IA Scholar Query: Hyperedge Substitution in Basic Atom-Replacement Languages.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgFri, 04 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Compound Logics for Modification Problems
https://scholar.archive.org/work/lpjop6xt6zafjiqvz7ly5s4jvu
We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of sentences, expressing graph modification: the modulator sentence, defining some property of the modified part of the graph, and the target sentence, defining some property of the resulting graph. In our framework, modulator sentences are in counting monadic second-order logic (CMSOL) and have models of bounded treewidth, while target sentences express first-order logic (FOL) properties along with minor-exclusion. Our logic captures problems that are not definable in first-order logic and, moreover, may have instances of unbounded treewidth. Also, it permits the modeling of wide families of problems involving vertex/edge removals, alternative modulator measures (such as elimination distance or 𝒢-treewidth), multistage modifications, and various cut problems. Our main result is that, for this compound logic, model-checking can be done in quadratic time. All derived algorithms are constructive and this, as a byproduct, extends the constructibility horizon of the algorithmic applications of the Graph Minors theorem of Robertson and Seymour. The proposed logic can be seen as a general framework to capitalize on the potential of the irrelevant vertex technique. It gives a way to deal with problem instances of unbounded treewidth, for which Courcelle's theorem does not apply. The proof of our meta-theorem combines novel combinatorial results related to the Flat Wall theorem along with elements of the proof of Courcelle's theorem and Gaifman's theorem. We finally prove extensions where the target property is expressible in FOL+DP, i.e., the enhancement of FOL with disjoint-paths predicates.Fedor V. Fomin and Petr A. Golovach and Ignasi Sau and Giannos Stamoulis and Dimitrios M. Thilikoswork_lpjop6xt6zafjiqvz7ly5s4jvuFri, 04 Nov 2022 00:00:00 GMTModel-Checking for First-Order Logic with Disjoint Paths Predicates in Proper Minor-Closed Graph Classes
https://scholar.archive.org/work/uvd7bz7t2nfd5na4n6fubs2iha
The disjoint paths logic, FOL+DP, is an extension of First-Order Logic (FOL) with the extra atomic predicate dp_k(x_1,y_1,...,x_k,y_k), expressing the existence of internally vertex-disjoint paths between x_i and y_i, for i∈{1,..., k}. This logic can express a wide variety of problems that escape the expressibility potential of FOL. We prove that for every proper minor-closed graph class, model-checking for FOL+DP can be done in quadratic time. We also introduce an extension of FOL+DP, namely the scattered disjoint paths logic, FOL+SDP, where we further consider the atomic predicate s -sdp_k(x_1,y_1,...,x_k,y_k), demanding that the disjoint paths are within distance bigger than some fixed value s. Using the same technique we prove that model-checking for FOL+SDP can be done in quadratic time on classes of graphs with bounded Euler genus.Petr A. Golovach and Giannos Stamoulis and Dimitrios M. Thilikoswork_uvd7bz7t2nfd5na4n6fubs2ihaThu, 03 Nov 2022 00:00:00 GMTTowards Discovering Neural Architectures from Scratch
https://scholar.archive.org/work/6f35kq6fdbbzfcnytoe4dbml2m
The discovery of neural architectures from scratch is the long-standing goal of Neural Architecture Search (NAS). Searching over a wide spectrum of neural architectures can facilitate the discovery of previously unconsidered but well-performing architectures. In this work, we take a large step towards discovering neural architectures from scratch by expressing architectures algebraically. This algebraic view leads to a more general method for designing search spaces, which allows us to compactly represent search spaces that are 100s of orders of magnitude larger than common spaces from the literature. Further, we propose a Bayesian Optimization strategy to efficiently search over such huge spaces, and demonstrate empirically that both our search space design and our search strategy can be superior to existing baselines. We open source our algebraic NAS approach and provide APIs for PyTorch and TensorFlow.Simon Schrodi, Danny Stoll, Binxin Ru, Rhea Sukthanker, Thomas Brox, Frank Hutterwork_6f35kq6fdbbzfcnytoe4dbml2mThu, 03 Nov 2022 00:00:00 GMTTensor Algebra and its Applications to Data Science and Statistics
https://scholar.archive.org/work/gprstwks2rbuxm366plgivxnzy
This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in the literature, and to explain how these usages are manifestations of a common concept. Not all relevant topics are discussed in detail, but the attempt is made to briefly describe and give references for some of the most important topics not included in the main survey. Particular attention is given to tensor decompositions.William Krinsmanwork_gprstwks2rbuxm366plgivxnzyTue, 25 Oct 2022 00:00:00 GMTA Topological Representation of Semantics of First-order Logic and Its Application as a Method in Model Theory
https://scholar.archive.org/work/aebxagchmzdzzire6c2mpu2e4e
Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean algebra is represented as the algebra of the clopen sets of a Stone space. And based on this, a natural connection is established between the structure of Stone space and the semantics of propositional logic. In other words, models of a propositional theory are represented as points in a Stone space. This enables us to use the concepts of topology to describe many facts in logic. In this paper, we do the same thing for the first-order logic. That is, we organize the basic objects of semantics of first-order logic, such as theories, models, elementary embeddings, and so on, into a kind of topological structure defined abstractly. To be precise, this kind of structure is a kind of enriched-topological space which we call cylindric space in this paper. Furthermore, based on this topological representation of semantics of first-order logic, we systematically introduce a method of point-set topology into the research of model theory. We demonstrate the great advantages of this topological method with an example and provide a general discussion of its features, advantages, and connection to the type space.Yunfei Qinwork_aebxagchmzdzzire6c2mpu2e4eMon, 17 Oct 2022 00:00:00 GMTGeometry of nonequilibrium reaction networks
https://scholar.archive.org/work/zyawisfdtvgufbugklvhzistki
The modern thermodynamics of discrete systems is based on graph theory, which provides both algebraic methods to define observables and a geometric intuition of their meaning and role. However, because chemical reactions are usually many-to-many, chemical networks are rather described by hypergraphs, which lack a systematized algebraic treatment and a clear geometric intuition. Here we fill this gap by building fundamental bases of chemical cycles (encoding stationary behavior) and cocycles (encoding finite-time relaxation). We interpret them in terms of circulations and gradients on the hypergraph, and use them to properly identify nonequilibrium observables. As application, we unveil hidden symmetries in linear response and, within this regime, propose a reconstruction algorithm for large metabolic networks consistent with Kirchhoff's Voltage and Current Laws.Sara Dal Cengio, Vivien Lecomte, Matteo Polettiniwork_zyawisfdtvgufbugklvhzistkiMon, 17 Oct 2022 00:00:00 GMTNotes on CSPs and Polymorphisms
https://scholar.archive.org/work/kouwgol6o5h55lxjkqyjupnv2i
These are notes from a multi-year learning seminar on the algebraic approach to Constraint Satisfaction Problems (CSPs). The main topics covered are the theory of algebraic structures with few subpowers, the theory of absorbing subalgebras and its applications to studying CSP templates which can be solved by local consistency methods, and the dichotomy theorem for conservative CSP templates. Subsections and appendices cover supplementary material.Zarathustra Bradywork_kouwgol6o5h55lxjkqyjupnv2iThu, 13 Oct 2022 00:00:00 GMTAgenda manipulation-proofness, stalemates, and redundant elicitation in preference aggregation. Exposing the bright side of Arrow's theorem
https://scholar.archive.org/work/k5g4lxhmv5aoriutltesic4jjq
This paper provides a general framework to explore the possibility of agenda manipulation-proof and proper consensus-based preference aggregation rules, so powerfully called in doubt by a disputable if widely shared understanding of Arrow's 'general possibility theorem'. We consider two alternative versions of agenda manipulation-proofness for social welfare functions, that are distinguished by 'parallel' vs. 'sequential' execution of agenda formation and preference elicitation, respectively. Under the 'parallel' version, it is shown that a large class of anonymous and idempotent social welfare functions that satisfy both agenda manipulation-proofness and strategy-proofness on a natural domain of single-peaked 'meta-preferences' induced by arbitrary total preference preorders are indeed available. It is only under the second, 'sequential' version that agenda manipulation-proofness on the same natural domain of single-peaked 'meta-preferences' is in fact shown to be tightly related to the classic Arrowian 'independence of irrelevant alternatives' (IIA) for social welfare functions. In particular, it is shown that using IIA to secure such 'sequential' version of agenda manipulation-proofness and combining it with a very minimal requirement of distributed responsiveness results in a characterization of the 'global stalemate' social welfare function, the constant function which invariably selects universal social indifference. It is also argued that, altogether, the foregoing results provide new significant insights concerning the actual content and the constructive implications of Arrow's 'general possibility theorem' from a mechanism-design perspective.Stefano Vannucciwork_k5g4lxhmv5aoriutltesic4jjqThu, 06 Oct 2022 00:00:00 GMTType checking data structures more complex than trees
https://scholar.archive.org/work/f6lf3zda4jadbedycjr7c5azn4
Graphs are a generalized concept that encompasses more complex data structures than trees, such as difference lists, doubly-linked lists, skip lists, and leaf-linked trees. Normally, these structures are handled with destructive assignments to heaps, which is opposed to a purely functional programming style and makes verification difficult. We propose a new purely functional language, λ_GT, that handles graphs as immutable, first-class data structures with a pattern matching mechanism based on Graph Transformation and developed a new type system, F_GT, for the language. Our approach is in contrast with the analysis of pointer manipulation programs using separation logic, shape analysis, etc. in that (i) we do not consider destructive operations but pattern matchings over graphs provided by the new higher-level language that abstract pointers and heaps away and that (ii) we pursue what properties can be established automatically using a rather simple typing framework.Jin Sano, Naoki Yamamoto, Kazunori Uedawork_f6lf3zda4jadbedycjr7c5azn4Mon, 12 Sep 2022 00:00:00 GMTKochen-Specker Contextuality
https://scholar.archive.org/work/vub2wqx3bnfvhfcecbkbdcbkku
A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here, compatible measurements are those that can be implemented simultaneously, or more generally, those who are jointly measurable. This conflict is generically called quantum contextuality. In this article, we present an introduction to this subject and its current status. We review several proofs of the Kochen-Specker theorem and different notions of contextuality. We explain how to experimentally test some of these notions and discuss connections between contextuality and nonlocality or graph theory. Finally, we review some applications of contextuality in quantum information processing.Costantino Budroni, Adán Cabello, Otfried Gühne, Matthias Kleinmann, Jan-Åke Larssonwork_vub2wqx3bnfvhfcecbkbdcbkkuWed, 31 Aug 2022 00:00:00 GMTExplaining Ontology-Mediated Query Answers using Proofs over Universal Models (Technical Report)
https://scholar.archive.org/work/ugllkmsewnhrlkoyhbotjhacz4
In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology, which can be formulated in a description logic (DL) or using existential rules. In the literature, there exists a multitude of complex techniques for incorporating ontological knowledge into queries. However, few of these approaches were designed for explainability of the query answers. We tackle this challenge by adapting an existing proof framework toward conjunctive query answering, based on the notion of universal models. We investigate the data and combined complexity of determining the existence of a proof below a given quality threshold, which can be measured in different ways. By distinguishing various parameters such as the shape of the query, we obtain an overview of the complexity of this problem for several Horn DLs.Christian Alrabbaa and Stefan Borgwardt and Patrick Koopmann and Alisa Kovtunovawork_ugllkmsewnhrlkoyhbotjhacz4Tue, 30 Aug 2022 00:00:00 GMTSaturation-based Boolean conjunctive query answering and rewriting for the guarded quantification fragments
https://scholar.archive.org/work/bgx5fbakvndv3lzzjrkoafyo3m
Answering Boolean conjunctive query over logical constraints is an essential problem in knowledge representation. Other problems in computer science such as constraint satisfaction and homomorphism problems can also be seen as Boolean conjunctive query answering problems. This paper develops saturation-based Boolean conjunctive query answering and rewriting procedures for the guarded, the loosely guarded and the clique guarded fragments. We improve existing resolution-based decision procedures for the guarded and the loosely guarded fragments, and devise a saturation-based approach deciding Boolean conjunctive query answering problems for the guarded, the loosely guarded and the clique guarded fragments. Based on the saturation-based query answering procedure, we introduce a novel saturation-based query rewriting setting that aims to back-translate the saturated clausal set derived from saturation-based query answering procedures, to a (Skolem-symbol-free) first-order formula, and devise a saturation-based query rewriting procedures for all these guarded fragments. Unlike mainstream query answering and rewriting approaches, our procedures derive a compact saturation that is reusable even if the data changes. This paper lays the theoretical foundations for the first practical Boolean conjunctive query answering and the first saturation-based Boolean conjunctive query rewriting procedures for the guarded, the loosely guarded and the clique guarded fragments.Sen Zheng, Renate A. Schmidtwork_bgx5fbakvndv3lzzjrkoafyo3mWed, 10 Aug 2022 00:00:00 GMTMultiplicative linear logic from a resolution-based tile system
https://scholar.archive.org/work/i4whznoe4jcopi7fe6iqz5lg2e
We present the stellar resolution, a "flexible" tile system based on Robinson's first-order resolution. After establishing formal definitions and basic properties of the stellar resolution, we show its Turing-completeness and to illustrate the model, we exhibit how it naturally represents computation with Horn clauses and automata as well as nondeterministic tiling constructions used in DNA computing. In the second and main part, by using the stellar resolution, we formalise and extend ideas of a new alternative to proof-net theory sketched by Girard in his transcendental syntax programme. In particular, we encode both cut-elimination and logical correctness for the multiplicative fragment of linear logic (MLL). We finally obtain completeness results for both MLL and MLL extended with the so-called MIX rule. By extending the ideas of Girard's geometry of interaction, this suggests a first step towards a new understanding of the interplay between logic and computation where linear logic is seen as a (constructed) way to format computation.Boris Engwork_i4whznoe4jcopi7fe6iqz5lg2eMon, 18 Jul 2022 00:00:00 GMTOASIcs, Volume 99, AIB 2022, Complete Volume
https://scholar.archive.org/work/bwook3qzlnh4rcdq3po2nchqpe
OASIcs, Volume 99, AIB 2022, Complete VolumeCamille Bourgaux, Ana Ozaki, Rafael Peñalozawork_bwook3qzlnh4rcdq3po2nchqpeWed, 25 May 2022 00:00:00 GMTAny-k Algorithms for Enumerating Ranked Answers to Conjunctive Queries
https://scholar.archive.org/work/bneguqa6vzgsleq7zb2v4qwk4a
We study ranked enumeration for Conjunctive Queries (CQs) where the answers are ordered by a given ranking function (e.g., an ORDER BY clause in SQL). We develop "any-k" algorithms which, without knowing the number k of desired answers, push the ranking into joins and avoid materializing the join output earlier than necessary. For this to be possible, the ranking function needs to obey a certain kind of monotonicity; the supported ranking functions include the common sum-of-weights case where query answers are compared by sums of input weights, as well as any commutative selective dioid. One core insight of our work is that the problem is closely related to the fundamental task of path enumeration in a weighted DAG. We generalize and improve upon classic research on finding the k'th shortest path and unify into the same framework several solutions from different areas that had been studied in isolation. For the time to the k'th ranked CQ answer (for every value of k), our approach is optimal in data complexity precisely for the same class of queries where unranked enumeration is optimal -- and only slower by a logarithmic factor. In a more careful analysis of combined complexity, we uncover a previously unknown tradeoff between two different any-k algorithms: one has lower complexity when the number of returned results is small, the other when the number is very large. This tradeoff is eliminated under a stricter monotonicity property that we exploit to design a novel algorithm that asymptotically dominates all previously known alternatives, including the well-known algorithm of Eppstein for sum-of-weights path enumeration. We empirically demonstrate the findings of our theoretical analysis in an experimental study that highlights the superiority of our approach over the join-then-rank approach that existing database systems typically follow.Nikolaos Tziavelis, Wolfgang Gatterbauer, Mirek Riedewaldwork_bneguqa6vzgsleq7zb2v4qwk4aWed, 11 May 2022 00:00:00 GMTDecision Problems in a Logic for Reasoning about Reconfigurable Distributed Systems
https://scholar.archive.org/work/no2jcoe3m5af7czqhwjq35pzje
We consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded number of components and interactions, written using a multiplicative conjunction, reminiscent of Bunched Implications and Separation Logic. We study the complexity of the satisfiability and entailment problems for the configuration logic under consideration. Additionally, we consider robustness properties, such as tightness (are all interactions entirely connected to components?) and degree boundedness (is every component involved in a bounded number of interactions?), the latter being an ingredient for decidability of entailments.Marius Bozga and Lucas Bueri and Radu Iosifwork_no2jcoe3m5af7czqhwjq35pzjeTue, 26 Apr 2022 00:00:00 GMTA Structural Investigation of the Approximability of Polynomial-Time Problems
https://scholar.archive.org/work/2vby33lhwbbvrponzu7wdyptnq
We initiate the systematic study of a recently introduced polynomial-time analogue of MaxSNP, which includes a large number of well-studied problems (including Nearest and Furthest Neighbor in the Hamming metric, Maximum Inner Product, optimization variants of k-XOR and Maximum k-Cover). Specifically, MaxSP_k denotes the class of O(m^k)-time problems of the form max_x_1,..., x_k#{y:ϕ(x_1,...,x_k,y)} where ϕ is a quantifier-free first-order property and m denotes the size of the relational structure. Assuming central hypotheses about clique detection in hypergraphs and MAX3SAT, we show that for any MaxSP_k problem definable by a quantifier-free m-edge graph formula ϕ, the best possible approximation guarantee in faster-than-exhaustive-search time O(m^k-δ) falls into one of four categories: * optimizable to exactness in time O(m^k-δ), * an (inefficient) approximation scheme, i.e., a (1+ϵ)-approximation in time O(m^k-f(ϵ)), * a (fixed) constant-factor approximation in time O(m^k-δ), or * an m^ϵ-approximation in time O(m^k-f(ϵ)). We obtain an almost complete characterization of these regimes, for MaxSP_k as well as for an analogously defined minimization class MinSP_k. As our main technical contribution, we rule out approximation schemes for a large class of problems admitting constant-factor approximations, under the Sparse MAX3SAT hypothesis posed by (Alman, Vassilevska Williams'20). As general trends for the problems we consider, we find: (1) Exact optimizability has a simple algebraic characterization, (2) only few maximization problems do not admit a constant-factor approximation; these do not even have a subpolynomial-factor approximation, and (3) constant-factor approximation of minimization problems is equivalent to deciding whether the optimum is equal to 0.Karl Bringmann, Alejandro Cassis, Nick Fischer, Marvin Künnemannwork_2vby33lhwbbvrponzu7wdyptnqMon, 25 Apr 2022 00:00:00 GMTTuple-Independent Representations of Infinite Probabilistic Databases
https://scholar.archive.org/work/knwwnitlqzbjhghcovclo5yvfy
Probabilistic databases (PDBs) are probability spaces over database instances. They provide a framework for handling uncertainty in databases, as occurs due to data integration, noisy data, data from unreliable sources or randomized processes. Most of the existing theory literature investigated finite, tuple-independent PDBs (TI-PDBs) where the occurrences of tuples are independent events. Only recently, Grohe and Lindner (PODS '19) introduced independence assumptions for PDBs beyond the finite domain assumption. In the finite, a major argument for discussing the theoretical properties of TI-PDBs is that they can be used to represent any finite PDB via views. This is no longer the case once the number of tuples is countably infinite. In this paper, we systematically study the representability of infinite PDBs in terms of TI-PDBs and the related block-independent disjoint PDBs. The central question is which infinite PDBs are representable as first-order views over tuple-independent PDBs. We give a necessary condition for the representability of PDBs and provide a sufficient criterion for representability in terms of the probability distribution of a PDB. With various examples, we explore the limits of our criteria. We show that conditioning on first order properties yields no additional power in terms of expressivity. Finally, we discuss the relation between purely logical and arithmetic reasons for (non-)representability.Nofar Carmeli, Martin Grohe, Peter Lindner, Christoph Standkework_knwwnitlqzbjhghcovclo5yvfyTue, 19 Apr 2022 00:00:00 GMTTractable Parsing for CCGs of Bounded Degree
https://scholar.archive.org/work/kj4dmoqgbzew7c5fkwxk3ljgte
Unlike other mildly context-sensitive formalisms, Combinatory Categorial Grammar (CCG) cannot be parsed in polynomial time when the size of the grammar is taken into account. Refining this result, we show that the parsing complexity of CCG is exponential only in the maximum degree of composition. When that degree is fixed, parsing can be carried out in polynomial time. Our finding is interesting from a linguistic perspective because a bounded degree of composition has been suggested as a universal constraint on natural language grammar. Moreover, ours is the first complexity result for a version of CCG that includes substitution rules, which are used in practical grammars but have been ignored in theoretical work.Lena Katharina Schiffer, Marco Kuhlmann, Giorgio Sattawork_kj4dmoqgbzew7c5fkwxk3ljgteThu, 07 Apr 2022 00:00:00 GMTScrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
https://scholar.archive.org/work/7isryklgfzholkq4p6vnwb6pde
This tutorial article introduces the physics of quantum information scrambling in quantum many-body systems. The goals are to understand how to quantify the spreading of quantum information precisely and how causality emerges in complex quantum systems. We introduce the general framework to study the dynamics of quantum information, including detection and decoding. We show that the dynamics of quantum information is closely related to operator dynamics in the Heisenberg picture, and, in certain circumstances, can be precisely quantified by the so-called out-the-time ordered correlator (OTOC). The general behavior of OTOC is discussed based on several toy models, including the Sachdev-Ye-Kitaev model, random circuit models, and Brownian models, in which OTOC is analytically tractable. We introduce numerical methods, both exact diagonalization and tensor network methods, to calculate OTOC for generic quantum many-body systems. We also survey current experiment schemes to measure OTOC in various quantum simulators.Shenglong Xu, Brian Swinglework_7isryklgfzholkq4p6vnwb6pdeTue, 01 Mar 2022 00:00:00 GMT