Deciding equivalence of finite tree automata
SIAM Journal on Computing
Infinite trees and automaton-definable relations over &ohgr;-words
Theoretical Computer Science - Selected papers of the 7th Annual Symposium on theoretical aspects of computer science (STACS '90) Rouen, France, February 1990
An automata-theoretic approach to linear temporal logic
Proceedings of the VIII Banff Higher order workshop conference on Logics for concurrency : structure versus automata: structure versus automata
Languages, automata, and logic
Handbook of formal languages, vol. 3
Validating streaming XML documents
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Query automata over finite trees
Theoretical Computer Science
Reasoning about The Past with Two-Way Automata
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
A Linear-Time Model-Checking Algorithm for the Alternation-Free Modal Mu-Calculus
CAV '91 Proceedings of the 3rd International Workshop on Computer Aided Verification
Logics For Context-Free Languages
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
XPath queries on streaming data
Proceedings of the 2003 ACM SIGMOD international conference on Management of data
Definable relations and first-order query languages over strings
Journal of the ACM (JACM)
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Temporal Logics over Unranked Trees
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
A fixpoint calculus for local and global program flows
Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Logical definability and query languages over ranked and unranked trees
ACM Transactions on Computational Logic (TOCL)
First-Order and Temporal Logics for Nested Words
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
On the complexity of omega -automata
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
On relations defined by generalized finite automata
IBM Journal of Research and Development
Regularity problems for visibly pushdown languages
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Adding nesting structure to words
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Weighted Logics for Nested Words and Algebraic Formal Power Series
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
State Complexity of Nested Word Automata
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Nondeterministic state complexity of nested word automata
Theoretical Computer Science
Limitations of lower bound methods for deterministic nested word automata
Information and Computation
Evolving schemas for streaming XML
Theoretical Computer Science
Descriptional complexity of unambiguous nested word automata
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
Temporal reasoning for procedural programs
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Evolving schemas for streaming XML
FoIKS'10 Proceedings of the 6th international conference on Foundations of Information and Knowledge Systems
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Nested words are a restriction of the class of visibly pushdown languages that provide a natural model of runs of programs with recursive procedure calls. The usual connection between monadic second-order logic (MSO) and automata extends from words to nested words and gives us a natural notion of regular languages of nested words. In this paper we look at some well-known aspects of regular languages - their characterization via fixed points, deterministic and alternating automata for them, and synchronization for defining regular relations - and extend them to nested words. We show that mu-calculus is as expressive as MSO over finite and infinite nested words, and the equivalence holds, more generally, for mu-calculus with past modalities evaluated in arbitrary positions in a word, not only in the first position. We introduce the notion of alternating automata for nested words, show that they are as expressive as the usual automata, and also prove that Muller automata can be determinized (unlike in the case of visibly pushdown languages). Finally we look at synchronization over nested words. We show that the usual letter-to-letter synchronization is completely incompatible with nested words (in the sense that even the weakest form of it leads to an undecidable formalism) and present an alternative form of synchronization that gives us decidable notions of regular relations.