IA Scholar Query: On Finite Alphabets and Infinite Bases II: Completed and Ready Simulation.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgFri, 30 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Nested Session Types
https://scholar.archive.org/work/cdzjx4x355eyjn7slpugmdj6di
Session types statically describe communication protocols between concurrent message-passing processes. Unfortunately, parametric polymorphism even in its restricted prenex form is not fully understood in the context of session types. In this article, we present the metatheory of session types extended with prenex polymorphism and, as a result, nested recursive datatypes. Remarkably, we prove that type equality is decidable by exhibiting a reduction to trace equivalence of deterministic first-order grammars. Recognizing the high theoretical complexity of the latter, we also propose a novel type equality algorithm and prove its soundness. We observe that the algorithm is surprisingly efficient and, despite its incompleteness, sufficient for all our examples. We have implemented our ideas by extending the Rast programming language with nested session types. We conclude with several examples illustrating the expressivity of our enhanced type system.Ankush Das, Henry Deyoung, Andreia Mordido, Frank Pfenningwork_cdzjx4x355eyjn7slpugmdj6diFri, 30 Sep 2022 00:00:00 GMTOn Completeness of Cost Metrics and Meta-Search Algorithms in -Calculus
https://scholar.archive.org/work/h4lp7jrk2fgldkq2bo5dj47qd4
In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete (Diagonalization complete) and H-complete (Hypercomputation complete) classes. In the paper, in the spirit of Cook/Levin/Karp, we started the population process of these new classes assigning several undecidable problems to them. We justify that some super-Turing models of computation, i.e., models going beyond Turing machines, are tremendously expressive and they allow to accept arbitrary languages over a given alphabet including those undecidable ones. We prove also that one of such super-Turing models of computation - the $-Calculus, designed as a tool for automatic problem solving and automatic programming, has also such tremendous expressiveness. We investigate also completeness of cost metrics and meta-search algorithms in $-calculus.Eugene Eberbachwork_h4lp7jrk2fgldkq2bo5dj47qd4Mon, 26 Sep 2022 00:00:00 GMTCharacterising memory in infinite games
https://scholar.archive.org/work/5ht65gfryfgm7eiajp5ot35zsi
This paper is concerned with games of infinite duration played over potentially infinite graphs. Recently, Ohlmann (LICS 2022) presented a characterisation of objectives admitting optimal positional strategies, by means of universal graphs: an objective is positional if and only if it admits well-ordered monotone universal graphs. We extend Ohlmann's characterisation to encompass (finite or infinite) memory upper bounds. We prove that objectives admitting optimal strategies with ε-memory less than m (a memory that cannot be updated when reading an ε-edge) are exactly those which admit well-founded monotone universal graphs whose antichains have size bounded by m. We also give a characterisation of chromatic memory by means of appropriate universal structures. Our results apply to finite as well as infinite memory bounds (for instance, to objectives with finite but unbounded memory, or with countable memory strategies). We illustrate the applicability of our framework by carrying out a few case studies, we provide examples witnessing limitations of our approach, and we discuss general closure properties which follow from our results.Antonio Casares, Pierre Ohlmannwork_5ht65gfryfgm7eiajp5ot35zsiSat, 24 Sep 2022 00:00:00 GMTSynthesizing Nested Relational Queries from Implicit Specifications
https://scholar.archive.org/work/j5j65p5q5zawtl5fr6rroyuaya
Derived datasets can be defined implicitly or explicitly. An implicit definition (of dataset O in terms of datasets I⃗) is a logical specification involving the source data I⃗ and the interface data O. It is a valid definition of O in terms of I⃗, if any two models of the specification agreeing on I⃗ agree on O. In contrast, an explicit definition is a query that produces O from I⃗. Variants of Beth's theorem state that one can convert implicit definitions to explicit ones. Further, this conversion can be done effectively given a proof witnessing implicit definability in a suitable proof system. We prove the analogous effective implicit-to-explicit result for nested relations: implicit definitions, given in the natural logic for nested relations, can be effectively converted to explicit definitions in the nested relational calculus NRC. As a consequence, we can effectively extract rewritings of NRC queries in terms of NRC views, given a proof witnessing that the query is determined by the views.Michael Benedikt, Pierre Pradic, Christoph Wernhardwork_j5j65p5q5zawtl5fr6rroyuayaSat, 17 Sep 2022 00:00:00 GMTExperimental Multi-state Quantum Discrimination in the Frequency Domain with Quantum Dot Light
https://scholar.archive.org/work/entbfjlwmrby3faquun3g57fae
The quest for the realization of effective quantum state discrimination strategies is of great interest for quantum information technology, as well as for fundamental studies. Therefore, it is crucial to develop new and more efficient methods to implement discrimination protocols for quantum states. Among the others, single photon implementations are more advisable, because of their inherent security advantage in quantum communication scenarios. In this work, we present the experimental realization of a protocol employing a time-multiplexing strategy to optimally discriminate among eight non-orthogonal states, encoded in the four-dimensional Hilbert space spanning both the polarization degree of freedom and photon energy. The experiment, built on a custom-designed bulk optics analyser setup and single photons generated by a nearly deterministic solid-state source, represents a benchmarking example of minimum error discrimination with actual quantum states, requiring only linear optics and two photodetectors to be realized. Our work paves the way for more complex applications and delivers a novel approach towards high-dimensional quantum encoding and decoding operations.Alessandro Laneve, Michele B. Rota, Francesco Basso Basset, Nicola P. Fiorente, Tobias M. Krieger, Saimon F. Covre da Silva, Quirin Buchinger, Sandra Stroj, Sven Hoefling, Tobias Huber-Loyola, Armando Rastelli, Rinaldo Trotta, Paolo Mataloniwork_entbfjlwmrby3faquun3g57faeSat, 17 Sep 2022 00:00:00 GMTAlmost Ramanujan Expanders from Arbitrary Expanders via Operator Amplification
https://scholar.archive.org/work/5mrwukheqffgvfoykq7munqdhq
We give an efficient algorithm that transforms any bounded degree expander graph into another that achieves almost optimal (namely, near-quadratic, d ≤ 1/λ^2+o(1)) trade-off between (any desired) spectral expansion λ and degree d. Furthermore, the algorithm is local: every vertex can compute its new neighbors as a subset of its original neighborhood of radius O(log(1/λ)). The optimal quadratic trade-off is known as the Ramanujan bound, so our construction gives almost Ramanujan expanders from arbitrary expanders. The locality of the transformation preserves structural properties of the original graph, and thus has many consequences. Applied to Cayley graphs, our transformation shows that any expanding finite group has almost Ramanujan expanding generators. Similarly, one can obtain almost optimal explicit constructions of quantum expanders, dimension expanders, monotone expanders, etc., from existing (suboptimal) constructions of such objects. Another consequence is a "derandomized" random walk on the original (suboptimal) expander with almost optimal convergence rate. Our transformation also applies when the degree is not bounded or the expansion is not constant. We obtain our results by a generalization of Ta-Shma's technique in his breakthrough paper [STOC 2017], used to obtain explicit almost optimal binary codes. Specifically, our spectral amplification extends Ta-Shma's analysis of bias amplification from scalars to matrices of arbitrary dimension in a very natural way. Curiously, while Ta-Shma's explicit bias amplification derandomizes a well-known probabilistic argument (underlying the Gilbert–Varshamov bound), there seems to be no known probabilistic (or other existential) way of achieving our explicit ("high-dimensional") spectral amplification.Fernando Granha Jeronimo, Tushant Mittal, Sourya Roy, Avi Wigdersonwork_5mrwukheqffgvfoykq7munqdhqThu, 15 Sep 2022 00:00:00 GMTOn New Notions of Algorithmic Dimension, Immunity, and Medvedev Degree
https://scholar.archive.org/work/tbcsjisqcbe5ph2n3dufpyw3ha
We prove various results connected together by the common thread of computability theory. First, we investigate a new notion of algorithmic dimension, the inescapable dimension, which lies between the effective Hausdorff and packing dimensions. We also study its generalizations, obtaining an embedding of the Turing degrees into notions of dimension. We then investigate a new notion of computability theoretic immunity that arose in the course of the previous study, that of a set of natural numbers with no co-enumerable subsets. We demonstrate how this notion of Π^0_1-immunity is connected to other immunity notions, and construct Π^0_1-immune reals throughout the high/low and Ershov hierarchies. We also study those degrees that cannot compute or cannot co-enumerate a Π^0_1-immune set. Finally, we discuss a recently discovered truth-table reduction for transforming a Kolmogorov–Loveland random input into a Martin-Löf random output by exploiting the fact that at least one half of such a KL-random is itself ML-random. We show that there is no better algorithm relying on this fact, i.e., there is no positive, linear, or bounded truth-table reduction which does this. We also generalize these results to the problem of outputting randomness from infinitely many inputs, only some of which are random.David J. Webbwork_tbcsjisqcbe5ph2n3dufpyw3haTue, 13 Sep 2022 00:00:00 GMTUsing Genetics to Aid Management in the Promotion of Connectivity, Recruitment, and Genetic Diversity for Australian Fish Species
https://scholar.archive.org/work/k3huj6tovjaetc26vorjvy46wy
Submitted in total fulfilment of the requirements for the degree of Doctor of Philosophy to the Department of Ecology, Environment and Evolution, School of Agriculture, Biomedicine and Environment, La Trobe University, Victoria, Australia.James O'Dwyerwork_k3huj6tovjaetc26vorjvy46wyTue, 13 Sep 2022 00:00:00 GMTSpace-Efficient Representations of Graphs
https://scholar.archive.org/work/vjtulzxmxnaunai4oh7eybsmkq
Computer science is no more about computers than astronomy is about telescopes. -Edsger Dijkstra To my sister, Tamara. . . Completing a Ph.D. is a long and arduous journey, and would have been neither possible nor worth doing without all the people that helped me along the way. I am immensely thankful to all those who have contributed either to my work or to my life during these past five years. First and foremost, I would like to express my gratitude to my advisor, Michael Kapralov, for his continued guidance, encouragement, and motivation throughout my time at EPFL. One could not ask for a better mentor. His apparent love of research, and his limitless energy made him a truly inspiring person to work with. It never ceased to amaze me how many projects he could juggle simultaneously while still being able to meet regularly on each of them, and come up with brilliant insights and helpful suggestions. I'm also grateful to the culture of collaboration he cultivated, always encouraging us to share, discuss, and work together on projects; this I think is one of the biggest reasons I found my work at EPFL so enjoyable. I would also like to thank my other jury members, Mika Göös, Sanjeev Khanna, Ola Svensson, and Luca Trevisan for their time and effort in reading this thesis, as well as their insightful questions and comments during the defense. Research is not a solo endeavor, and I could never have produced the quality and quantity of work that this thesis represents without my many collaborators. It is no accident that this is the only page of my thesis written in the singular first person. Both for directly contributing to the works contained in the following chapters, and perhaps more importantly, for shaping me as a researcher through our many discussions, I am indebted to my collaborators. For this reason, I would like to express my immense gratitude to MarwaJakab Tardoswork_vjtulzxmxnaunai4oh7eybsmkqMon, 12 Sep 2022 00:00:00 GMTDeterministic algorithms for the Lovasz Local Lemma: simpler, more general, and more parallel
https://scholar.archive.org/work/jgtxbzqt2jeylc662sq7jtm3u4
The Lovász Local Lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid a collection ℬ of "bad" events which are mostly independent and have low probability. In its simplest "symmetric" form, it asserts that whenever a bad-event has probability p and affects at most d bad-events, and e p d < 1, then a configuration avoiding all ℬ exists. A seminal algorithm of Moser Tardos (2010) gives nearly-automatic randomized algorithms for most constructions based on the LLL. However, deterministic algorithms have lagged behind. We address three specific shortcomings of the prior deterministic algorithms. First, our algorithm applies to the LLL criterion of Shearer (1985); this is more powerful than alternate LLL criteria and also removes a number of nuisance parameters and leads to cleaner and more legible bounds. Second, we provide parallel algorithms with much greater flexibility in the functional form of of the bad-events. Third, we provide a derandomized version of the MT-distribution, that is, the distribution of the variables at the termination of the MT algorithm. We show applications to non-repetitive vertex coloring, independent transversals, strong coloring, and other problems. These give deterministic algorithms which essentially match the best previous randomized sequential and parallel algorithms.David G. Harriswork_jgtxbzqt2jeylc662sq7jtm3u4Mon, 12 Sep 2022 00:00:00 GMTPrograms as Diagrams: From Categorical Computability to Computable Categories
https://scholar.archive.org/work/symgo7adkvdfzhreu2ez7uykai
This is a draft of the first 7 chapters of a textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later chapters contain new ideas and results about categorical computability and some first steps into computable category theory. The underlying categorical view of computation is based on monoidal categories with program evaluators, called *monoidal computers*. This categorical structure can be viewed as a single-instruction diagrammatic programming language called Run, whose only instruction is called RUN. This version: changed the title, worked on improving the text. (Also added lots of exercises and workouts, but that was overflowing the arxiv size bounds already in the earlier version, which is why the "workouts" and the "stories" are commented out.)Dusko Pavlovicwork_symgo7adkvdfzhreu2ez7uykaiSat, 10 Sep 2022 00:00:00 GMTDecisions over Sequences
https://scholar.archive.org/work/ho6vuz53f5hj7i7eb7npyswgvu
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such as receiving recommendations. Within the class of decision rules, we study natural subclasses: stopping and uniform stopping rules. Our main result establishes the equivalence of these two subclasses of decision rules. Next, we introduce the notion of computability of decision rules using Turing machines and show that computable rules can be implemented using a simpler computational device: a finite automaton. We further show that computability of choice rules -- an important subclass of decision rules -- is implied by their continuity with respect to a natural topology. Finally, we introduce some natural heuristics in this framework and provide their behavioral characterization.Bhavook Bhardwaj, Siddharth Chatterjeework_ho6vuz53f5hj7i7eb7npyswgvuFri, 09 Sep 2022 00:00:00 GMTSubsystem entropies of shifts of finite type and sofic shifts on countable amenable groups
https://scholar.archive.org/work/mozl3irflndtpgrcnwzlein4iy
In this work, we study the entropies of subsystems of shifts of finite type (SFTs) and sofic shifts on countable amenable groups. We prove that for any countable amenable group G, if X is a G-SFT with positive topological entropy $h(X)> 0$ , then the entropies of the SFT subsystems of X are dense in the interval $[0, h(X)]$ . In fact, we prove a 'relative' version of the same result: if X is a G-SFT and $Y \subset X$ is a subshift such that $h(Y) < h(X)$ , then the entropies of the SFTs Z for which $Y \subset Z \subset X$ are dense in $[h(Y), h(X)]$ . We also establish analogous results for sofic G-shifts.ROBERT BLAND, KEVIN MCGOFF, RONNIE PAVLOVwork_mozl3irflndtpgrcnwzlein4iyThu, 08 Sep 2022 00:00:00 GMTDigital Imaging: its current and future influence upon the creative practice of textile and surface pattern designers
https://scholar.archive.org/work/lwvnbqykfbfi5fncl7flqxlzdu
This thesis describes research into the impact of digital imaging technology on the creative practice of artists and designers in the field of printed surface pattern for textiles. It examines how digital tools support creative thinking and enhance innovation through the visualisation, manipulation and communication of imagery, and assesses the role and importance of memory and physical experience in creative digital practice. Recent developments in digital ink jet printing technology now enable practitioners to translate digital imagery directly onto textiles. The research provides evidence to assist future technological development, and effective design strategies are identified for implementation within creative textile practice. A contextual review, informed by visits to practitioners, industry and education, and a critical review of published literature, identifies key issues examined in the research. These include the ways in which digital technology supports creative thinking and how communication of visual data facilitates collaborative practice. The rationale for the use of qualitative research methods in the project is explained. A case study, documented using video and audio recordings of interviews, and photography and research journals to gather data on site, is described. Practical investigations, emanating from the field study visits, and an independent experimental body of work created by the researcher, provide additional data to elucidate how digital tools support creative practice. The findings are informed by feedback and evaluation from telephone conversations and personal correspondence from the participants, along with analysis of the research data. Digital tools are shown to support creative thinking, providing a means of stimulating, manipulating, and outputting printed digital imagery. The collaborative investigations demonstrate how communication of visual imagery, via the Internet and portable digital memory storage media, is able to enhance creative practice. Recommendations are also [...]Cathy Treadawaywork_lwvnbqykfbfi5fncl7flqxlzduThu, 08 Sep 2022 00:00:00 GMTWeak Progressive Forward Simulation Is Necessary and Sufficient for Strong Observational Refinement
https://scholar.archive.org/work/vsizqou4hjb2jhv7optwv4633e
Hyperproperties are correctness conditions for labelled transition systems that are more expressive than traditional trace properties, with particular relevance to security. Recently, Attiya and Enea studied a notion of strong observational refinement that preserves all hyperproperties. They analyse the correspondence between forward simulation and strong observational refinement in a setting with only finite traces. We study this correspondence in a setting with both finite and infinite traces. In particular, we show that forward simulation does not preserve hyperliveness properties in this setting. We extend the forward simulation proof obligation with a (weak) progress condition, and prove that this weak progressive forward simulation is equivalent to strong observational refinement.Brijesh Dongol, Gerhard Schellhorn, Heike Wehrheim, Bartek Klin, Sławomir Lasota, Anca Muschollwork_vsizqou4hjb2jhv7optwv4633eTue, 06 Sep 2022 00:00:00 GMTTransfigurative Access and Journal-Keeping Practice: Theorizing Anti-Oppressive Rhetorical Scholarship
https://scholar.archive.org/work/yebtdcscozcqjgfp2lbqtyww7y
This dissertation theorizes practices of personal writing and reflection—specifically, journal-keeping—within the context of college writing classrooms. Journal-keeping enables practitioners to understand and shift relations of power and oppression that are forged through everyday habits of meaning-making. Journal-keeping theory addresses the need for college writing instruction to better support the difficult and vulnerable self-investigative work of anti-racism, feminism, disability justice, climate justice, and/or decolonization. Emerging from reflection on the author's own teaching and journal-keeping practices, the project offers a theoretical approach to these questions: what if college writing pedagogies held personal writing practice as a core component of anti-oppressive teaching and learning? How would it work in college classrooms? What kinds of transformations could it make more possible? Closely reading work by Sara Ahmed, adrienne maree brown, Jay Dolmage, Tanya Titchkosky, and others, the four main essays here present a theoretical approach to journal-keeping by leveraging tropes, practice, and figurative access. As methodological concepts, tropes and practice each refer to different yet interdependent ways of thinking about what we're doing in rhetorical scholarship. "Methodology of Tropes," a study of scholarly work on tropes and rhetorical figures as key resources of meaning-making, identifies some critical methods of troping, or intentional ways of exploiting the functions of tropes to engage in critical analysis and action upon social and cultural discourses. "Methodology of Practice" draws from Buddhist and Black Feminist teachings to understand practice as a framework for critical reflection on meaning-making that accounts for both personal intentions and larger systems of value. Figurative access and journal-keeping can each be thought of as different practical combinations of the methodologies of tropes and practice. "The Question of Figurative Access" asks how metaphors and other rhetoric [...]Esther Witte, University, Mywork_yebtdcscozcqjgfp2lbqtyww7yTue, 06 Sep 2022 00:00:00 GMTEmbodiment Design Cartography: A Conceptual Framework for Design Space Mapping to Support the Development of Physically-Interactive Products
https://scholar.archive.org/work/azuwcact6jbyjeqsxysjm3ku6i
Embodiment design is the process of taking an idea for a product and bringing it into the real world by specifying key parameters. In this process, numerous decisions are made that ultimately lead to a solution. By entering the real world, however, a host of complexities are introduced to the design problem by external actors. The different people that physically interact with the product, as well as the situations for these interactions, may all factor into shaping the way this solution is received in a manner that is outside of the designer's control. To truly understand the outcomes of the options that exist within this solution space, there is a web of considerations that must be navigated in the problem space. Together, the considerations in this problem space and the relations between them, as well as the options in the solution space comprise the overall design space. The term 'cartography' refers to the creation of maps—this dissertation presents a conceptual framework for systematically mapping out this design space such that the paths along this web of considerations may be navigated, and the resulting outcomes that may be achieved are understood. There are existing methods from different design disciplines that can help understand the solution space, however each imparts a distinct, fixed perspective on how it conceives the problem space and therefore only recognizes the portion it considers to be important. The Embodiment Design Cartography framework developed in this dissertation is illustrated by mapping out these methods on a uniform scale that enables their direct comparison and combination. New design methods are also constructed within this framework, which may be tailored to the problem at hand, and more holistically cover the design space without the limiting preconceptions of existing methods. This practice is employed in two case studies for products that exemplify questions in embodiment design. The first regards how tradeoffs between competing outcomes may be successfully negotiated. The s [...]Jesse Velleu, University, Mywork_azuwcact6jbyjeqsxysjm3ku6iTue, 06 Sep 2022 00:00:00 GMTHistory-Deterministic Timed Automata
https://scholar.archive.org/work/jshknxjmszhjhorfdzcpoky3ly
We explore the notion of history-determinism in the context of timed automata (TA). History-deterministic automata are those in which nondeterminism can be resolved on the fly, based on the run constructed thus far. History-determinism is a robust property that admits different game-based characterisations, and history-deterministic specifications allow for game-based verification without an expensive determinization step. We show yet another characterisation of history-determinism in terms of fair simulation, at the general level of labelled transition systems: a system is history-deterministic precisely if and only if it fairly simulates all language smaller systems. For timed automata over infinite timed words it is known that universality is undecidable for Büchi TA. We show that for history-deterministic TA with arbitrary parity acceptance, timed universality, inclusion, and synthesis all remain decidable and are ExpTime-complete. For the subclass of TA with safety or reachability acceptance, we show that checking whether such an automaton is history-deterministic is decidable (in ExpTime), and history-deterministic TA with safety acceptance are effectively determinizable without introducing new automata states.Thomas A. Henzinger, Karoliina Lehtinen, Patrick Totzke, Bartek Klin, Sławomir Lasota, Anca Muschollwork_jshknxjmszhjhorfdzcpoky3lyTue, 06 Sep 2022 00:00:00 GMTAutomata-based Controller Synthesis for Stochastic Systems: A Game Framework via Approximate Probabilistic Relations
https://scholar.archive.org/work/nbd2wrobq5cidfjbkhe5frov5y
In this work, we propose an abstraction and refinement methodology for the controller synthesis of discrete-time stochastic systems to enforce complex logical properties expressed by deterministic finite automata (a.k.a. DFA). Our proposed scheme is based on a notion of so-called (ϵ,δ)-approximate probabilistic relations, allowing one to quantify the similarity between stochastic systems modeled by discrete-time stochastic games and their corresponding finite abstractions. Leveraging this type of relations, the lower bound for the probability of satisfying the desired specifications can be well ensured by refining controllers synthesized over abstract systems to the original games. Moreover, we propose an algorithmic procedure to construct such a relation for a particular class of nonlinear stochastic systems with slope restrictions on the nonlinearity. The proposed methods are demonstrated on a quadrotor example, and the results indicate that the desired lower bound for the probability of satisfaction is guaranteed.Bingzhuo Zhong, Abolfazl Lavaei, Majid Zamani, Marco Caccamowork_nbd2wrobq5cidfjbkhe5frov5yMon, 05 Sep 2022 00:00:00 GMTLocally Checkable Problems in Rooted Trees
https://scholar.archive.org/work/ctyqeiv325a2ff2wcvxlvecpaq
Consider any locally checkable labeling problem Π in rooted regular trees: there is a finite set of labels Σ, and for each label x ∈Σ we specify what are permitted label combinations of the children for an internal node of label x (the leaf nodes are unconstrained). This formalism is expressive enough to capture many classic problems studied in distributed computing, including vertex coloring, edge coloring, and maximal independent set. We show that the distributed computational complexity of any such problem Π falls in one of the following classes: it is O(1), Θ(log^* n), Θ(log n), or n^Θ(1) rounds in trees with n nodes (and all of these classes are nonempty). We show that the complexity of any given problem is the same in all four standard models of distributed graph algorithms: deterministic 𝖫𝖮𝖢𝖠𝖫, randomized 𝖫𝖮𝖢𝖠𝖫, deterministic 𝖢𝖮𝖭𝖦𝖤𝖲𝖳, and randomized 𝖢𝖮𝖭𝖦𝖤𝖲𝖳 model. In particular, we show that randomness does not help in this setting, and the complexity class Θ(loglog n) does not exist (while it does exist in the broader setting of general trees). We also show how to systematically determine the complexity class of any such problem Π, i.e., whether Π takes O(1), Θ(log^* n), Θ(log n), or n^Θ(1) rounds. While the algorithm may take exponential time in the size of the description of Π, it is nevertheless practical: we provide a freely available implementation of the classifier algorithm, and it is fast enough to classify many problems of interest.Alkida Balliu, Sebastian Brandt, Yi-Jun Chang, Dennis Olivetti, Jan Studený, Jukka Suomela, Aleksandr Tereshchenkowork_ctyqeiv325a2ff2wcvxlvecpaqFri, 02 Sep 2022 00:00:00 GMT