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Polynomial closure and unambiguous product

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1006/jabr.1996.0192openalex-snapshot

Profinite Semigroups, Mal'cev Products, and Identities

inferredcites →https://doi.org/10.1006/jcss.1995.1071openalex-snapshot

Some Logical Characterizations of the Dot-Depth Hierarchy and Applications

inferredcites →https://doi.org/10.1007/3-540-07407-4_23openalex-snapshot

Piecewise testable events

inferredcites →https://doi.org/10.1007/3-540-09118-1_27openalex-snapshot

Sur les varietes de langages et de monoïdes

inferredcites →https://doi.org/10.1007/3-540-10003-2_93openalex-snapshot

Proprietes syntactiques du produit non ambigu

inferredcites →https://doi.org/10.1007/3-540-56939-1_92openalex-snapshot

The product of rational languages

inferredcites →https://doi.org/10.1007/3-540-58201-0_87openalex-snapshot

Polynomial closure of group languages and open sets of the Hall topology

inferredcites →https://doi.org/10.1007/978-94-011-0149-3_1openalex-snapshot

Finite Semigroups and Recognizable Languages: An Introduction

inferredcites →https://doi.org/10.1007/978-94-011-0149-3_2openalex-snapshot

BG = PG: A Success Story

inferredcites →https://doi.org/10.1007/978-94-011-0149-3_4openalex-snapshot

Relatively Free Profinite Monoids: An Introduction and Examples

inferredcites →https://doi.org/10.1007/bf01243597openalex-snapshot

A Reiterman theorem for pseudovarieties of finite first-order structures

inferredcites →https://doi.org/10.1007/bf02127803openalex-snapshot

Logic, semigroups and automata on words

inferredcites →https://doi.org/10.1007/bf02194921openalex-snapshot

Sur Le Produit De Concatenation Non Ambigu

inferredcites →https://doi.org/10.1007/bf02483902openalex-snapshot

The Birkhoff theorem for finite algebras

inferredcites →https://doi.org/10.1007/bf02572788openalex-snapshot

Sur mon article “une topologie du monoide libre”

inferredcites →https://doi.org/10.1007/bf02573090openalex-snapshot

A property of the Schützenberger product

inferredcites →https://doi.org/10.1007/bf02573578openalex-snapshot

Some results on the dot-depth hierarchy

inferredcites →https://doi.org/10.1007/bf02573768openalex-snapshot

Equations and dot-depth one

inferredcites →https://doi.org/10.1007/bf02574174openalex-snapshot

Une Topologie du Monoïde Libre

inferredcites →https://doi.org/10.1007/bfb0013118openalex-snapshot

Equations for pseudovarieties

inferredcites →https://doi.org/10.1007/bfb0015770openalex-snapshot

Finite group topology and p-adic topology for free monoids

inferredcites →https://doi.org/10.1007/bfb0028813openalex-snapshot

Products of group languages

inferredcites →https://doi.org/10.1007/bfb0036895openalex-snapshot

Topological characterizations of infinite behaviours of transition systems

inferredcites →https://doi.org/10.1007/bfb0039607openalex-snapshot

Polynomial operations on rational languages

inferredcites →https://doi.org/10.1016/0021-8693(88)90067-1openalex-snapshot

Partially ordered finite monoids and a theorem of I. Simon

inferredcites →https://doi.org/10.1016/0021-8693(91)90094-oopenalex-snapshot

Topologies for the free monoid

inferredcites →https://doi.org/10.1016/0022-0000(78)90049-1openalex-snapshot

The dot-depth hierarchy of star-free languages is infinite

inferredcites →https://doi.org/10.1016/0022-0000(82)90016-2openalex-snapshot

Classifying regular events in symbolic logic

inferredcites →https://doi.org/10.1016/0022-0000(86)90037-1openalex-snapshot

First-order logic and star-free sets

inferredcites →https://doi.org/10.1016/0022-0000(92)90029-iopenalex-snapshot

Closure of varieties of languages under products with counter

inferredcites →https://doi.org/10.1016/0022-4049(79)90025-2openalex-snapshot

Aperiodic homomorphisms and the concatenation product of recognizable sets

inferredcites →https://doi.org/10.1016/0022-4049(85)90062-3openalex-snapshot

Finite semigroup varieties of the form V ∗ D

inferredcites →https://doi.org/10.1016/0022-4049(88)90097-7openalex-snapshot

Locally trivial categories and unambiguous concatenation

inferredcites →https://doi.org/10.1016/0022-4049(91)90019-xopenalex-snapshot

Implicit operations on finite J-trivial semigroups and a conjecture of I. Simon

inferredcites →https://doi.org/10.1016/0166-218x(92)90161-3openalex-snapshot

Games, equations and dot-depth two monoids

inferredcites →https://doi.org/10.1016/0166-218x(94)90161-9openalex-snapshot

On a complete set of generators for dot-depth two

inferredcites →https://doi.org/10.1016/0304-3975(81)90036-0openalex-snapshot

A generalization of the Schützenberger product of finite monoids

inferredcites →https://doi.org/10.1016/0304-3975(81)90057-8openalex-snapshot

Classification of finite monoids: the language approach

inferredcites →https://doi.org/10.1016/0304-3975(85)90003-9openalex-snapshot

Characterizations of some classes of regular events

inferredcites →https://doi.org/10.1016/0304-3975(88)90034-5openalex-snapshot

Semigroups and languages of dot-depth two

inferredcites →https://doi.org/10.1016/0304-3975(89)90151-5openalex-snapshot

Inverse monoids of dot-depth two

inferredcites →https://doi.org/10.1016/0304-3975(90)90047-lopenalex-snapshot

Factorization forests of finite height

inferredcites →https://doi.org/10.1016/0304-3975(91)90268-7openalex-snapshot

Opérations polynomiales et hiérarchies de concaténation

inferredcites →https://doi.org/10.1016/0304-3975(92)90121-uopenalex-snapshot

On a conjecture concerning dot-depth two languages

inferredcites →https://doi.org/10.1016/0898-1221(89)90179-xopenalex-snapshot

Games, equations and the dot-depth hierarchy

inferredcites →https://doi.org/10.1016/s0012-365x(73)80005-6openalex-snapshot

Characterizations of locally testable events

inferredcites →https://doi.org/10.1016/s0019-9958(65)90108-7openalex-snapshot

On finite monoids having only trivial subgroups

inferredcites →https://doi.org/10.1016/s0022-0000(76)80030-xopenalex-snapshot

Varieties of ordered algebras

inferredcites →https://doi.org/10.1016/s0304-3975(96)00120-xopenalex-snapshot

Polynomial closure of group languages and open sets of the Hall topology

inferredcites →https://doi.org/10.1051/ita/197610r200331openalex-snapshot

Hierarchies of aperiodic languages

inferredcites →https://doi.org/10.1051/ita/1981150201491openalex-snapshot

Relational morphisms and operations on recognizable sets

inferredcites →https://doi.org/10.1051/ita/1983170403211openalex-snapshot

A semigroup characterization of dot-depth one languages

inferredcites →https://doi.org/10.1051/ita/1983170403311openalex-snapshot

Some theorems on graph congruences

inferredcites →https://doi.org/10.1051/ita/1984180100231openalex-snapshot

Hiérarchies de concaténation

inferredcites →https://doi.org/10.1051/ita/1990240605211openalex-snapshot

On dot-depth two

inferredcites →https://doi.org/10.1112/blms/12.3.230bopenalex-snapshot

SEMIGROUPS AND COMBINATORIAL APPLICATIONS

inferredcites →https://doi.org/10.1112/blms/23.4.356openalex-snapshot

A Conjecture on the Hall Topology for the Free Group

inferredcites →https://doi.org/10.1112/blms/25.1.37openalex-snapshot

On The Profinite Topology on a Free Group

inferredcites →https://doi.org/10.1142/2481openalex-snapshot

Finite Semigroups and Universal Algebra

inferredcites →https://doi.org/10.1142/9789814540803openalex-snapshot

Monoids and Semigroups with Applications

inferredcites →https://doi.org/10.1142/s0218196791000079openalex-snapshot

INEVITABLE GRAPHS: A PROOF OF THE TYPE II CONJECTURE AND SOME RELATED DECISION PROCEDURES

inferredcites →https://doi.org/10.1142/s0218196791000298openalex-snapshot

ASH'S TYPE II THEOREM, PROFINITE TOPOLOGY AND MALCEV PRODUCTS: PART I

inferredcites →https://doi.org/10.1142/s0218196793000263openalex-snapshot

INVERSE MONOIDS OF DOT-DEPTH TWO

inferredcites →https://doi.org/10.1515/9781400882618-002openalex-snapshot

Representation of Events in Nerve Nets and Finite Automata

inferredcites →https://doi.org/10.2307/1969513openalex-snapshot

A Topology for Free Groups and Related Groups

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Some Reducibilities on Regular Sets

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Finite Automata and Unions of Regular Patterns with Bounded Constant Segments

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Piecewise FIFO Channels Are Analyzable

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Perfect Correspondences Between Dot-Depth and Polynomial-Time Hierarchy

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Polynomials, Fragments of Temporal Logic and the Variety DA over Traces

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Machines that Can Output Empty Words

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Decidable Hierarchies of Starfree Languages

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Relating Automata-Theoretic Hierarchies to Complexity-Theoretic Hierarchies

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Regular Languages Defined by Generalized First-Order Formulas with a Bounded Number of Bound Variables

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On a Conjecture of Schnoebelen

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Partially-Ordered Two-Way Automata: A New Characterization of DA

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Level 5/2 of the Straubing-Thérien Hierarchy for Two-Letter Alphabets

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Languages of Dot-Depth 3/2

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Languages, Rewriting Systems, and Verification of Infinite-State Systems

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Marking the chops: an unambiguous temporal logic

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Ordered Monoids and J-Trivial Monoids

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Geometrical Closure of Binary $$V_{3/2}$$ Languages

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Deciding Classes of Regular Languages: The Covering Approach

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How Many Times Do You Need to Go Back to the Future in Unary Temporal Logic?

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In Orbit with MeSCaL: Higher in Concatenation and Navigational Hierarchies of Regular Languages

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Seventy Years of Algebraic, Logical, and Topological Methods for Regular Languages

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Block Products and Nesting Negations in FO2

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On the State Complexity of Closures and Interiors of Regular Languages with Subwords

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Unambiguity in Automata Theory

inferred← citeshttps://doi.org/10.1007/978-3-319-21500-6_4openalex-snapshot

On Decidability of Intermediate Levels of Concatenation Hierarchies

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A Note on Decidable Separability by Piecewise Testable Languages

inferred← citeshttps://doi.org/10.1007/978-3-319-58747-9_5openalex-snapshot

Concatenation Hierarchies: New Bottle, Old Wine

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Inequalities for One-Step Products

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A Reducibility for the Dot-Depth Hierarchy

inferred← citeshttps://doi.org/10.1007/978-3-540-28629-5_8openalex-snapshot

Algebraic Recognizability of Languages

inferred← citeshttps://doi.org/10.1007/978-3-540-30550-7_8openalex-snapshot

The Dot-Depth and the Polynomial Hierarchy Correspond on the Delta Levels

inferred← citeshttps://doi.org/10.1007/978-3-540-31856-9_14openalex-snapshot

Polylog-Time Reductions Decrease Dot-Depth

inferred← citeshttps://doi.org/10.1007/978-3-540-73208-2_1openalex-snapshot

On First-Order Fragments for Words and Mazurkiewicz Traces

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A Combinatorial Theorem for Trees

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Factorisation Forests for Infinite Words

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Structure Theorem and Strict Alternation Hierarchy for FO2 on Words

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Post Embedding Problem Is Not Primitive Recursive, with Applications to Channel Systems

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The Common Fragment of ACTL and LTL

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The Height of Factorization Forests

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Hierarchies of Piecewise Testable Languages

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On the Non-deterministic Communication Complexity of Regular Languages

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Equations Defining the Polynomial Closure of a Lattice of Regular Languages

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On FO 2 Quantifier Alternation over Words

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Computing Blocker Sets for the Regular Post Embedding Problem

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Around Dot Depth Two

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Codes Base on Unambiguous Products

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Partially Ordered Two-Way Büchi Automata

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Green’s Relations and Their Use in Automata Theory

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Theme and Variations on the Concatenation Product

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Regular Ideal Languages and Their Boolean Combinations

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An Explicit Formula for the Intersection of Two Polynomials of Regular Languages

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Deterministic Logics for UL

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Separating Regular Languages by Piecewise Testable and Unambiguous Languages

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Going Higher in the First-Order Quantifier Alternation Hierarchy on Words

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Quantifier Alternation for Infinite Words

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System Description: A Theorem-Prover for Subregular Systems: The Language Toolkit and Its Interpreter, Plebby

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A Reiterman theorem for pseudovarieties of finite first-order structures

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Logic, semigroups and automata on words

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Varieties and pseudovarieties of ordered normal bands

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Positive varieties and infinite words

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On Existentially First-Order Definable Languages and Their Relation to NP

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Bridges for concatenation hierarchies

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Languages of Dot-Depth 3/2

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The Half-Levels of the FO2 Alternation Hierarchy

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Generic Results for Concatenation Hierarchies

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The influence of Imre Simon’s work in the theory of automata, languages and semigroups

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A purely algebraic proof of the omega-reducibility of pseudovarieties representing low half levels of concatenation hierarchies

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Expressive power of existential first-order sentences of Büchi's sequential calculus

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Regularity Results for FIFO Channels

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Permutation rewriting and algorithmic verification

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Regular languages and partial commutations

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Conservative groupoids recognize only regular languages

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A note on partially ordered tree automata

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A counterexample to a conjecture concerning concatenation hierarchies

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Languages polylog-time reducible to dot-depth 1/2

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Perfect correspondences between dot-depth and polynomial-time hierarchies

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Schreier split extensions of preordered monoids

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Pseudovarieties defining classes of sofic subshifts closed under taking shift equivalent subshifts

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A reducibility for the dot-depth hierarchy

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Two algebraic approaches to variants of the concatenation product

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Polynomials, fragments of temporal logic and the variety DA over traces

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Factorization forests for infinite words and applications to countable scattered linear orderings

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On the state complexity of closures and interiors of regular languages with subwords and superwords

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Local testability from words to traces, a suitable definition

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Efficient algorithms for membership in boolean hierarchies of regular languages

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References

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Algebraic tools for the concatenation product

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Some complexity results for polynomial rational expressions

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A conjecture on the concatenation product

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Relating Automata-theoretic Hierarchies to Complexity-theoretic Hierarchies

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On Shuffle Ideals

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The globals of pseudovarieties of ordered semigroups containingB2and an application to a problem proposed by Pin

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Some results onC-varieties

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Imre Simon: an exceptional graduate student

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Efficiency of automata in semi-commutation verification techniques

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SEMIDIRECT PRODUCTS OF ORDERED SEMIGROUPS

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ORDERED CATEGORIES AND ORDERED SEMIGROUPS

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THE WREATH PRODUCT PRINCIPLE FOR ORDERED SEMIGROUPS

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Representations of relatively free profinite semigroups, irreducibility, and order primitivity

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Permutation rewriting and algorithmic verification

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First Order Formulas with Modular Ppredicates

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Languages of Dot-Depth One over Infinite Words

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Separating Regular Languages with Two Quantifiers Alternations

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Navigational hierarchies of regular languages

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OPEN PROBLEMS ON REGULAR LANGUAGES: A HISTORICAL PERSPECTIVE

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THE DOT-DEPTH AND THE POLYNOMIAL HIERARCHIES CORRESPOND ON THE DELTA LEVELS

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A SURVEY ON SMALL FRAGMENTS OF FIRST-ORDER LOGIC OVER FINITE WORDS

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ON THE NON-DETERMINISTIC COMMUNICATION COMPLEXITY OF REGULAR LANGUAGES

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HIERARCHIES OF PIECEWISE TESTABLE LANGUAGES

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PARTIALLY ORDERED TWO-WAY BÜCHI AUTOMATA

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EQUATIONAL DESCRIPTIONS OF LANGUAGES

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AROUND DOT-DEPTH ONE

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PROFINITE METHODS IN SEMIGROUP THEORY

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On fixed points of the lower set operator

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Reducibility vs. definability for pseudovarieties of semigroups

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The omega-reducibility of pseudovarieties of ordered monoids representing low levels of concatenation hierarchies

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Over words, two variables are as powerful as one quantifier alternation

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The tale of the quantifier alternation hierarchy of first-order logic over words

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Going Higher in First-Order Quantifier Alternation Hierarchies on Words

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Adding Successor

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The Regular Languages of First-Order Logic with One Alternation

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Dot-depth three, return of the J-class

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Closing Star-Free Closure

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The ω-inequality problem for concatenation hierarchies of star-free languages

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The expressive power of simple logical fragments over traces

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First-order fragments with successor over infinite words

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Formal language theory of logic fragments

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Logic Meets Algebra: the Case of Regular Languages

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Structure Theorem and Strict Alternation Hierarchy for FO^2 on Words

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Tree Languages Defined in First-Order Logic with One Quantifier Alternation

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Separating regular languages with two quantifier alternations

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Covering and separation for logical fragments with modular predicates

inferred← citeshttps://doi.org/10.23638/lmcs-15(2:6)2019openalex-snapshot

The height of piecewise-testable languages and the complexity of the logic of subwords

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Partially Ordered Automata and Piecewise Testability

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On the Trace Product and Some Families of Languages Closed Under Partial Commutations

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Defining long words succinctly in FO and MSO

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The factorisation forest theorem

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On Varieties of Automata Enriched with an Algebraic Structure (Extended Abstract)

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Deterministic Temporal Logics and Interval Constraints

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The FO2 alternation hierarchy is decidable

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Profinite Methods in Automata Theory

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First-order Fragments with Successor over Infinite Words

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Quantifier Alternation in Two-Variable First-Order Logic with Successor Is Decidable

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Separation and the Successor Relation

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New decidable upper bound of the second level in the Straubing-Therien concatenation hierarchy of star-free languages

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Languages of Dot-depth One over Infinite Words

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Regular Ideal Languages and Their Boolean Combinations

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Going higher in the First-order Quantifier Alternation Hierarchy on Words

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Quantifier Alternation for Infinite Words

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Adding successor: A transfer theorem for separation and covering

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Efficient Membership Testing for Pseudovarieties of Finite Semigroups

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Languages recognised by finite semigroups, and their generalisations to objects such as trees and graphs, with an emphasis on definability in monadic second-order logic

inferred← citeshttps://doi.org/10.48550/arxiv.cs/9809118openalex-snapshot

The Boolean Hierarchy over Level 1/2 of the Straubing-Therien Hierarchy

inferred← citeshttps://doi.org/10.70675/6c9d51cbze0efz4fdezb9b8z4ddc2f8fce0fopenalex-snapshot

Subwords : automata, embedding problems, and verification

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Synchronous relations and complexity of query evaluation

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Decidable characterizations for tree logics

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