation tree logic) path quantifiers /spl forall/ (for all paths) and /spl exist/ (there is a path). We show that every branching time property is the intersection of an existentially safe property and an existentially live property, a universally safe property and a universally live property, and an existentially safe property and a universally live property. We also examine how our closure operators behave on linear-time properties. We then focus on sets of finitely branching trees and show that our closure operators agree on linear-time safety properties. Furthermore, if a set of trees is given implicitly as a Rabin tree automaton /spl Bscr/, we show that it is possible to compute the Rabin automata corresponding to the closures of the language of /spl Bscr/. This allows us to effectively compute /spl Bscr//sub safe/ and /spl Bscr//sub live/ such that the language of /spl Bscr/ is the intersection of the languages of /spl Bscr//sub safe/ and /spl Bscr//sub live/. As above, /spl Bscr//sub safe/ and /spl Bscr//sub live/ can be chosen so that their languages are existentially safe and existentially live, universally safe and universally live, or existentially safe and universally live.
{"title":"Safety and liveness in branching time","authors":"P. Manolios, Richard J. Trefler","doi":"10.1109/LICS.2001.932512","DOIUrl":"https://doi.org/10.1109/LICS.2001.932512","url":null,"abstract":"Extends B. Alpern & F.B. Schneider's linear time characterization of safety and liveness properties to branching time, where properties are sets of trees. We define two closure operators that give rise to the following four extremal types of properties: universally safe, existentially safe, universally live and existentially live. The distinction between universal and existential properties captures the difference between the CTL (computation tree logic) path quantifiers /spl forall/ (for all paths) and /spl exist/ (there is a path). We show that every branching time property is the intersection of an existentially safe property and an existentially live property, a universally safe property and a universally live property, and an existentially safe property and a universally live property. We also examine how our closure operators behave on linear-time properties. We then focus on sets of finitely branching trees and show that our closure operators agree on linear-time safety properties. Furthermore, if a set of trees is given implicitly as a Rabin tree automaton /spl Bscr/, we show that it is possible to compute the Rabin automata corresponding to the closures of the language of /spl Bscr/. This allows us to effectively compute /spl Bscr//sub safe/ and /spl Bscr//sub live/ such that the language of /spl Bscr/ is the intersection of the languages of /spl Bscr//sub safe/ and /spl Bscr//sub live/. As above, /spl Bscr//sub safe/ and /spl Bscr//sub live/ can be chosen so that their languages are existentially safe and existentially live, universally safe and universally live, or existentially safe and universally live.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126031902","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 : 2001-06-16DOI: 10.1109/LICS.2001.932477
John C. Mitchell, A. Ramanathan, A. Scedrov, Vanessa Teague
Abstract: We describe properties of a process calculus that has been developed for the purpose of analyzing security protocols. The process calculus is a restricted form of p-calculus, with bounded replication and probabilistic polynomial-time expressions allowed in messages and boolean tests. To avoid problems expressing security in the presence of nondeterminism, messages are scheduled probabilistically instead of nondeterministically. We prove that evaluation may be completed in probabilistic polynomial time and develop properties of a form of asymptotic protocol equivalence that allows security to be speci£ed using observational equivalence, a standard relation from programming language theory that involves quantifying over possible environments that might interact with the protocol. We also relate process equivalence to cryptographic concepts such as pseudorandom number generators and polynomial-time statistical tests.
{"title":"Probabilistic polynomial-time process calculus and security protocol analysis","authors":"John C. Mitchell, A. Ramanathan, A. Scedrov, Vanessa Teague","doi":"10.1109/LICS.2001.932477","DOIUrl":"https://doi.org/10.1109/LICS.2001.932477","url":null,"abstract":"Abstract: We describe properties of a process calculus that has been developed for the purpose of analyzing security protocols. The process calculus is a restricted form of p-calculus, with bounded replication and probabilistic polynomial-time expressions allowed in messages and boolean tests. To avoid problems expressing security in the presence of nondeterminism, messages are scheduled probabilistically instead of nondeterministically. We prove that evaluation may be completed in probabilistic polynomial time and develop properties of a form of asymptotic protocol equivalence that allows security to be speci£ed using observational equivalence, a standard relation from programming language theory that involves quantifying over possible environments that might interact with the protocol. We also relate process equivalence to cryptographic concepts such as pseudorandom number generators and polynomial-time statistical tests.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123693729","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 : 2001-06-16DOI: 10.1109/LICS.2001.932503
E. Asarin, A. Bouajjani
Investigates the computational power of several models of dynamical systems under infinitesimal perturbations of their dynamics. We consider models for both discrete- and continuous-time dynamical systems: Turing machines, piecewise affine maps, linear hybrid automata and piecewise-constant derivative systems (a simple model of hybrid systems). We associate with each of these models a notion of perturbed dynamics by a small /spl epsi/ (w.r.t. to a suitable metric), and define the perturbed reachability relation as the intersection of all reachability relations obtained by /spl epsi/-perturbations, for all possible values of /spl epsi/. We show that, for the four kinds of models we consider, the perturbed reachability relation is co-recursively enumerable (co-r.e.), and that any co-r.e. relation can be defined as the perturbed reachability relation of such models. A corollary of this result is that systems that are robust (i.e. whose reachability relation is stable under infinitesimal perturbation) are decidable.
{"title":"Perturbed Turing machines and hybrid systems","authors":"E. Asarin, A. Bouajjani","doi":"10.1109/LICS.2001.932503","DOIUrl":"https://doi.org/10.1109/LICS.2001.932503","url":null,"abstract":"Investigates the computational power of several models of dynamical systems under infinitesimal perturbations of their dynamics. We consider models for both discrete- and continuous-time dynamical systems: Turing machines, piecewise affine maps, linear hybrid automata and piecewise-constant derivative systems (a simple model of hybrid systems). We associate with each of these models a notion of perturbed dynamics by a small /spl epsi/ (w.r.t. to a suitable metric), and define the perturbed reachability relation as the intersection of all reachability relations obtained by /spl epsi/-perturbations, for all possible values of /spl epsi/. We show that, for the four kinds of models we consider, the perturbed reachability relation is co-recursively enumerable (co-r.e.), and that any co-r.e. relation can be defined as the perturbed reachability relation of such models. A corollary of this result is that systems that are robust (i.e. whose reachability relation is stable under infinitesimal perturbation) are decidable.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130998668","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 : 2001-06-16DOI: 10.1109/LICS.2001.932492
A. Arnold, G. Lenzi, J. Marcinkowski
Closed monadic /spl Sigma//sub 1/, as proposed in (Ajtai et al., 1998), is the existential monadic second order logic where alternation between existential monadic second order quantifiers and first order quantifiers is allowed. Despite some effort very little is known about the expressive power of this logic on finite structures. We construct a tree automaton which exactly characterizes closed monadic /spl Sigma//sub 1/ on the Rabin tree and give a full analysis of the expressive power of closed monadic /spl Sigma//sub 1/ in this context. In particular we prove that the hierarchy inside closed monadic /spl Sigma//sub 1/, defined by the number of alternations between blocks of first order quantifiers and blocks of existential monadic second order quantifiers collapses, on the infinite tree, to the level 2.
{"title":"The hierarchy inside closed monadic /spl Sigma//sub 1/ collapses on the infinite binary tree","authors":"A. Arnold, G. Lenzi, J. Marcinkowski","doi":"10.1109/LICS.2001.932492","DOIUrl":"https://doi.org/10.1109/LICS.2001.932492","url":null,"abstract":"Closed monadic /spl Sigma//sub 1/, as proposed in (Ajtai et al., 1998), is the existential monadic second order logic where alternation between existential monadic second order quantifiers and first order quantifiers is allowed. Despite some effort very little is known about the expressive power of this logic on finite structures. We construct a tree automaton which exactly characterizes closed monadic /spl Sigma//sub 1/ on the Rabin tree and give a full analysis of the expressive power of closed monadic /spl Sigma//sub 1/ in this context. In particular we prove that the hierarchy inside closed monadic /spl Sigma//sub 1/, defined by the number of alternations between blocks of first order quantifiers and blocks of existential monadic second order quantifiers collapses, on the infinite tree, to the level 2.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132018604","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 : 2001-06-16DOI: 10.1109/LICS.2001.932506
Thorsten Altenkirch, P. Dybjer, M. Hofmann, P. Scott
Solves the decision problem for the simply typed lambda calculus with a strong binary sum, or, equivalently, the word problem for free Cartesian closed categories with binary co-products. Our method is based on the semantic technique known as "normalization by evaluation", and involves inverting the interpretation of the syntax in a suitable sheaf model and, from this, extracting an appropriate unique normal form. There is no rewriting theory involved and the proof is completely constructive, allowing program extraction from the proof.
{"title":"Normalization by evaluation for typed lambda calculus with coproducts","authors":"Thorsten Altenkirch, P. Dybjer, M. Hofmann, P. Scott","doi":"10.1109/LICS.2001.932506","DOIUrl":"https://doi.org/10.1109/LICS.2001.932506","url":null,"abstract":"Solves the decision problem for the simply typed lambda calculus with a strong binary sum, or, equivalently, the word problem for free Cartesian closed categories with binary co-products. Our method is based on the semantic technique known as \"normalization by evaluation\", and involves inverting the interpretation of the syntax in a suitable sheaf model and, from this, extracting an appropriate unique normal form. There is no rewriting theory involved and the proof is completely constructive, allowing program extraction from the proof.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125863303","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 : 2001-06-16DOI: 10.1109/LICS.2001.932502
D. Kozen, J. Tiuryn
We formulate a Gentzen-style sequent calculus for partial correctness that subsumes propositional Hoare logic. The system is a noncommutative intuitionistic linear logic. We prove soundness and completeness over relational and trace models. As a corollary, we obtain a complete sequent calculus for the inclusion and equivalence of regular expressions.
{"title":"Intuitionistic linear logic and partial correctness","authors":"D. Kozen, J. Tiuryn","doi":"10.1109/LICS.2001.932502","DOIUrl":"https://doi.org/10.1109/LICS.2001.932502","url":null,"abstract":"We formulate a Gentzen-style sequent calculus for partial correctness that subsumes propositional Hoare logic. The system is a noncommutative intuitionistic linear logic. We prove soundness and completeness over relational and trace models. As a corollary, we obtain a complete sequent calculus for the inclusion and equivalence of regular expressions.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125646555","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 : 2001-06-16DOI: 10.1109/LICS.2001.932485
H. Ganzinger
Compares three approaches to polynomial-time decidability for uniform word problems for quasi-varieties. Two of the approaches, by T. Evans (1951) and S. Burris (1995), respectively, are semantic, referring to certain embeddability and axiomatizability properties. The third approach is more proof-theoretic in nature, inspired by D. McAllester's (1993) concept of local inference. We define two closely related notions of locality for equational Horn theories and show that both of the criteria of Evans and Burris lie in between these two concepts. In particular, the variant we call "stable locality" is shown to subsume both Evans' and Burris's methods.
{"title":"Relating semantic and proof-theoretic concepts for polynomial time decidability of uniform word problems","authors":"H. Ganzinger","doi":"10.1109/LICS.2001.932485","DOIUrl":"https://doi.org/10.1109/LICS.2001.932485","url":null,"abstract":"Compares three approaches to polynomial-time decidability for uniform word problems for quasi-varieties. Two of the approaches, by T. Evans (1951) and S. Burris (1995), respectively, are semantic, referring to certain embeddability and axiomatizability properties. The third approach is more proof-theoretic in nature, inspired by D. McAllester's (1993) concept of local inference. We define two closely related notions of locality for equational Horn theories and show that both of the criteria of Evans and Burris lie in between these two concepts. In particular, the variant we call \"stable locality\" is shown to subsume both Evans' and Burris's methods.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126222052","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 : 2001-06-16DOI: 10.1109/LICS.2001.932505
R. Alur, S. L. Torre
Deciding infinite two-player games on finite graphs with the winning condition specified by a linear temporal logic (LTL) formula is known to be 2EXPTIME-complete. In this paper, we identify LTL fragments of lower complexity. Solving LTL games typically involves a doubly-exponential translation from LTL formulas to deterministic /spl omega/-automata. First, we show that the longest distance (length of the longest simple path) of the generator is also an important parameter, by giving an O(d log n)-space procedure to solve a Buchi game on a graph with n vertices and longest distance d. Then, for the LTL fragment with only eventualities and conjunctions, we provide a translation to deterministic generators of exponential size and linear longest distance, show both of these bounds to be optimal and prove the corresponding games to be PSPACE-complete. Introducing "next" modalities in this fragment, we provide a translation to deterministic generators that is still of exponential size but also with exponential longest distance, show both bounds to be optimal and prove the corresponding games to be EXPTIME-complete. For the fragment resulting by further adding disjunctions, we provide a translation to deterministic generators of doubly-exponential size and exponential longest distance, show both bounds to be optimal and prove the corresponding games to be EXPSPACE. Finally, we show tightness of the double-exponential bound on the size as well as the longest distance for deterministic generators for LTL, even in the absence of "next" and "until" modalities.
{"title":"Deterministic generators and games for LTL fragments","authors":"R. Alur, S. L. Torre","doi":"10.1109/LICS.2001.932505","DOIUrl":"https://doi.org/10.1109/LICS.2001.932505","url":null,"abstract":"Deciding infinite two-player games on finite graphs with the winning condition specified by a linear temporal logic (LTL) formula is known to be 2EXPTIME-complete. In this paper, we identify LTL fragments of lower complexity. Solving LTL games typically involves a doubly-exponential translation from LTL formulas to deterministic /spl omega/-automata. First, we show that the longest distance (length of the longest simple path) of the generator is also an important parameter, by giving an O(d log n)-space procedure to solve a Buchi game on a graph with n vertices and longest distance d. Then, for the LTL fragment with only eventualities and conjunctions, we provide a translation to deterministic generators of exponential size and linear longest distance, show both of these bounds to be optimal and prove the corresponding games to be PSPACE-complete. Introducing \"next\" modalities in this fragment, we provide a translation to deterministic generators that is still of exponential size but also with exponential longest distance, show both bounds to be optimal and prove the corresponding games to be EXPTIME-complete. For the fragment resulting by further adding disjunctions, we provide a translation to deterministic generators of doubly-exponential size and exponential longest distance, show both bounds to be optimal and prove the corresponding games to be EXPSPACE. Finally, we show tightness of the double-exponential bound on the size as well as the longest distance for deterministic generators for LTL, even in the absence of \"next\" and \"until\" modalities.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124251797","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：