
Developments in Language Theory
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The 34 regular papers presented were carefully reviewed and selected from numerous submissions. The volume also contains the papers or extended abstracts of 4 invited lectures, as well as a special memorial presentation in honor of Sheng Yu. The topics covered include grammars, acceptors and transducers for words, trees and graphs; algebraic theories of automata; algorithmic, combinatorial and algebraic properties of words and languages; variable length codes; symbolic dynamics; cellular automata; polyominoes and multidimensional patterns; decidability questions; image manipulation and compression; efficient text algorithms; relationships to cryptography, concurrency, complexity theory and logic; bio-inspired computing; quantum computing.
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Content
- Title
- Preface
- Organization
- Table of Contents
- Invited Talks
- The Kind Hearted Dragon Prof. Sheng Yu, 1950-2012
- References
- P and dP Automata: Unconventional versus Classical Automata
- Introduction
- Preliminaries
- P Automata
- Discussion of Features of P Automata
- Accepting Power of P Automata
- dP Automata
- Accepting Power of dP Automata
- Multi-head Finite Automata versus Finite dP Automata
- Conclusions
- References
- Recovering Strings in Oracles: Quantum and Classic
- Determinism vs. Nondeterminism for Two-Way Automata
- Introduction
- Liveness Problems
- Reasonable Automata
- Main Results
- Lower Bounds
- Upper Bounds
- Conclusion
- References
- Cellular Automata, the Collatz Conjecture and Powers of 3/2
- Introduction
- Definitions
- A Universal Pattern Generator
- Strong Pattern Generation
- Relation to Some Open Problems in Number Theory
- Mahler's Z-Numbers
- Collatz Function
- Concluding Remarks
- References
- Regular Papers
- Quotient Complexities of Atoms of Regular Languages
- Introduction
- Upper Bounds on the Quotient Complexities of Atoms
- Automata and Átomata of Regular Languages
- The Witness Languages and Automata
- Tightness of the Upper Bounds
- Conclusions
- References
- Decidability of Geometricity of Regular Languages
- Introduction
- Geometrical Languages
- Semilinear Sets
- Regular Geometrical Languages
- References
- Inside the Class of REGEX Languages
- Introduction
- General Definitions
- Patterns with Regular Operators and Types
- Pattern Expressions
- REGEX
- REGEX with a Bounded Number of Backreferences
- References
- Computing the Edit-Distance between a Regular Language and a Context-Free Language
- Introduction
- Preliminaries
- Edit-Distance
- The Edit-Distance between an RL and a CFL
- Alignment PDA
- Computing an Optimal Alignment from A(A,P)
- Edit-Distance and Unary Homomorphism
- References
- Semigroups with a Context-Free Word Problem
- Introduction
- Preliminaries
- Semigroups with Context-Free Word Problem
- Finite Rees Index
- Completely Simple Semigroups
- Rational Semigroups and Linear World Problems
- References
- Generalized Derivations with Synchronized Context-Free Grammars
- Introduction
- Preliminaries
- Transducer Synchronization
- Unary Transducers
- References
- Non-erasing Variants of the Chomsky-Sch¨utzenberger Theorem
- Introduction
- Normal Form
- Homomorphic Characterization of Even-Length Languages
- Characterizations
- Concluding Remarks
- References
- Regular and Context-Free Pattern Languages over Small Alphabets
- Introduction
- Definitions and Known Results
- Regularity and Context-Freeness of Pattern Languages: Sufficient Conditions and Necessary Conditions
- Regularity of E-Pattern Languages: A Sufficient Condition Taking Terminal Symbols into Account
- References
- On Context-Free Languages of Scattered Words
- Introduction
- Basic Notions
- Linear Orderings
- Words and Languages
- Linear Context-Free Languages
- Context-Free Languages of Scattered Words of Bounded Rank
- Operational Characterization of BCFLs of Scattered Words
- An Application
- Future Research
- References
- Homomorphisms Preserving Deterministic Context-Free Languages
- Introduction
- Context-Free Languages and Their Special Cases
- Codes and Their Deciphering Delay
- Codes Preserving Deterministic and LL Context-Free Languages
- Non-codes Preserving Deterministic and LL Context-Free Languages
- References
- Unary Coded NP-Complete Languages in ASPACE (log log n)
- Introduction
- Preliminaries
- Encoding Boolean Formulas
- Encoded 3-Satisfiability
- Conclusion
- References
- Dense Completeness
- Introduction
- Preliminaries
- The Context-Free Languages and the Class SAC1
- The One-Counter Languages and the Class NL
- The Indexed Languages and the Class NP
- The Regular Languages and the Class NC1
- Discussion
- References
- From Equivalence to Almost-Equivalence, and Beyond-Minimizing Automata with Errors
- Introduction
- Preliminaries
- Finite Automata Equivalence, Minimization, and Related Problems
- Equivalence Problems
- Canonical Languages
- Minimization Problems
- Deciding Minimality
- Counting Minimal Automata
- References
- Analogs of Fagin's Theorem for Small Nondeterministic Finite Automata
- Introduction
- Preparation
- Nondeterministic Finite Automata
- Monadic Second-Order Logic with Successor
- Existential Anchor-Slide Sentences
- From Automata to Formulas
- From Formulas to Automata
- Conclusion
- References
- States and Heads Do Count for Unary Multi-head Finite Automata
- Introduction
- Preliminaries and Definitions
- State and Head Double Hierarchy
- Head Hierarchy for Stateless Finite Automata
- Four States Are Too Much for Two-Head Automata
- References
- Visibly Pushdown Automata with Multiplicities: Finiteness and K-Boundedness
- Introduction
- Definitions
- Preliminaries
- Visibly Pushdown Automata with Multiplicities
- Relating Tree Automata and VPA
- Characterization and Decision of Infinite N-VPA
- Characterization
- Decidability of Finiteness
- Finite Bounds for N-VPA
- Deciding K-Bounded Multiplicity
- Deciding K-Bounded Multiplicity (for a Fixed K)
- Back to Trees
- References
- Unambiguous Constrained Automata
- Introduction
- Preliminaries
- Closure Properties and Expressiveness of UnCA
- Decision Problems for UnCA
- A Deterministic Form of UnCA
- Conclusion
- References
- Two-Dimensional Sgraffito Automata
- Introduction
- Preliminaries
- Sgraffito Automata
- Closure Properties
- A Taxonomy of Picture Languages
- Conclusions
- References
- Two-Way Transducers with a Two-Way Output Tape
- Introduction
- Two-Way Transducers
- Rational Relations and One-Way Transducers
- Special Case
- Deterministic Two-Way Transducers
- Conclusion
- References
- Learning Rational Functions
- Introduction
- Rational Functions
- Transducers with Look-Ahead
- Building the Look-Ahead Automaton
- The Learning Algorithm
- Characteristic Samples
- References
- Converting Nondeterministic Automata and Context-Free Grammars into Parikh Equivalent Deterministic Automata
- Introduction
- Preliminaries
- From NFAs to Parikh Equivalent DFAs
- From CFGs to Parikh Equivalent DFAs
- Conclusion
- References
- Fine and Wilf 's Theorem for k-Abelian Periods
- Introduction
- Preliminaries
- Existence of Bounds
- Initial 2-Abelian Periods
- General Upper Bounds
- Conclusion
- References
- Pseudoperiodic Words
- Introduction
- Definitions and Notation
- Words
- Permutations
- Pseudopalindromes
- Generalized Pseudostandard Words
- Pseudoperiodicity
- Graphs
- Fine and Wilf's Theorem
- Pseudocentral Words
- Concluding Remarks and Future Work
- References
- Acceptance Conditions for $\omega$-Languages
- Introduction
- Notations and Background
- The Accepting Conditions A and A and the Borel Hierarchy
- The Accepting Conditions (ninf,) and (ninf,)
- Towards a Characterization of (fin, =) and (fin,)
- Conclusions
- References
- Checking Determinism of Regular Expressions with Counting
- Introduction
- Preliminaries
- Computing followlast Sets
- Properties of Expressions in RE(#)
- Strong Determinism
- Adaption to Weak Determinism
- The Local Nondeterminism-Locating Feature and Discussion
- References
- Biautomata for k-Piecewise Testable Languages
- Introduction
- Preliminaries
- Piecewise Testable Languages and Syntactic Monoids
- Biautomata for Piecewise Testable Languages
- Proof of the Theorem
- Estimates Using J-Trivial Monoids
- Concluding Remarks
- References
- On Centralized PC Grammar Systems with Context-Sensitive Components
- Introduction
- The Complexity Classes NSPACE(n) and NEXT
- Centralized PC Grammar Systems
- String-Rewriting Systems
- The Main Result
- Concluding Remarks
- References
- Unidirectional Derivation Semantics for Synchronous Tree-Adjoining Grammars
- Introduction
- Preliminaries
- Synchronous Tree-Adjoining Grammars
- Relating STAG and XTOP
- Bimorphism Semantics
- Relating STAG and XTOP, Again
- Results
- References
- The State Complexity of Star-Complement-Star
- Introduction
- Upper Bound
- Lower Bound
- Applications
- References
- On State Complexity of Finite Word and Tree Languages
- Introduction
- Preliminaries
- Finite Language with Bounded Word Length
- Union and Intersection of Finite Languages
- Tree Automata and Tree Languages
- References
- Squares in Binary Partial Words
- Introduction
- Square Positions
- Square Occurrences
- Distinct Squares
- Conclusion
- References
- The Avoidability of Cubes under Permutations
- Introduction
- Preliminaries
- The Morphic Case
- The Antimorphic Case
- Conclusions
- References
- Hairpin Completion with Bounded Stem-Loop
- Introduction and Preliminaries
- Pseudopalindromic Regular Languages
- Iterated Pseudopalindromic Completion
- Decidability Questions
- References
- Morphic Primitivity and Alphabet Reductions
- Introduction
- Definitions
- Unambiguous Alphabet Reductions
- Alphabet Reductions Preserving Morphic Primitivity
- References
- Short Papers
- On a Hierarchy of Languages with Catenation and Shuffle
- Introduction
- Definitions and Basic Structures
- Basic Structures
- Systems of Equations
- Algebraic Closures
- Normal Forms
- Hierarchies
- The Lower Hierarchy
- The Upper Hierarchy
- Outlook
- References
- Characterizing Languages by Normalization and Termination in String Rewriting
- Motivation
- Preliminaries
- Sets of Strings with Alphabet Extension
- Reducing the Alphabet to
- Complexity of Languages Characterizable in
- Conclusion and Future Work
- References
- Geometry and Dynamics of the Besicovitch and Weyl Spaces
- Introduction
- Definitions
- Sofic Shifts and Simplicial Complexes
- CA-Like Functions and B-Nontransitivity of CA
- References
- A Generalization of Girod's Bidirectional Decoding Method to Codes with a Finite Deciphering Delay
- Preliminaries: Codes and Transducers
- Generalization of Girod's Method to f.d.d. Codes
- Transducers for Decoding
- A Remarkable Strongly Connected Component
- References
- Author Index
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