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pin j handbook automata theory vol i 2021

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Textbook in PDF format Preface List of contributors Foundations Finite automata Basic algebraic structures Words, languages and automata Operations on recognisable languages Minimal automaton and syntactic monoid Rational versus recognisable Algebraic approach References Automata and rational expressions A new look at Kleene's theorem Rationality and recognisability From automata to expressions: the AtEs-maps From expressions to automata: the EtAs-maps Changing the monoid Introducing weights Notes References Finite transducers and rational transductions Introduction Basic definitions Morphic representations Applications Undecidability in transductions Further reading References Weighted automata Introduction Weighted automata and their behaviour Linear representations The Kleene–Schützenberger theorem Semimodules Nivat's theorem Weighted monadic second-order logic Decidability of "r_=r_"? Characteristic series and supports Further results References Max-plus automata Introduction Preliminaries One-letter max-plus automata General max-plus automata Bibliographic notes References ω-Automata Introduction Types of omega-automata Basic properties of Büchi automata Basic constructions Run DAG’s of Büchi automata Run trees of Büchi automata Congruence relations Loop structure Alternation Applications in logic More complex recurrence conditions References Automata on finite trees Introduction Fundamentals on tree automata Ground-tree rewriting Tree-walking automata Automata on unranked trees Classification of regular tree languages Conclusion References Automata on infinite trees Introduction Automata on infinite trees Constructions for complementation and simulation Decision problems Applications in logic References Two-dimensional models Introduction Basic concepts for picture definition Tiling recognition Grammars Comparison of language families Conclusion References Complexity issues Minimisation of automata Introduction Definitions and notation Brzozowski's algorithm Moore's algorithm Hopcroft's algorithm Slow automata Minimisation by fusion Dynamic minimisation Extensions and special cases References Learning algorithms Introduction Preliminaries Classical results Learning from given data Learning non-deterministic finite automata Learning regular tree languages PAC learning Applications and further material References Descriptional complexity of regular languages Introduction Descriptional complexity and lower bound techniques Transformation between models for regular languages Operations on regular languages Some recent developments References Enumerating regular expressions and their languages Introduction and overview On measuring the size of a regular expression A simple grammar for valid regular expressions Unambiguous context-free grammars and the Chomsky–Schützenberger theorem Solving algebraic equations using Gröbner bases Asymptotic bounds via singularity analysis Lower bounds on enumeration of regular languages by regular expressions Upper bounds on enumeration of regular languages by regular expressions Exact enumerations Conclusion and open problems References Circuit complexity of regular languages Introduction Circuits Syntactic monoid Regular expressions Circuit complexity of regular languages Circuit size of regular languages Final remarks References Černý's conjecture and the road colouring problem Synchronising automata, their origins and importance Algorithmic and complexity issues Around the Černý's conjecture The road colouring problem References Part III Algebraic and topological theory of automata Varieties Motivation and examples Equations, identities and families of languages Connections with logic Operations on classes of languages Varieties in other algebraic frameworks References Profinite topologies Introduction Profinite topologies for general algebras The case of semigroups Relatively free profinite semigroups References The factorisation forest theorem Introduction Some definitions The factorisation forest theorem Algebraic applications Variants of the factorisation forest theorem Applications as an accelerating structure References Wadge–Wagner hierarchies The Wadge hierarchy The Wagner hierarchy References Equational theories for automata Introduction Conway semirings Automata in Conway semirings Iteration semirings Complete semirings Continuous semirings Completeness Inductive *-semirings and Kleene algebras Residuation Some extensions References Language equations Introduction General properties of operations Equations with one-sided concatenation Resolved systems of equations Equations with constant sides Equations of the general form Equations with erasing operations References Algebra for trees Introduction Trees as ground terms A recipe for designing an algebra Preclones Forest algebra Seminearring Nesting algebras Recent developments References Index

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pin j handbook automata theory vol i 2021

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