The μ-calculus alternation hierarchy collapses over structures with restricted connectivity

The alternation hierarchy of least and greatest fixpoint operators in the μ-calculus is strict. However, the strictness of the hierarchy does not necessarily carry over when considering restricted classes of structures. For instance, over the class of infinite words the alternation-free fragment of the μ-calculus is already as expressive as the full logic. Our current understanding of when and why the μ-calculus alternation hierarchy is (and is not) strict is limited. This article makes progress in answering these questions by showing that the alternation hierarchy of the μ-calculus collapses to the alternation-free fragment over some classes of structures, including infinite nested words and finite graphs with feedback vertex sets of a bounded size. Common to these classes is that the connectivity between the components in a structure from such a class is restricted in the sense that the removal of certain vertices from the structure's graph decomposes it into graphs in which all paths are of finite length. The collapse results herein are obtained in an automata-theoretic setting. They subsume, generalize, and strengthen several prior results on the expressivity of the μ-calculus over restricted classes of structures

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

The μ-calculus alternation hierarchy collapses over structures with restricted connectivity

The alternation hierarchy of least and greatest fixpoint operators in the and#956;-calculus is strict. However, the strictness of the hierarchy does not necessarily carry over when considering restricted classes of structures. For instance, over the class of infinite words the alternation-free fragment of the and#956;-calculus is already as expressive as the full logic. Our current understanding of when and why the and#956;-calculus alternation hierarchy is (and is not) strict is limited. This article makes progress in answering these questions by showing that the alternation hierarchy of the and#956;-calculus collapses to the alternation-free fragment over some classes of structures, including infinite nested words and finite graphs with feedback vertex sets of a bounded size. Common to these classes is that the connectivity between the components in a structure from such a class is restricted in the sense that the removal of certain vertices from the structure's graph decomposes it into graphs in which all paths are of finite length. The collapse results herein are obtained in an automata-theoretic setting. They subsume, generalize, and strengthen several prior results on the expressivity of the and#956;-calculus over restricted classes of structures

Intermittency and Self-Organisation in Turbulence and Statistical Mechanics

There is overwhelming evidence, from laboratory experiments, observations, and computational studies, that coherent structures can cause intermittent transport, dramatically enhancing transport. A proper description of this intermittent phenomenon, however, is extremely difficult, requiring a new non-perturbative theory, such as statistical description. Furthermore, multi-scale interactions are responsible for inevitably complex dynamics in strongly non-equilibrium systems, a proper understanding of which remains a main challenge in classical physics. As a remarkable consequence of multi-scale interaction, a quasi-equilibrium state (the so-called self-organisation) can however be maintained. This special issue aims to present different theories of statistical mechanics to understand this challenging multiscale problem in turbulence. The 14 contributions to this Special issue focus on the various aspects of intermittency, coherent structures, self-organisation, bifurcation and nonlocality. Given the ubiquity of turbulence, the contributions cover a broad range of systems covering laboratory fluids (channel flow, the Von Kármán flow), plasmas (magnetic fusion), laser cavity, wind turbine, air flow around a high-speed train, solar wind and industrial application

Handbook of Lexical Functional Grammar

Lexical Functional Grammar (LFG) is a nontransformational theory of linguistic structure, first developed in the 1970s by Joan Bresnan and Ronald M. Kaplan, which assumes that language is best described and modeled by parallel structures representing different facets of linguistic organization and information, related by means of functional correspondences. This volume has five parts. Part I, Overview and Introduction, provides an introduction to core syntactic concepts and representations. Part II, Grammatical Phenomena, reviews LFG work on a range of grammatical phenomena or constructions. Part III, Grammatical modules and interfaces, provides an overview of LFG work on semantics, argument structure, prosody, information structure, and morphology. Part IV, Linguistic disciplines, reviews LFG work in the disciplines of historical linguistics, learnability, psycholinguistics, and second language learning. Part V, Formal and computational issues and applications, provides an overview of computational and formal properties of the theory, implementations, and computational work on parsing, translation, grammar induction, and treebanks. Part VI, Language families and regions, reviews LFG work on languages spoken in particular geographical areas or in particular language families. The final section, Comparing LFG with other linguistic theories, discusses LFG work in relation to other theoretical approaches