2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)最新文献_第9页

PTAS for Sparse General-Valued CSPs 稀疏一般值csp的PTAS

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-12-23 DOI: 10.1109/LICS52264.2021.9470599

Balázs F. Mezei, Marcin Wrochna, Stanislav Živný

{"title":"PTAS for Sparse General-Valued CSPs","authors":"Balázs F. Mezei, Marcin Wrochna, Stanislav Živný","doi":"10.1109/LICS52264.2021.9470599","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470599","url":null,"abstract":"We study polynomial-time approximation schemes (PTASes) for constraint satisfaction problems (CSPs) such as Maximum Independent Set or Minimum Vertex Cover on sparse graph classes.Baker’s approach gives a PTAS on planar graphs, excluded-minor classes, and beyond. For Max-CSPs, and even more generally, maximisation finite-valued CSPs (where constraints are arbitrary non-negative functions), Romero, Wrochna, and Živný [SODA’21] showed that the Sherali-Adams LP relaxation gives a simple PTAS for all fractionally-treewidth-fragile classes, which is the most general \"sparsity\" condition for which a PTAS is known. We extend these results to general-valued CSPs, which include \"crisp\" (or \"strict\") constraints that have to be satisfied by every feasible assignment. The only condition on the crisp constraints is that their domain contains an element which is at least as feasible as all the others (but possibly less valuable).For minimisation general-valued CSPs with crisp constraints, we present a PTAS for all Baker graph classes — a definition by Dvořák [SODA’20] which encompasses all classes where Baker’s technique is known to work, except for fractionally-treewidth-fragile classes. While this is standard for problems satisfying a certain monotonicity condition on crisp constraints, we show this can be relaxed to diagonalisability — a property of relational structures connected to logics, statistical physics, and random CSPs.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123496328","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: 3

Combining Nondeterminism, Probability, and Termination: Equational and Metric Reasoning 结合非决定论、概率和终止:等式和度量推理

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-12-01 DOI: 10.1109/LICS52264.2021.9470717

M. Mio, Ralph Sarkis, Valeria Vignudelli

引用次数: 14

Behavioural Preorders via Graded Monads 通过分级单子进行行为预购

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-11-29 DOI: 10.1109/LICS52264.2021.9470517

Chase Ford, Stefan Milius, Lutz Schröder

{"title":"Behavioural Preorders via Graded Monads","authors":"Chase Ford, Stefan Milius, Lutz Schröder","doi":"10.1109/LICS52264.2021.9470517","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470517","url":null,"abstract":"Like notions of process equivalence, behavioural preorders on processes come in many flavours, ranging from fine-grained comparisons such as ready simulation to coarse-grained ones such as trace inclusion. Often, such behavioural preorders are characterized in terms of theory inclusion in dedicated characteristic logics; e.g. simulation is characterized by theory inclusion in the positive fragment of Hennessy-Milner logic. We introduce a unified semantic framework for behavioural preorders and their characteristic logics in which we parametrize the system type as a functor on the category Pos of partially ordered sets following the paradigm of universal coalgebra, while behavioural preorders are captured as graded monads on Pos, in generalization of a previous approach to notions of process equivalence. We show that graded monads on Pos are induced by a form of graded inequational theories that we introduce here. Moreover, we provide a general notion of modal logic compatible with a given graded behavioural preorder, along with a criterion for expressiveness, in the indicated sense of characterization of the behavioural preorder by theory inclusion. We illustrate our main result on various behavioural preorders on labelled transition systems and probabilistic transition systems.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"6 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114013477","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: 8

Categorical models of Linear Logic with fixed points of formulas 具有公式不动点的线性逻辑范畴模型

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-11-19 DOI: 10.1109/LICS52264.2021.9470664

T. Ehrhard, Farzad Jafarrahmani

引用次数: 11

Constraint Satisfaction Problems over Finite Structures 有限结构的约束满足问题

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-10-10 DOI: 10.1109/LICS52264.2021.9470670

L. Barto, William DeMeo, A. Mottet

引用次数: 2

Internal ∞-Categorical Models of Dependent Type Theory : Towards 2LTT Eating HoTT 依赖类型理论的内部∞-范畴模型:走向2LTT进食热

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-09-03 DOI: 10.1109/LICS52264.2021.9470667

Nicolai Kraus

{"title":"Internal ∞-Categorical Models of Dependent Type Theory : Towards 2LTT Eating HoTT","authors":"Nicolai Kraus","doi":"10.1109/LICS52264.2021.9470667","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470667","url":null,"abstract":"Using dependent type theory to formalise the syntax of dependent type theory is a very active topic of study and goes under the name of \"type theory eating itself\" or \"type theory in type theory.\" Most approaches are at least loosely based on Dybjer’s categories with families (CwF’s) and come with a type Con of contexts, a type family Ty indexed over it modelling types, and so on. This works well in versions of type theory where the principle of unique identity proofs (UIP) holds. In homotopy type theory (HoTT) however, it is a long-standing and frequently discussed open problem whether the type theory \"eats itself\" and can serve as its own interpreter. The fundamental underlying difficulty seems to be that categories are not suitable to capture a type theory in the absence of UIP.In this paper, we develop a notion of ∞-categories with families (∞-CwF’s). The approach to higher categories used relies on the previously suggested semi-Segal types, with a new construction of identity substitutions that allow for both univalent and non-univalent variations. The type-theoretic universe as well as the internalised (set-level) syntax are models, although it remains a conjecture that the latter is initial. To circumvent the known unsolved problem of constructing semisimplicial types, the definition is presented in two-level type theory (2LTT).Apart from introducing ∞-CwF’s, the paper explains the shortcomings of 1-categories in type theory without UIP as well as the difficulties of and approaches to internal higher-dimensional categories.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131005106","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: 8

Comonadic semantics for guarded fragments 保护片段的共元语义

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-08-25 DOI: 10.1109/LICS52264.2021.9470594

S. Abramsky, Dan Marsden

引用次数: 18

Canonical Polymorphisms of Ramsey Structures and the Unique Interpolation Property Ramsey结构的典型多态性和唯一插值性质

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-08-24 DOI: 10.1109/LICS52264.2021.9470683

M. Bodirsky, Bertalan Bodor

引用次数: 11

A Bunched Logic for Conditional Independence 条件独立的束逻辑

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-08-20 DOI: 10.1109/LICS52264.2021.9470712

Jialu Bao, Simon Docherty, Justin Hsu, Alexandra Silva

引用次数: 8

Forbidden Induced Subgraphs and the Łoś–Tarski Theorem 禁止诱导子图和Łoś-Tarski定理

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-08-02 DOI: 10.1109/LICS52264.2021.9470742

Yijia Chen, J. Flum

{"title":"Forbidden Induced Subgraphs and the Łoś–Tarski Theorem","authors":"Yijia Chen, J. Flum","doi":"10.1109/LICS52264.2021.9470742","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470742","url":null,"abstract":"Let $mathcal{C}$ be a class of finite and infinite graphs that is closed under induced subgraphs. The well-known Łoś–Tarski Theorem from classical model theory implies that $mathcal{C}$ is definable in first-order logic (FO) by a sentence φ if and only if $mathcal{C}$ has a finite set of forbidden induced finite subgraphs. It provides a powerful tool to show nontrivial characterizations of graphs of small vertex cover, of bounded tree-depth, of bounded shrub-depth, etc. in terms of forbidden induced finite subgraphs. Furthermore, by the Completeness Theorem, we can compute from φ the corresponding forbidden induced subgraphs. Our results (a) and (b) show that this machinery fails on finite graphs.(a)There is a class of finite graphs that is definable in FO and closed under induced subgraphs but has no finite set of forbidden induced subgraphs.(b)Even if we only consider classes $mathcal{C}$ of finite graphs that can be characterized by a finite set of forbidden induced subgraphs such a characterization cannot be computed from an FO-sentence φ that defines $mathcal{C}$ and the size of the characterization cannot be bounded by f(|φ|) for any computable function f.Besides their importance in graph theory, our results also significantly strengthen similar known theorems for arbitrary structures.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123996165","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: 3