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Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science最新文献

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Higher Groups in Homotopy Type Theory 同伦型论中的高群
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-02-12 DOI: 10.1145/3209108.3209150
Ulrik Buchholtz, Floris van Doorn, E. Rijke
{"title":"Higher Groups in Homotopy Type Theory","authors":"Ulrik Buchholtz, Floris van Doorn, E. Rijke","doi":"10.1145/3209108.3209150","DOIUrl":"https://doi.org/10.1145/3209108.3209150","url":null,"abstract":"We present a development of the theory of higher groups, including infinity groups and connective spectra, in homotopy type theory. An infinity group is simply the loops in a pointed, connected type, where the group structure comes from the structure inherent in the identity types of Martin-Löf type theory. We investigate ordinary groups from this viewpoint, as well as higher dimensional groups and groups that can be delooped more than once. A major result is the stabilization theorem, which states that if an n-type can be delooped n + 2 times, then it is an infinite loop type. Most of the results have been formalized in the Lean proof assistant.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127216140","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}
引用次数: 31
Unification nets: canonical proof net quantifiers 统一网:规范证明网量词
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-02-09 DOI: 10.1145/3209108.3209159
Dominic J. D. Hughes
{"title":"Unification nets: canonical proof net quantifiers","authors":"Dominic J. D. Hughes","doi":"10.1145/3209108.3209159","DOIUrl":"https://doi.org/10.1145/3209108.3209159","url":null,"abstract":"Proof nets for MLL (unit-free Multiplicative Linear Logic) are concise graphical representations of proofs which are canonical in the sense that they abstract away syntactic redundancy such as the order of non-interacting rules. We argue that Girard's extension to MLL1 (first-order MLL) fails to be canonical because of redundant existential witnesses, and present canonical MLL1 proof nets called unification nets without them. For example, while there are infinitely many cut-free Girard nets ∀x Px ⊢ ∃x Px, one per arbitrary witness for ∃x, there is a unique cut-free unification net, with no specified witness. Cut elimination for unification nets is local and linear time, while Girard's is non-local and exponential time. Since some unification nets are exponentially smaller than corresponding Girard nets and sequent proofs, technical delicacy is required to ensure correctness is polynomial-time (quadratic). These results transcend MLL1 via a methodological insight: for canonical quantifiers, the standard parallel/sequential dichotomy of proof nets is insufficient; an implicit/explicit witness dichotomy is needed. Current work extends unification nets to additives and uses them to extend combinatorial proofs [Proofs without syntax, Annals of Mathematics, 2006] to classical first-order logic.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128843558","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}
引用次数: 12
A universal-algebraic proof of the complexity dichotomy for Monotone Monadic SNP 单调一元SNP复杂度二分的一般代数证明
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-02-09 DOI: 10.1145/3209108.3209156
M. Bodirsky, Florent R. Madelaine, A. Mottet
{"title":"A universal-algebraic proof of the complexity dichotomy for Monotone Monadic SNP","authors":"M. Bodirsky, Florent R. Madelaine, A. Mottet","doi":"10.1145/3209108.3209156","DOIUrl":"https://doi.org/10.1145/3209108.3209156","url":null,"abstract":"The logic MMSNP is a restricted fragment of existential second-order logic which allows to express many interesting queries in graph theory and finite model theory. The logic was introduced by Feder and Vardi who showed that every MMSNP sentence is computationally equivalent to a finite-domain constraint satisfaction problem (CSP); the involved probabilistic reductions were derandomized by Kun using explicit constructions of expander structures. We present a new proof of the reduction to finite-domain CSPs that does not rely on the results of Kun. This new proof allows us to obtain a stronger statement and to verify the Bodirsky-Pinsker dichotomy conjecture for CSPs in MMSNP. Our approach uses the fact that every MMSNP sentence describes a finite union of CSPs for countably infinite ω-categorical structures; moreover, by a recent result of Hubička and Nešetřil, these structures can be expanded to homogeneous structures with finite relational signature and the Ramsey property. This allows us to use the universal-algebraic approach to study the computational complexity of MMSNP.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124401857","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}
引用次数: 31
Impredicative Encodings of (Higher) Inductive Types (高级)归纳类型的谓词编码
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-02-08 DOI: 10.1145/3209108.3209130
S. Awodey, Jonas Frey, S. Speight
{"title":"Impredicative Encodings of (Higher) Inductive Types","authors":"S. Awodey, Jonas Frey, S. Speight","doi":"10.1145/3209108.3209130","DOIUrl":"https://doi.org/10.1145/3209108.3209130","url":null,"abstract":"Postulating an impredicative universe in dependent type theory allows System F style encodings of finitary inductive types, but these fail to satisfy the relevant η-equalities and consequently do not admit dependent eliminators. To recover η and dependent elimination, we present a method to construct refinements of these impredicative encodings, using ideas from homotopy type theory. We then extend our method to construct impredicative encodings of some higher inductive types, such as 1-truncation and the unit circle S1.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115314872","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}
引用次数: 22
Definable Ellipsoid Method, Sums-of-Squares Proofs, and the Isomorphism Problem 可定义椭球法，平方和证明，和同构问题
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-02-07 DOI: 10.1145/3209108.3209186
Albert Atserias, Joanna Ochremiak
{"title":"Definable Ellipsoid Method, Sums-of-Squares Proofs, and the Isomorphism Problem","authors":"Albert Atserias, Joanna Ochremiak","doi":"10.1145/3209108.3209186","DOIUrl":"https://doi.org/10.1145/3209108.3209186","url":null,"abstract":"The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem. We observe that the previously known method for showing that this reduction can be done in fixed-point logic with counting (FPC) for linear and semidefinite programs applies to any family of explicitly bounded convex sets. We use this observation to show that the exact feasibility problem for semidefinite programs is expressible in the infinitary version of FPC. As a corollary we get that, for the graph isomorphism problem, the Lasserre/Sums-of-Squares semidefinite programming hierarchy of relaxations collapses to the Sherali-Adams linear programming hierarchy, up to a small loss in the degree.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129122325","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}
引用次数: 42
Polynomial Invariants for Affine Programs 仿射规划的多项式不变量
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-02-06 DOI: 10.1145/3209108.3209142
E. Hrushovski, J. Ouaknine, Amaury Pouly, J. Worrell
{"title":"Polynomial Invariants for Affine Programs","authors":"E. Hrushovski, J. Ouaknine, Amaury Pouly, J. Worrell","doi":"10.1145/3209108.3209142","DOIUrl":"https://doi.org/10.1145/3209108.3209142","url":null,"abstract":"We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that hold at each location of a given affine program (i.e., a program having only non-deterministic (as opposed to conditional) branching and all of whose assignments are given by affine expressions). Our main tool is an algebraic result of independent interest: given a finite set of rational square matrices of the same dimension, we show how to compute the Zariski closure of the semigroup that they generate.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130844733","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}
引用次数: 51
Cellular Cohomology in Homotopy Type Theory 同伦型理论中的细胞上同调
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-02-06 DOI: 10.1145/3209108.3209188
Ulrik Buchholtz, Kuen-Bang Hou
{"title":"Cellular Cohomology in Homotopy Type Theory","authors":"Ulrik Buchholtz, Kuen-Bang Hou","doi":"10.1145/3209108.3209188","DOIUrl":"https://doi.org/10.1145/3209108.3209188","url":null,"abstract":"We present a development of cellular cohomology in homotopy type theory. Cohomology associates to each space a sequence of abelian groups capturing part of its structure, and has the advantage over homotopy groups in that these abelian groups of many common spaces are easier to compute. Cellular cohomology is a special kind of cohomology designed for cell complexes: these are built in stages by attaching spheres of progressively higher dimension, and cellular cohomology defines the groups out of the combinatorial description of how spheres are attached. Our main result is that for finite cell complexes, a wide class of cohomology theories (including the ones defined through Eilenberg-MacLane spaces) can be calculated via cellular cohomology. This result was formalized in the Agda proof assistant.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116480907","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}
引用次数: 12
Can One Escape Red Chains?: Regular Path Queries Determinacy is Undecidable 一个人能逃脱红色枷锁吗?:常规路径查询的确定性是不可确定的
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-02-05 DOI: 10.1145/3209108.3209120
Grzegorz Gluch, J. Marcinkowski, Piotr Ostropolski-Nalewaja
{"title":"Can One Escape Red Chains?: Regular Path Queries Determinacy is Undecidable","authors":"Grzegorz Gluch, J. Marcinkowski, Piotr Ostropolski-Nalewaja","doi":"10.1145/3209108.3209120","DOIUrl":"https://doi.org/10.1145/3209108.3209120","url":null,"abstract":"For a given set of queries (which are expressions in some query language) Q = {Q1, Q2, ... Qk} and for another query Q0 we say that Q determines Q0 if -- informally speaking -- for every database D, the information contained in the views Q(D) is sufficient to compute Q0(D). Query Determinacy Problem is the problem of deciding, for given Q and Q0. whether Q determines Q0. Many versions of this problem, for different query languages, were studied in database theory. In this paper we solve a problem stated in [CGLV02] and show that Query Determinacy Problem is undecidable for the Regular Path Queries -- the paradigmatic query language of graph databases.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126155887","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}
引用次数: 4
Unary negation fragment with equivalence relations has the finite model property 具有等价关系的一元负片段具有有限模型性质
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-02-05 DOI: 10.1145/3209108.3209205
Daniel Danielski, Emanuel Kieronski
{"title":"Unary negation fragment with equivalence relations has the finite model property","authors":"Daniel Danielski, Emanuel Kieronski","doi":"10.1145/3209108.3209205","DOIUrl":"https://doi.org/10.1145/3209108.3209205","url":null,"abstract":"We consider an extension of the unary negation fragment of first-order logic in which arbitrarily many binary symbols may be required to be interpreted as equivalence relations. We show that this extension has the finite model property. More specifically, we show that every satisfiable formula has a model of at most doubly exponential size. We argue that the satisfiability (= finite satisfiability) problem for this logic is 2-ExpTime-complete. We also transfer our results to a restricted variant of the guarded negation fragment with equivalence relations.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114749523","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}
引用次数: 5
Regular Transducer Expressions for Regular Transformations 正则变换的正则换能器表达式
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-02-05 DOI: 10.1145/3209108.3209182
V. Dave, P. Gastin, Krishna Shankara Narayanan
{"title":"Regular Transducer Expressions for Regular Transformations","authors":"V. Dave, P. Gastin, Krishna Shankara Narayanan","doi":"10.1145/3209108.3209182","DOIUrl":"https://doi.org/10.1145/3209108.3209182","url":null,"abstract":"Functional MSO transductions, deterministic two-way transducers, as well as streaming string transducers are all equivalent models for regular functions. In this paper, we show that every regular function, either on finite words or on infinite words, captured by a deterministic two-way transducer, can be described with a regular transducer expression (RTE). For infinite words, the transducer uses Muller acceptance and ω-regular look-ahead. RTEs are constructed from constant functions using the combinators if-then-else (deterministic choice), Hadamard product, and unambiguous versions of the Cauchy product, the 2-chained Kleene-iteration and the 2-chained omega-iteration. Our proof works for transformations of both finite and infinite words, extending the result on finite words of Alur et al. in LICS'14. In order to construct an RTE associated with a deterministic two-way Muller transducer with look-ahead, we introduce the notion of transition monoid for such two-way transducers where the look-ahead is captured by some backward deterministic Büchi automaton. Then, we use an unambiguous version of Imre Simon's famous forest factorization theorem in order to derive a \"good\" (ω-)regular expression for the domain of the two-way transducer. \"Good\" expressions are unambiguous and Kleene-plus as well as ω-iterations are only used on subexpressions corresponding to idempotent elements of the transition monoid. The combinator expressions are finally constructed by structural induction on the \"good\" (ω-)regular expression describing the domain of the transducer.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133036259","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}
引用次数: 23
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