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检索条件"任意字段=37th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2022"

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Proceedings of the 37th annual acm/ieee symposium on logic in computer science, lics 2022

Proceedings of the 37th Annual ACM/IEEE Symposium on Logic i...

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37th annual acm/ieee symposium on logic in computer science, lics 2022

ISBN: (纸本)9781450393515

the proceedings contain 64 papers. the topics discussed include: transducers of polynomial growth;normalization for multimodal type theory;computing the density of the positivity set for linear recurrence sequences;quantum weakest preconditions for reasoning about expected runtimes of quantum programs;on the Skolem problem and the Skolem conjecture;on the satisfiability of context-free string constraints with subword-ordering;identity testing for radical expressions;varieties of quantitative algebras and their monads;quantum expectation transformers for cost analysis;solvability of orbit-finite systems of linear equations;semantics for two-dimensional type theory;and the amazing mixed polynomial closure and its applications to two-variable first-order logic.

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Diagrammatic Algebra of First Order logic 39

Diagrammatic Algebra of First Order Logic

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39th annual acm/ieee symposium on logic in computer science (lics)

作者： Bonchi, Filippo Di Giorgio, Alessandro Haydon, Nathan Sobocinski, Pawel Univ Pisa Pisa Italy UCL London England Tallinn Univ Technol Tallinn Estonia

We introduce the calculus of neo-Peircean relations, a string diagrammatic extension of the calculus of binary relations that has the same expressivity as first order logic and comes with a complete axiomatisation. th... 详细信息

ISBN: (纸本)9798400706608

关键词： calculus of relations string diagrams deep inference

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Rank-decreasing transductions 24

Rank-decreasing transductions

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39th annual acm/ieee symposium on logic in computer science (lics)

作者： Bojanczyk, Mikolaj Ohlmann, Pierre University of Warsaw Warsaw Poland Computer Science CNRS LIS Université Aix-Marseille Marseille France

ISBN: (纸本)9798400706608

We propose to study transformations on graphs, and more generally structures, by looking at how the cut-rank (as introduced by Oum) of subsets is affected when going from the input structure to the output structure. We consider transformations in which the underlying sets are the same for both the input and output, and so the cut-ranks of subsets can be easily compared. the purpose of this paper is to give a characterisation of logically defined transductions that is expressed in purely structural terms, without referring to logic: transformations which decrease the cut-rank, in the asymptotic sense, are exactly those that can be defined in monadic second-order logic. this characterisation assumes that the transduction has inputs of bounded treewidth;we also show that the characterisation fails in the absence of any assumptions.

关键词： Cut-rank transductions monadic second-order logic

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Separating LREC from LFP 22

Separating LREC from LFP

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37th annual acm/ieee symposium on logic in computer science, lics 2022

作者： Dawar, Anuj Santos, Felipe Ferreira Department of Computer Science and Technology University of Cambridge Cambridge United Kingdom

ISBN: (纸本)9781450393515

LREC= is an extension of frst-order logic with a logarithmic recursion operator. It was introduced by Grohe et al. and shown to capture the complexity class L over trees and interval graphs. It does not capture L in general as it is contained in FPC-fxed-point logic with counting. We show that this containment is strict. In particular, we show that the path systems problem, a classic Pcomplete problem which is defnable in LFP-fxed-point logic-is not defnable in LREC=. this shows that the logarithmic recursion mechanism is provably weaker than general least fxed points. © 2022 Copyright held by the owner/author(s). Publication rights licensed to acm.

关键词： computer circuits

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Probability monads with submonads of deterministic states 22

Probability monads with submonads of deterministic states

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37th annual acm/ieee symposium on logic in computer science, lics 2022

作者： Moss, Sean Perrone, Paolo University of Oxford Department of Computer Science Oxford United Kingdom

ISBN: (纸本)9781450393515

Probability theory can be studied synthetically as the computational effect embodied by a commutative monad. In the recently proposed Markov categories, one works with an abstraction of the Kleisli category and then defnes deterministic morphisms equationally in terms of copying and discarding. the resulting difference between 'pure' and 'deterministic' leads us to investigate the 'sober' objects for a probability monad, for which the two concepts coincide. We propose natural conditions on a probability monad which allow us to identify the sober objects and defne an idempotent sobrifcation functor. Our framework applies to many examples of interest, including the Giry monad on measurable spaces, and allows us to sharpen a previously given version of de Finetti's theorem for Markov categories. © 2022 Copyright held by the owner/author(s). Publication rights licensed to acm.

关键词： Probability

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Syllepsis in Homotopy Type theory 22

Syllepsis in Homotopy Type Theory

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37th annual acm/ieee symposium on logic in computer science, lics 2022

作者： Sojakova, Kristina Kavvos, G.A. Inria Paris Prosecco Paris France University of Bristol Department of Computer Science Bristol United Kingdom

ISBN: (纸本)9781450393515

the Eckmann-Hilton argument shows that any two monoid structures on the same set satisfying the interchange law are in fact the same operation, which is moreover commutative. When the monoids correspond to the vertical and horizontal composition of a sufciently higher-dimensional category, the Eckmann-Hilton argument itself appears as a higher cell. this cell is often required to satisfy an additional piece of coherence, which is known as the syllepsis. We show that the syllepsis can be constructed from the elimination rule of intensional identity types in Martin-Löf type theory. © 2022 Copyright held by the owner/author(s). Publication rights licensed to acm.

关键词： Formal languages

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Exponentials as Substitutions and the Cost of Cut Elimination in Linear logic 22

Exponentials as Substitutions and the Cost of Cut Eliminatio...

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37th annual acm/ieee symposium on logic in computer science, lics 2022

作者： Accattoli, Beniamino Inria and Lix École Polytechnique France

ISBN: (纸本)9781450393515

this paper introduces the exponential substitution calculus (ESC), a new presentation of cut elimination for IMELL, based on proof terms and building on the idea that exponentials can be seen as explicit substitutions. the idea in itself is not new, but here it is pushed to a new level, inspired by Accattoli and Kesner's linear substitution calculus (LSC). One of the key properties of the LSC is that it naturally models the sub-term property of abstract machines, which is the key ingredient for the study of reasonable time cost models for the w-calculus. the new ESC is then used to design a cut elimination strategy with the sub-term property, providing the frst polynomial cost model for cut elimination with unconstrained exponentials. For the ESC, we also prove untyped confluence and typed strong normalization, showing that it is an alternative to proof nets for an advanced study of cut elimination. © 2022 Copyright held by the owner/author(s). Publication rights licensed to acm.

关键词： Calculations

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A Functorial Excursion Between Algebraic Geometry and Linear logic 22

A Functorial Excursion Between Algebraic Geometry and Linear...

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37th annual acm/ieee symposium on logic in computer science, lics 2022

作者： Melliès, Paul-André CNRS Université Paris Cité Inria France

ISBN: (纸本)9781450393515

the language of Algebraic Geometry combines two complementary and dependent levels of discourse: on the geometric side, schemes defne spaces of the same cohesive nature as manifolds;on the vectorial side, every scheme X comes equipped with a symmetric monoidal category of quasicoherent modules, which may be seen as generalised vector bundles on the scheme X. In this paper, we use the functor of points approach to Algebraic Geometry developed by Grothendieck in the 1970s to establish that every covariant presheaf X on the category of commutative rings - and in particular every scheme X - comes equipped "above it"with a symmetric monoidal closed category PshModX of presheaves of modules. this category PshModX defnes moreover a model of intuitionistic linear logic, whose exponential modality is obtained by glueing together in an appropriate way the Sweedler dual construction on ring algebras. © 2022 Copyright held by the owner/author(s). Publication rights licensed to acm.

关键词： Vector spaces

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Greatest HITs: Higher inductive types in coinductive definitions via induction under clocks 22

Greatest HITs: Higher inductive types in coinductive definit...

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37th annual acm/ieee symposium on logic in computer science, lics 2022

作者： Kristensen, Magnus Baunsgaard Møgelberg, Rasmus Ejlers Vezzosi, Andrea Department of Computer Science It University of Copenhagen Denmark

ISBN: (纸本)9781450393515

We present Clocked Cubical Type theory, the frst type theory combining multi-clocked guarded recursion with the features of Cubical Type theory. Guarded recursion is an abstract form of step-indexing, which can be used for construction of advanced programming language models. In its multi-clocked version, it can also be used for coinductive programming and reasoning, encoding productivity in types. Combining this with Higher Inductive Types (HITs) the encoding extends to coinductive types that are traditionally hard to represent in type theory, such as the type of fnitely branching labelled transition systems. Among our technical contributions is a new principle of induction under clocks, providing computational content to one of the main axioms required for encoding coinductive types. this principle is verifed using a denotational semantics in a presheaf model. © 2022 Copyright held by the owner/author(s). Publication rights licensed to acm.

关键词： Clocks

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Smooth approximations and CSPs over finitely bounded homogeneous structures 22

Smooth approximations and CSPs over finitely bounded homogen...

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37th annual acm/ieee symposium on logic in computer science, lics 2022

作者： Mottet, Antoine Pinsker, Michael Tu Hamburg Institute for Theoretical Computer Science Hamburg Germany Tu Wien Institute of Discrete Mathematics and Geometry Vienna Austria

ISBN: (纸本)9781450393515

We introduce the novel machinery of smooth approximations, and apply it to confrm the CSP dichotomy conjecture for frst-order reducts of the random tournament, and to give new short proofs of the conjecture for various homogeneous graphs including the random graph (STOC'11, ICALP'16), and for expansions of the order of the rationals (STOC'08). Apart from obtaining these dichotomy results, we show how our new proof technique allows to unify and signifcantly simplify the previous results from the literature. For all but the last structure, we moreover characterize for the frst time those CSPs which are solvable by local consistency methods, again using the same machinery. © 2022 Copyright held by the owner/author(s). Publication rights licensed to acm.

关键词： Machinery

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